Mysticism and Logic and Other Essays
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CE","Url":"https://chrisdeasy.com/theos/humanities/philosophy/eras-of-thought/philosophers-of-contemporary-history/"},{"Label":"Era","Key":"Era:12","Title":"World War Era","DateText":"1914 CE – 1944 CE","Url":"https://chrisdeasy.com/theos/humanities/philosophy/eras-of-thought/philosophers-of-modern-history/philosophers-of-the-world-war-era/"},{"Label":"Composition","Title":"1918 CE","Url":"","DateText":""}],"DateNote":"Displayed year is the publication year of the collection.","GeoCards":[{"Label":"Region","Key":"Region:1"},{"Label":"Terra Avita","Key":"TerraAvita:1"},{"Label":"Terra Avita Region","Key":"TerraAvitaRegion:2"},{"Label":"Modern Country","Key":"Country:GBR:1"}],"OriginalTitle":"","Language":"English","DisciplineCards":[{"Label":"Primary Discipline","Key":"Discipline:logic"},{"Label":"Secondary Discipline","Key":"Discipline:metaphysics"}],"Tradition":"Analytic philosophy, logicism, British empiricism, social criticism, secular humanism, and twentieth-century public reason","FullText":{"Title":"Full Text","Copy":"Public-domain full text from Project Gutenberg eBook #25447 .","Url":"","Label":"","Kicker":"","Cards":[]},"CoreThesis":["The essays contrast mysticism and scientific logic while developing Russell\u0027s views on mathematics, knowledge, universals, and philosophy."],"Classification":{"AlternateTitles":"","KeyConcepts":"Mysticism and Logic and Other Essays; Bertrand Russell; logicism; descriptions; logical atomism; knowledge; language; science; ethics; politics; religion; public reason","Methodology":"Logical analysis, formal argument, empiricist reconstruction, linguistic analysis, public criticism, historical explanation, and social-philosophical argument.","Structure":"Accepted work page for Russell under the Core Major scope; minor journalism, duplicate anthologies, individual letters, source/testimony pages, and works merely about Russell are excluded."},"Arguments":["Connects Russell\u0027s technical work in logic and language with his epistemology, philosophy of science, ethics, politics, secular criticism, and public writing."],"Influence":{"InfluencedBy":"Frege, Peano, Leibniz, Hume, Mill, Moore, Whitehead, Cantor, Cambridge mathematics, British empiricism, and anti-idealism.","InfluenceOn":""},"Significance":["Part of the Core Major Russell corpus that made him central to analytic philosophy, mathematical logic, public ethics, secular critique, and twentieth-century intellectual life.","Used in debates about reference, logic, mathematics, science, knowledge, mind, language, liberalism, religion, education, power, and public responsibility."],"EvidenceNote":["Accepted as a major philosophical essay collection."],"MainSections":[{"Kind":"RawSection","Title":"Full Versions","BodyHtml":"\u003cdiv class=\"dz-philo__full-version-grid\"\u003e\n \u003carticle class=\"dz-philo__full-version-card\"\u003e\n \u003cp class=\"dz-philo__full-version-provider\"\u003eProject Gutenberg\u003c/p\u003e\n \u003ch3 class=\"dz-philo__full-version-title\"\u003eProject Gutenberg eBook #25447\u003c/h3\u003e\n \u003cp class=\"dz-philo__full-version-meta\"\u003eHtmlText · Imported\u003c/p\u003e\n \u003ca class=\"dz-philo__full-version-link\" href=\"https://www.gutenberg.org/ebooks/25447\"\u003eOpen full version\u003c/a\u003e\n \u003c/article\u003e\n \u003c/div\u003e"},{"Kind":"TextSection","Title":"Core Thesis","Paragraphs":["The essays contrast mysticism and scientific logic while developing Russell\u0027s views on mathematics, knowledge, universals, and philosophy."]},{"Kind":"FieldSection","Title":"Classification","Fields":[{"Label":"Alternate Titles","Value":""},{"Label":"Key Concepts","Value":"Mysticism and Logic and Other Essays; Bertrand Russell; logicism; descriptions; logical atomism; knowledge; language; science; ethics; politics; religion; public reason"},{"Label":"Methodology","Value":"Logical analysis, formal argument, empiricist reconstruction, linguistic analysis, public criticism, historical explanation, and social-philosophical argument."},{"Label":"Structure","Value":"Accepted work page for Russell under the Core Major scope; minor journalism, duplicate anthologies, individual letters, source/testimony pages, and works merely about Russell are excluded."}]},{"Kind":"TextSection","Title":"Arguments","Paragraphs":["Connects Russell\u0027s technical work in logic and language with his epistemology, philosophy of science, ethics, politics, secular criticism, and public writing."]},{"Kind":"FieldSection","Title":"Influence","Fields":[{"Label":"Influenced By","Value":"Frege, Peano, Leibniz, Hume, Mill, Moore, Whitehead, Cantor, Cambridge mathematics, British empiricism, and anti-idealism."},{"Label":"Influence On","Value":"Analytic philosophy, mathematical logic, philosophy of language, logical atomism, logical positivism, secular humanism, public philosophy, peace activism, and twentieth-century liberal thought."}]},{"Kind":"TextSection","Title":"Significance","Paragraphs":["Part of the Core Major Russell corpus that made him central to analytic philosophy, mathematical logic, public ethics, secular critique, and twentieth-century intellectual life.","Used in debates about reference, logic, mathematics, science, knowledge, mind, language, liberalism, religion, education, power, and public responsibility."]},{"Kind":"TextSection","Title":"Evidence Note","Paragraphs":["Accepted as a major philosophical essay collection."]},{"Kind":"RawSection","Title":"Full Text","BodyHtml":"\u003cp class=\"dz-philo__section-copy dz-philo__full-text-source\"\u003ePublic-domain full text from \u003ca href=\"https://www.gutenberg.org/ebooks/25447\"\u003eProject Gutenberg eBook #25447\u003c/a\u003e.\u003c/p\u003e\n \u003carticle class=\"dz-philo__full-text-body\"\u003e\r\n\u003ch2\u003eBERTRAND RUSSELL\u003c/h2\u003e\r\n\r\n\u003ch1\u003eMYSTICISM AND\r\nLOGIC\u003c/h1\u003e\r\n\r\n\u003ch2\u003eAND OTHER ESSAYS\u003c/h2\u003e\r\n\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003ch4\u003e\u003ci\u003eLONDON\u003c/i\u003e\u003cbr /\u003e\r\nGEORGE ALLEN \u0026amp; UNWIN LTD\u003cbr /\u003e\r\nRUSKIN HOUSE MUSEUM STREET\u003c/h4\u003e\r\n\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003chr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003ch4\u003eMYSTICISM AND LOGIC\u003cbr /\u003e\r\nAND OTHER ESSAYS\u003c/h4\u003e\r\n\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003chr /\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003ch4\u003eBY BERTRAND RUSSELL\u003c/h4\u003e\r\n\r\n\u003cp class=\"cen\"\u003e\u003ci\u003eThe ABC of Relativity\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eThe Analysis of Matter\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eHuman Society in Ethics and Politics\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eThe Impact of Science on Society\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eNew Hopes for a Changing World\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eAuthority and the Individual\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eHuman Knowledge\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eHistory of Western Philosophy\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eThe Principles of Mathematics\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eIntroduction to Mathematical Philosophy\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eThe Analysis of Mind\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eOur Knowledge of the External World\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eAn Outline of Philosophy\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eThe Philosophy of Leibniz\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eAn Inquiry into Meaning and Truth\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eLogic and Knowledge\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eThe Problems of Philosophy\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003ePrincipia Mathematica\u003c/i\u003e\u003c/p\u003e\r\n\r\n\u003cp class=\"cen\"\u003e\u003ci\u003eCommon Sense and Nuclear Warfare\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eWhy I am Not a Christian\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003ePortraits from Memory\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eMy Philosophical Development\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eUnpopular Essays\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003ePower\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eIn Praise of Idleness\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eThe Conquest of Happiness\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eSceptical Essays\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eThe Scientific Outlook\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eMarriage and Morals\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eEducation and the Social Order\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eOn Education\u003c/i\u003e\u003c/p\u003e\r\n\r\n\u003cp class=\"cen\"\u003e\u003ci\u003eFreedom and Organization\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003ePrinciples of Social Reconstruction\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eRoads to Freedom\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003ePractice and Theory of Bolshevism\u003c/i\u003e\u003c/p\u003e\r\n\r\n\u003cp class=\"cen\"\u003e\u003ci\u003eSatan in The Suburbs\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eNightmares of Eminent Persons\u003c/i\u003e\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\u003chr /\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003cdiv class=\"centered\"\u003e\r\n\u003ctable border=\"0\" cellpadding=\"0\" cellspacing=\"0\" width=\"60%\" summary=\"dates published\"\u003e\r\n \u003ctr\u003e\r\n \u003ctd class=\"tdl\" width=\"70%\"\u003e\u003ci\u003eFirst published as \"Philosophical Essays\"\u003c/i\u003e\u003c/td\u003e\r\n \u003ctd class=\"tdr\" width=\"30%\"\u003e\u003ci\u003eOctober 1910\u003c/i\u003e\u003c/td\u003e\r\n \u003c/tr\u003e\r\n \u003ctr\u003e\r\n \u003ctd class=\"tdl\"\u003e\u003ci\u003eSecond Edition as \"Mysticism and Logic\"\u003c/i\u003e\u003c/td\u003e\r\n \u003ctd class=\"tdr\"\u003e\u003ci\u003eDecember 1917\u003c/i\u003e\u003c/td\u003e\r\n \u003c/tr\u003e\r\n \u003ctr\u003e\r\n \u003ctd class=\"tdl\"\u003e\u003ci\u003eThird Impression\u003c/i\u003e\u003c/td\u003e\r\n \u003ctd class=\"tdr\"\u003e\u003ci\u003eApril 1918\u003c/i\u003e\u003c/td\u003e\r\n \u003c/tr\u003e\r\n \u003ctr\u003e\r\n \u003ctd class=\"tdl\"\u003e\u003ci\u003eFourth Impression\u003c/i\u003e\u003c/td\u003e\r\n \u003ctd class=\"tdr\"\u003e\u003ci\u003eFebruary 1919\u003c/i\u003e\u003c/td\u003e\r\n \u003c/tr\u003e\r\n \u003ctr\u003e\r\n \u003ctd class=\"tdl\"\u003e\u003ci\u003eFifth Impression\u003c/i\u003e\u003c/td\u003e\r\n \u003ctd class=\"tdr\"\u003e\u003ci\u003eOctober 1921\u003c/i\u003e\u003c/td\u003e\r\n \u003c/tr\u003e\r\n \u003ctr\u003e\r\n \u003ctd class=\"tdl\"\u003e\u003ci\u003eSixth Impression\u003c/i\u003e\u003c/td\u003e\r\n \u003ctd class=\"tdr\"\u003e\u003ci\u003eAugust 1925\u003c/i\u003e\u003c/td\u003e\r\n \u003c/tr\u003e\r\n \u003ctr\u003e\r\n \u003ctd class=\"tdl\"\u003e\u003ci\u003eSeventh Impression\u003c/i\u003e\u003c/td\u003e\r\n \u003ctd class=\"tdr\"\u003e\u003ci\u003eJanuary 1932\u003c/i\u003e\u003c/td\u003e\r\n \u003c/tr\u003e\r\n \u003ctr\u003e\r\n \u003ctd class=\"tdl\"\u003e\u003ci\u003eEighth Impression\u003c/i\u003e\u003c/td\u003e\r\n \u003ctd class=\"tdr\"\u003e\u003ci\u003e1949\u003c/i\u003e\u003c/td\u003e\r\n \u003c/tr\u003e\r\n \u003ctr\u003e\r\n \u003ctd class=\"tdl\"\u003e\u003ci\u003eNinth Impression\u003c/i\u003e\u003c/td\u003e\r\n \u003ctd class=\"tdr\"\u003e\u003ci\u003e1950\u003c/i\u003e\u003c/td\u003e\r\n \u003c/tr\u003e\r\n \u003ctr\u003e\r\n \u003ctd class=\"tdl\"\u003e\u003ci\u003eTenth Impression\u003c/i\u003e\u003c/td\u003e\r\n \u003ctd class=\"tdr\"\u003e\u003ci\u003e1951\u003c/i\u003e\u003c/td\u003e\r\n \u003c/tr\u003e\r\n \u003ctr\u003e\r\n \u003ctd class=\"tdl\"\u003e\u003ci\u003eEleventh Impression\u003c/i\u003e\u003c/td\u003e\r\n \u003ctd class=\"tdr\"\u003e\u003ci\u003e1959\u003c/i\u003e\u003c/td\u003e\r\n \u003c/tr\u003e\r\n\u003c/table\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cbr /\u003e\r\n\r\n\u003cdiv class=\"block2\"\u003e\u003cp\u003e\u003ci\u003eThis book is copyright under the Berne Convention. Apart from any\r\nfair dealing for the purpose of private study, research, criticism\r\nor review, as permitted under the Copyright Act, 1956, no portion\r\nmay be reproduced by any process without written permission.\r\nEnquiry should be made to the publisher.\u003c/i\u003e\u003c/p\u003e\u003c/div\u003e\r\n\r\n\r\n\u003ch5\u003ePRINTED IN GREAT BRITAIN\u003cbr /\u003e\r\n\u003ci\u003eby Taylor Garnett Evans \u0026amp; Co. Ltd.,\u003cbr /\u003e\r\nWatford, Herts.\u003c/i\u003e\u003c/h5\u003e\r\n\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003chr /\u003e\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_v\" id=\"Page_v\"\u003e[v]\u003c/a\u003e\u003c/span\u003e\u003cbr /\u003e\r\n\r\n\u003ch3\u003ePREFACE\u003c/h3\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003cp\u003eThe following essays have been written and published at various times,\r\nand my thanks are due to the previous publishers for the permission to\r\nreprint them.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe essay on \"Mysticism and Logic\" appeared in the \u003ci\u003eHibbert Journal\u003c/i\u003e\r\nfor July, 1914. \"The Place of Science in a Liberal Education\" appeared\r\nin two numbers of \u003ci\u003eThe New Statesman\u003c/i\u003e, May 24 and 31, 1913. \"The Free\r\nMan\u0027s Worship\" and \"The Study of Mathematics\" were included in a\r\nformer collection (now out of print), \u003ci\u003ePhilosophical Essays\u003c/i\u003e, also\r\npublished by Messrs. Longmans, Green \u0026amp; Co. Both were written in 1902;\r\nthe first appeared originally in the \u003ci\u003eIndependent Review\u003c/i\u003e for 1903,\r\nthe second in the \u003ci\u003eNew Quarterly\u003c/i\u003e, November, 1907. In theoretical\r\nEthics, the position advocated in \"The Free Man\u0027s Worship\" is not\r\nquite identical with that which I hold now: I feel less convinced than\r\nI did then of the objectivity of good and evil. But the general\r\nattitude towards life which is suggested in that essay still seems to\r\nme, in the main, the one which must be adopted in times of stress and\r\ndifficulty by those who have no dogmatic religious beliefs, if inward\r\ndefeat is to be avoided.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe essay on \"Mathematics and the Metaphysicians\" was written in 1901,\r\nand appeared in an American magazine, \u003ci\u003eThe International Monthly\u003c/i\u003e,\r\nunder the title \"Recent Work in the Philosophy of Mathematics.\" Some\r\npoints \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_vi\" id=\"Page_vi\"\u003e[vi]\u003c/a\u003e\u003c/span\u003ein this essay require modification in view of later work.\r\nThese are indicated in footnotes. Its tone is partly explained by the\r\nfact that the editor begged me to make the article \"as romantic as\r\npossible.\"\u003c/p\u003e\r\n\r\n\u003cp\u003eAll the above essays are entirely popular, but those that follow are\r\nsomewhat more technical. \"On Scientific Method in Philosophy\" was the\r\nHerbert Spencer lecture at Oxford in 1914, and was published by the\r\nClarendon Press, which has kindly allowed me to include it in this\r\ncollection. \"The Ultimate Constituents of Matter\" was an address to\r\nthe Manchester Philosophical Society, early in 1915, and was published\r\nin the \u003ci\u003eMonist\u003c/i\u003e in July of that year. The essay on \"The Relation of\r\nSense-data to Physics\" was written in January, 1914, and first\r\nappeared in No. 4 of that year\u0027s volume of \u003ci\u003eScientia\u003c/i\u003e, an\r\nInternational Review of Scientific Synthesis, edited by M. Eugenio\r\nRignano, published monthly by Messrs. Williams and Norgate, London,\r\nNicola Zanichelli, Bologna, and F\u0026eacute;lix Alcan, Paris. The essay \"On the\r\nNotion of Cause\" was the presidential address to the Aristotelian\r\nSociety in November, 1912, and was published in their \u003ci\u003eProceedings\u003c/i\u003e\r\nfor 1912-13. \"Knowledge by Acquaintance and Knowledge by Description\"\r\nwas also a paper read before the Aristotelian Society, and published\r\nin their \u003ci\u003eProceedings\u003c/i\u003e for 1910-11.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\"sc\"\u003eLondon,\u003c/span\u003e\u003cbr /\u003e\r\n\u003cspan style=\"margin-left: 2em;\"\u003e\u003ci\u003eSeptember, 1917\u003c/i\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003ca name=\"toc\" id=\"toc\"\u003e\u003c/a\u003e\u003chr /\u003e\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_vii\" id=\"Page_vii\"\u003e[vii]\u003c/a\u003e\u003c/span\u003e\u003cbr /\u003e\r\n\r\n\u003ch3\u003eCONTENTS\u003c/h3\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003cdiv class=\"centered\"\u003e\r\n\u003ctable border=\"0\" cellpadding=\"2\" cellspacing=\"0\" width=\"70%\" summary=\"Table of Contents\"\u003e\r\n \u003ctr\u003e\r\n \u003ctd class=\"tdr\" width=\"10%\" style=\"font-size: 90%;\"\u003e\u003ci\u003eChapter\u003c/i\u003e\u003c/td\u003e\r\n \u003ctd class=\"tdl\" width=\"70%\"\u003e\u0026nbsp;\u003c/td\u003e\r\n \u003ctd class=\"tdr\" width=\"20%\" style=\"font-size: 90%;\"\u003e\u003ci\u003ePage\u003c/i\u003e\u003c/td\u003e\r\n \u003c/tr\u003e\r\n \u003ctr\u003e\r\n \u003ctd class=\"tdr\"\u003eI.\u003c/td\u003e\r\n \u003ctd class=\"tdl\"\u003e\u003ca href=\"#I\"\u003e\u003ci\u003eMysticism and Logic\u003c/i\u003e\u003c/a\u003e\u003c/td\u003e\r\n \u003ctd class=\"tdr\"\u003e1\u003c/td\u003e\r\n \u003c/tr\u003e\r\n \u003ctr\u003e\r\n \u003ctd class=\"tdr\"\u003eII.\u003c/td\u003e\r\n \u003ctd class=\"tdl\"\u003e\u003ca href=\"#II\"\u003e\u003ci\u003eThe Place of Science in a Liberal Education\u003c/i\u003e\u003c/a\u003e\u003c/td\u003e\r\n \u003ctd class=\"tdr\"\u003e33\u003c/td\u003e\r\n \u003c/tr\u003e\r\n \u003ctr\u003e\r\n \u003ctd class=\"tdr\"\u003eIII.\u003c/td\u003e\r\n \u003ctd class=\"tdl\"\u003e\u003ca href=\"#III\"\u003e\u003ci\u003eA Free Man\u0027s Worship\u003c/i\u003e\u003c/a\u003e\u003c/td\u003e\r\n \u003ctd class=\"tdr\"\u003e46\u003c/td\u003e\r\n \u003c/tr\u003e\r\n \u003ctr\u003e\r\n \u003ctd class=\"tdr\"\u003eIV.\u003c/td\u003e\r\n \u003ctd class=\"tdl\"\u003e\u003ca href=\"#IV\"\u003e\u003ci\u003eThe Study of Mathematics\u003c/i\u003e\u003c/a\u003e\u003c/td\u003e\r\n \u003ctd class=\"tdr\"\u003e58\u003c/td\u003e\r\n \u003c/tr\u003e\r\n \u003ctr\u003e\r\n \u003ctd class=\"tdr\"\u003eV.\u003c/td\u003e\r\n \u003ctd class=\"tdl\"\u003e\u003ca href=\"#V\"\u003e\u003ci\u003eMathematics and the Metaphysicians\u003c/i\u003e\u003c/a\u003e\u003c/td\u003e\r\n \u003ctd class=\"tdr\"\u003e74\u003c/td\u003e\r\n \u003c/tr\u003e\r\n \u003ctr\u003e\r\n \u003ctd class=\"tdr\"\u003eVI.\u003c/td\u003e\r\n \u003ctd class=\"tdl\"\u003e\u003ca href=\"#VI\"\u003e\u003ci\u003eOn Scientific Method in Philosophy\u003c/i\u003e\u003c/a\u003e\u003c/td\u003e\r\n \u003ctd class=\"tdr\"\u003e97\u003c/td\u003e\r\n \u003c/tr\u003e\r\n \u003ctr\u003e\r\n \u003ctd class=\"tdr\"\u003eVII.\u003c/td\u003e\r\n \u003ctd class=\"tdl\"\u003e\u003ca href=\"#VII\"\u003e\u003ci\u003eThe Ultimate Constituents of Matter\u003c/i\u003e\u003c/a\u003e\u003c/td\u003e\r\n \u003ctd class=\"tdr\"\u003e125\u003c/td\u003e\r\n \u003c/tr\u003e\r\n \u003ctr\u003e\r\n \u003ctd class=\"tdr\"\u003eVIII.\u003c/td\u003e\r\n \u003ctd class=\"tdl\"\u003e\u003ca href=\"#VIII\"\u003e\u003ci\u003eThe Relation of Sense-data to Physics\u003c/i\u003e\u003c/a\u003e\u003c/td\u003e\r\n \u003ctd class=\"tdr\"\u003e145\u003c/td\u003e\r\n \u003c/tr\u003e\r\n \u003ctr\u003e\r\n \u003ctd class=\"tdr\"\u003eIX.\u003c/td\u003e\r\n \u003ctd class=\"tdl\"\u003e\u003ca href=\"#IX\"\u003e\u003ci\u003eOn the Notion of Cause\u003c/i\u003e\u003c/a\u003e\u003c/td\u003e\r\n \u003ctd class=\"tdr\"\u003e180\u003c/td\u003e\r\n \u003c/tr\u003e\r\n \u003ctr\u003e\r\n \u003ctd class=\"tdr\"\u003eX.\u003c/td\u003e\r\n \u003ctd class=\"tdl\"\u003e\u003ca href=\"#X\"\u003e\u003ci\u003eKnowledge by Acquaintance and Knowledge by Description\u003c/i\u003e\u003c/a\u003e\u003c/td\u003e\r\n \u003ctd class=\"tdr\"\u003e209\u003c/td\u003e\r\n \u003c/tr\u003e\r\n \u003ctr\u003e\r\n \u003ctd class=\"tdr\"\u003e\u0026nbsp;\u003c/td\u003e\r\n \u003ctd class=\"tdl\"\u003e\u003ca href=\"#INDEX\"\u003eIndex\u003c/a\u003e\u003c/td\u003e\r\n \u003ctd class=\"tdr\"\u003e233\u003c/td\u003e\r\n \u003c/tr\u003e\r\n\u003c/table\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003ca name=\"I\" id=\"I\"\u003e\u003c/a\u003e\u003chr /\u003e\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_1\" id=\"Page_1\"\u003e[1]\u003c/a\u003e\u003c/span\u003e\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003ch1\u003eMYSTICISM AND LOGIC\u003cbr /\u003e AND OTHER ESSAYS\u003c/h1\u003e\r\n\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003ch3\u003eI\u003cspan class=\"totoc\"\u003e\u003ca href=\"#toc\"\u003eToC\u003c/a\u003e\u003c/span\u003e\u003c/h3\u003e\r\n\r\n\u003ch4\u003eMYSTICISM AND LOGIC\u003c/h4\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003cp\u003eMetaphysics, or the attempt to conceive the world as a whole by means\r\nof thought, has been developed, from the first, by the union and\r\nconflict of two very different human impulses, the one urging men\r\ntowards mysticism, the other urging them towards science. Some men\r\nhave achieved greatness through one of these impulses alone, others\r\nthrough the other alone: in Hume, for example, the scientific impulse\r\nreigns quite unchecked, while in Blake a strong hostility to science\r\nco-exists with profound mystic insight. But the greatest men who have\r\nbeen philosophers have felt the need both of science and of mysticism:\r\nthe attempt to harmonise the two was what made their life, and what\r\nalways must, for all its arduous uncertainty, make philosophy, to some\r\nminds, a greater thing than either science or religion.\u003c/p\u003e\r\n\r\n\u003cp\u003eBefore attempting an explicit characterisation of the scientific and\r\nthe mystical impulses, I will illustrate them by examples from two\r\nphilosophers whose greatness lies in the very intimate blending which\r\nthey achieved. The two philosophers I mean are Heraclitus and Plato.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_2\" id=\"Page_2\"\u003e[2]\u003c/a\u003e\u003c/span\u003eHeraclitus, as every one knows, was a believer in universal flux: time\r\nbuilds and destroys all things. From the few fragments that remain, it\r\nis not easy to discover how he arrived at his opinions, but there are\r\nsome sayings that strongly suggest scientific observation as the\r\nsource.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"The things that can be seen, heard, and learned,\" he says, \"are what\r\nI prize the most.\" This is the language of the empiricist, to whom\r\nobservation is the sole guarantee of truth. \"The sun is new every\r\nday,\" is another fragment; and this opinion, in spite of its\r\nparadoxical character, is obviously inspired by scientific reflection,\r\nand no doubt seemed to him to obviate the difficulty of understanding\r\nhow the sun can work its way underground from west to east during the\r\nnight. Actual observation must also have suggested to him his central\r\ndoctrine, that Fire is the one permanent substance, of which all\r\nvisible things are passing phases. In combustion we see things change\r\nutterly, while their flame and heat rise up into the air and vanish.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"This world, which is the same for all,\" he says, \"no one of gods or\r\nmen has made; but it was ever, is now, and ever shall be, an\r\never-living Fire, with measures kindling, and measures going out.\"\u003c/p\u003e\r\n\r\n\u003cp\u003e\"The transformations of Fire are, first of all, sea; and half of the\r\nsea is earth, half whirlwind.\"\u003c/p\u003e\r\n\r\n\u003cp\u003eThis theory, though no longer one which science can accept, is\r\nnevertheless scientific in spirit. Science, too, might have inspired\r\nthe famous saying to which Plato alludes: \"You cannot step twice into\r\nthe same rivers; for fresh waters are ever flowing in upon you.\" But\r\nwe find also another statement among the extant fragments: \"We step\r\nand do not step into the same rivers; we are and are not.\"\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_3\" id=\"Page_3\"\u003e[3]\u003c/a\u003e\u003c/span\u003eThe comparison of this statement, which is mystical, with the one\r\nquoted by Plato, which is scientific, shows how intimately the two\r\ntendencies are blended in the system of Heraclitus. Mysticism is, in\r\nessence, little more than a certain intensity and depth of feeling in\r\nregard to what is believed about the universe; and this kind of\r\nfeeling leads Heraclitus, on the basis of his science, to strangely\r\npoignant sayings concerning life and the world, such as:\u003c/p\u003e\r\n\r\n\u003cp\u003e\"Time is a child playing draughts, the kingly power is a child\u0027s.\"\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is poetic imagination, not science, which presents Time as despotic\r\nlord of the world, with all the irresponsible frivolity of a child. It\r\nis mysticism, too, which leads Heraclitus to assert the identity of\r\nopposites: \"Good and ill are one,\" he says; and again: \"To God all\r\nthings are fair and good and right, but men hold some things wrong and\r\nsome right.\"\u003c/p\u003e\r\n\r\n\u003cp\u003eMuch of mysticism underlies the ethics of Heraclitus. It is true that\r\na scientific determinism alone might have inspired the statement:\r\n\"Man\u0027s character is his fate\"; but only a mystic would have said:\u003c/p\u003e\r\n\r\n\u003cp\u003e\"Every beast is driven to the pasture with blows\"; and again:\u003c/p\u003e\r\n\r\n\u003cp\u003e\"It is hard to fight with one\u0027s heart\u0027s desire. Whatever it wishes to\r\nget, it purchases at the cost of soul\"; and again:\u003c/p\u003e\r\n\r\n\u003cp\u003e\"Wisdom is one thing. It is to know the thought by which all things\r\nare steered through all things.\"\u003ca name=\"FNanchor_1_1\" id=\"FNanchor_1_1\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_1_1\" class=\"fnanchor\"\u003e[1]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eExamples might be multiplied, but those that have been given are\r\nenough to show the character of the man: the facts of science, as they\r\nappeared to him, fed the \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_4\" id=\"Page_4\"\u003e[4]\u003c/a\u003e\u003c/span\u003eflame in his soul, and in its light he saw\r\ninto the depths of the world by the reflection of his own dancing\r\nswiftly penetrating fire. In such a nature we see the true union of\r\nthe mystic and the man of science\u0026mdash;the highest eminence, as I think,\r\nthat it is possible to achieve in the world of thought.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn Plato, the same twofold impulse exists, though the mystic impulse\r\nis distinctly the stronger of the two, and secures ultimate victory\r\nwhenever the conflict is sharp. His description of the cave is the\r\nclassical statement of belief in a knowledge and reality truer and\r\nmore real than that of the senses:\u003c/p\u003e\r\n\r\n\u003cdiv class=\"block\"\u003e\r\n\u003cp\u003e\"Imagine\u003ca name=\"FNanchor_2_2\" id=\"FNanchor_2_2\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_2_2\" class=\"fnanchor\"\u003e[2]\u003c/a\u003e a number of men living in an underground cavernous\r\nchamber, with an entrance open to the light, extending along the\r\nentire length of the cavern, in which they have been confined, from\r\ntheir childhood, with their legs and necks so shackled that they are\r\nobliged to sit still and look straight forwards, because their chains\r\nrender it impossible for them to turn their heads round: and imagine a\r\nbright fire burning some way off, above and behind them, and an\r\nelevated roadway passing between the fire and the prisoners, with a\r\nlow wall built along it, like the screens which conjurors put up in\r\nfront of their audience, and above which they exhibit their wonders.\u003c/p\u003e\r\n\r\n\u003cp\u003eI have it, he replied.\u003c/p\u003e\r\n\r\n\u003cp\u003eAlso figure to yourself a number of persons walking behind this wall,\r\nand carrying with them statues of men, and images of other animals,\r\nwrought in wood and stone and all kinds of materials, together with\r\nvarious other articles, which overtop the wall; and, as you might\r\nexpect, let some of the passers-by be talking, and others silent.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_5\" id=\"Page_5\"\u003e[5]\u003c/a\u003e\u003c/span\u003eYou are describing a strange scene, and strange prisoners.\u003c/p\u003e\r\n\r\n\u003cp\u003eThey resemble us, I replied.\u003c/p\u003e\r\n\r\n\u003cp\u003eNow consider what would happen if the course of nature brought them a\r\nrelease from their fetters, and a remedy for their foolishness, in the\r\nfollowing manner. Let us suppose that one of them has been released,\r\nand compelled suddenly to stand up, and turn his neck round and walk\r\nwith open eyes towards the light; and let us suppose that he goes\r\nthrough all these actions with pain, and that the dazzling splendour\r\nrenders him incapable of discerning those objects of which he used\r\nformerly to see the shadows. What answer should you expect him to\r\nmake, if some one were to tell him that in those days he was watching\r\nfoolish phantoms, but that now he is somewhat nearer to reality, and\r\nis turned towards things more real, and sees more correctly; above\r\nall, if he were to point out to him the several objects that are\r\npassing by, and question him, and compel him to answer what they are?\r\nShould you not expect him to be puzzled, and to regard his old visions\r\nas truer than the objects now forced upon his notice?\u003c/p\u003e\r\n\r\n\u003cp\u003eYes, much truer….\u003c/p\u003e\r\n\r\n\u003cp\u003eHence, I suppose, habit will be necessary to enable him to perceive\r\nobjects in that upper world. At first he will be most successful in\r\ndistinguishing shadows; then he will discern the reflections of men\r\nand other things in water, and afterwards the realities; and after\r\nthis he will raise his eyes to encounter the light of the moon and\r\nstars, finding it less difficult to study the heavenly bodies and the\r\nheaven itself by night, than the sun and the sun\u0027s light by day.\u003c/p\u003e\r\n\r\n\u003cp\u003eDoubtless.\u003c/p\u003e\r\n\r\n\u003cp\u003eLast of all, I imagine, he will be able to observe and \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_6\" id=\"Page_6\"\u003e[6]\u003c/a\u003e\u003c/span\u003econtemplate\r\nthe nature of the sun, not as it \u003ci\u003eappears\u003c/i\u003e in water or on alien\r\nground, but as it is in itself in its own territory.\u003c/p\u003e\r\n\r\n\u003cp\u003eOf course.\u003c/p\u003e\r\n\r\n\u003cp\u003eHis next step will be to draw the conclusion, that the sun is the\r\nauthor of the seasons and the years, and the guardian of all things in\r\nthe visible world, and in a manner the cause of all those things which\r\nhe and his companions used to see.\u003c/p\u003e\r\n\r\n\u003cp\u003eObviously, this will be his next step….\u003c/p\u003e\r\n\r\n\u003cp\u003eNow this imaginary case, my dear Glancon, you must apply in all its\r\nparts to our former statements, by comparing the region which the eye\r\nreveals to the prison house, and the light of the fire therein to the\r\npower of the sun: and if, by the upward ascent and the contemplation\r\nof the upper world, you understand the mounting of the soul into the\r\nintellectual region, you will hit the tendency of my own surmises,\r\nsince you desire to be told what they are; though, indeed, God only\r\nknows whether they are correct. But, be that as it may, the view which\r\nI take of the subject is to the following effect. In the world of\r\nknowledge, the essential Form of Good is the limit of our enquiries,\r\nand can barely be perceived; but, when perceived, we cannot help\r\nconcluding that it is in every case the source of all that is bright\r\nand beautiful,\u0026mdash;in the visible world giving birth to light and its\r\nmaster, and in the intellectual world dispensing, immediately and with\r\nfull authority, truth and reason;\u0026mdash;and that whosoever would act\r\nwisely, either in private or in public, must set this Form of Good\r\nbefore his eyes.\"\u003c/p\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eBut in this passage, as throughout most of Plato\u0027s teaching, there is\r\nan identification of the good with the truly real, which became\r\nembodied in the philosophical \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_7\" id=\"Page_7\"\u003e[7]\u003c/a\u003e\u003c/span\u003etradition, and is still largely\r\noperative in our own day. In thus allowing a legislative function to\r\nthe good, Plato produced a divorce between philosophy and science,\r\nfrom which, in my opinion, both have suffered ever since and are still\r\nsuffering. The man of science, whatever his hopes may be, must lay\r\nthem aside while he studies nature; and the philosopher, if he is to\r\nachieve truth, must do the same. Ethical considerations can only\r\nlegitimately appear when the truth has been ascertained: they can and\r\nshould appear as determining our feeling towards the truth, and our\r\nmanner of ordering our lives in view of the truth, but not as\r\nthemselves dictating what the truth is to be.\u003c/p\u003e\r\n\r\n\u003cp\u003eThere are passages in Plato\u0026mdash;among those which illustrate the\r\nscientific side of his mind\u0026mdash;where he seems clearly aware of this. The\r\nmost noteworthy is the one in which Socrates, as a young man, is\r\nexplaining the theory of ideas to Parmenides.\u003c/p\u003e\r\n\r\n\u003cp\u003eAfter Socrates has explained that there is an idea of the good, but\r\nnot of such things as hair and mud and dirt, Parmenides advises him\r\n\"not to despise even the meanest things,\" and this advice shows the\r\ngenuine scientific temper. It is with this impartial temper that the\r\nmystic\u0027s apparent insight into a higher reality and a hidden good has\r\nto be combined if philosophy is to realise its greatest possibilities.\r\nAnd it is failure in this respect that has made so much of idealistic\r\nphilosophy thin, lifeless, and insubstantial. It is only in marriage\r\nwith the world that our ideals can bear fruit: divorced from it, they\r\nremain barren. But marriage with the world is not to be achieved by an\r\nideal which shrinks from fact, or demands in advance that the world\r\nshall conform to its desires.\u003c/p\u003e\r\n\r\n\u003cp\u003eParmenides himself is the source of a peculiarly \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_8\" id=\"Page_8\"\u003e[8]\u003c/a\u003e\u003c/span\u003einteresting strain\r\nof mysticism which pervades Plato\u0027s thought\u0026mdash;the mysticism which may\r\nbe called \"logical\" because it is embodied in theories on logic. This\r\nform of mysticism, which appears, so far as the West is concerned, to\r\nhave originated with Parmenides, dominates the reasonings of all the\r\ngreat mystical metaphysicians from his day to that of Hegel and his\r\nmodern disciples. Reality, he says, is uncreated, indestructible,\r\nunchanging, indivisible; it is \"immovable in the bonds of mighty\r\nchains, without beginning and without end; since coming into being and\r\npassing away have been driven afar, and true belief has cast them\r\naway.\" The fundamental principle of his inquiry is stated in a\r\nsentence which would not be out of place in Hegel: \"Thou canst not\r\nknow what is not\u0026mdash;that is impossible\u0026mdash;nor utter it; for it is the same\r\nthing that can be thought and that can be.\" And again: \"It needs must\r\nbe that what can be thought and spoken of is; for it is possible for\r\nit to be, and it is not possible for what is nothing to be.\" The\r\nimpossibility of change follows from this principle; for what is past\r\ncan be spoken of, and therefore, by the principle, still is.\u003c/p\u003e\r\n\r\n\u003cp\u003eMystical philosophy, in all ages and in all parts of the world, is\r\ncharacterised by certain beliefs which are illustrated by the\r\ndoctrines we have been considering.\u003c/p\u003e\r\n\r\n\u003cp\u003eThere is, first, the belief in insight as against discursive analytic\r\nknowledge: the belief in a way of wisdom, sudden, penetrating,\r\ncoercive, which is contrasted with the slow and fallible study of\r\noutward appearance by a science relying wholly upon the senses. All\r\nwho are capable of absorption in an inward passion must have\r\nexperienced at times the strange feeling of unreality in common\r\nobjects, the loss of contact with daily things, in which the solidity\r\nof the outer world is lost, and the soul \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_9\" id=\"Page_9\"\u003e[9]\u003c/a\u003e\u003c/span\u003eseems, in utter loneliness,\r\nto bring forth, out of its own depths, the mad dance of fantastic\r\nphantoms which have hitherto appeared as independently real and\r\nliving. This is the negative side of the mystic\u0027s initiation: the\r\ndoubt concerning common knowledge, preparing the way for the reception\r\nof what seems a higher wisdom. Many men to whom this negative\r\nexperience is familiar do not pass beyond it, but for the mystic it is\r\nmerely the gateway to an ampler world.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe mystic insight begins with the sense of a mystery unveiled, of a\r\nhidden wisdom now suddenly become certain beyond the possibility of a\r\ndoubt. The sense of certainty and revelation comes earlier than any\r\ndefinite belief. The definite beliefs at which mystics arrive are the\r\nresult of reflection upon the inarticulate experience gained in the\r\nmoment of insight. Often, beliefs which have no real connection with\r\nthis moment become subsequently attracted into the central nucleus;\r\nthus in addition to the convictions which all mystics share, we find,\r\nin many of them, other convictions of a more local and temporary\r\ncharacter, which no doubt become amalgamated with what was essentially\r\nmystical in virtue of their subjective certainty. We may ignore such\r\ninessential accretions, and confine ourselves to the beliefs which all\r\nmystics share.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe first and most direct outcome of the moment of illumination is\r\nbelief in the possibility of a way of knowledge which may be called\r\nrevelation or insight or intuition, as contrasted with sense, reason,\r\nand analysis, which are regarded as blind guides leading to the morass\r\nof illusion. Closely connected with this belief is the conception of a\r\nReality behind the world of appearance and utterly different from it.\r\nThis Reality is regarded with an admiration often amounting to\r\nworship; it is \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_10\" id=\"Page_10\"\u003e[10]\u003c/a\u003e\u003c/span\u003efelt to be always and everywhere close at hand, thinly\r\nveiled by the shows of sense, ready, for the receptive mind, to shine\r\nin its glory even through the apparent folly and wickedness of Man.\r\nThe poet, the artist, and the lover are seekers after that glory: the\r\nhaunting beauty that they pursue is the faint reflection of its sun.\r\nBut the mystic lives in the full light of the vision: what others\r\ndimly seek he knows, with a knowledge beside which all other knowledge\r\nis ignorance.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe second characteristic of mysticism is its belief in unity, and its\r\nrefusal to admit opposition or division anywhere. We found Heraclitus\r\nsaying \"good and ill are one\"; and again he says, \"the way up and the\r\nway down is one and the same.\" The same attitude appears in the\r\nsimultaneous assertion of contradictory propositions, such as: \"We\r\nstep and do not step into the same rivers; we are and are not.\" The\r\nassertion of Parmenides, that reality is one and indivisible, comes\r\nfrom the same impulse towards unity. In Plato, this impulse is less\r\nprominent, being held in check by his theory of ideas; but it\r\nreappears, so far as his logic permits, in the doctrine of the primacy\r\nof the Good.\u003c/p\u003e\r\n\r\n\u003cp\u003eA third mark of almost all mystical metaphysics is the denial of the\r\nreality of Time. This is an outcome of the denial of division; if all\r\nis one, the distinction of past and future must be illusory. We have\r\nseen this doctrine prominent in Parmenides; and among moderns it is\r\nfundamental in the systems of Spinoza and Hegel.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe last of the doctrines of mysticism which we have to consider is\r\nits belief that all evil is mere appearance, an illusion produced by\r\nthe divisions and oppositions of the analytic intellect. Mysticism\r\ndoes not maintain that such things as cruelty, for example, are good,\r\nbut it denies that they are real: they belong to that lower \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_11\" id=\"Page_11\"\u003e[11]\u003c/a\u003e\u003c/span\u003eworld of\r\nphantoms from which we are to be liberated by the insight of the\r\nvision. Sometimes\u0026mdash;for example in Hegel, and at least verbally in\r\nSpinoza\u0026mdash;not only evil, but good also, is regarded as illusory, though\r\nnevertheless the emotional attitude towards what is held to be Reality\r\nis such as would naturally be associated with the belief that Reality\r\nis good. What is, in all cases, ethically characteristic of mysticism\r\nis absence of indignation or protest, acceptance with joy, disbelief\r\nin the ultimate truth of the division into two hostile camps, the good\r\nand the bad. This attitude is a direct outcome of the nature of the\r\nmystical experience: with its sense of unity is associated a feeling\r\nof infinite peace. Indeed it may be suspected that the feeling of\r\npeace produces, as feelings do in dreams, the whole system of\r\nassociated beliefs which make up the body of mystic doctrine. But this\r\nis a difficult question, and one on which it cannot be hoped that\r\nmankind will reach agreement.\u003c/p\u003e\r\n\r\n\u003cp\u003eFour questions thus arise in considering the truth or falsehood of\r\nmysticism, namely:\u003c/p\u003e\r\n\r\n\u003cdiv class=\"block\"\u003e\u003cp\u003eI. Are there two ways of knowing, which may be called respectively\r\nreason and intuition? And if so, is either to be preferred to the\r\nother?\u003c/p\u003e\r\n\r\n\u003cp\u003eII. Is all plurality and division illusory?\u003c/p\u003e\r\n\r\n\u003cp\u003eIII. Is time unreal?\u003c/p\u003e\r\n\r\n\u003cp\u003eIV. What kind of reality belongs to good and evil?\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cp\u003eOn all four of these questions, while fully developed mysticism seems\r\nto me mistaken, I yet believe that, by sufficient restraint, there is\r\nan element of wisdom to be learned from the mystical way of feeling,\r\nwhich does not seem to be attainable in any other manner. If this is\r\nthe truth, mysticism is to be commended as an attitude towards life,\r\nnot as a creed about the world. The \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_12\" id=\"Page_12\"\u003e[12]\u003c/a\u003e\u003c/span\u003emeta-physical creed, I shall\r\nmaintain, is a mistaken outcome of the emotion, although this emotion,\r\nas colouring and informing all other thoughts and feelings, is the\r\ninspirer of whatever is best in Man. Even the cautious and patient\r\ninvestigation of truth by science, which seems the very antithesis of\r\nthe mystic\u0027s swift certainty, may be fostered and nourished by that\r\nvery spirit of reverence in which mysticism lives and moves.\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\r\n\u003ch4\u003eI. REASON AND INTUITION\u003ca name=\"FNanchor_3_3\" id=\"FNanchor_3_3\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_3_3\" class=\"fnanchor\"\u003e[3]\u003c/a\u003e\u003c/h4\u003e\r\n\r\n\u003cp\u003eOf the reality or unreality of the mystic\u0027s world I know nothing. I\r\nhave no wish to deny it, nor even to declare that the insight which\r\nreveals it is not a genuine insight. What I do wish to maintain\u0026mdash;and\r\nit is here that the scientific attitude becomes imperative\u0026mdash;is that\r\ninsight, untested and unsupported, is an insufficient guarantee of\r\ntruth, in spite of the fact that much of the most important truth is\r\nfirst suggested by its means. It is common to speak of an opposition\r\nbetween instinct and reason; in the eighteenth century, the opposition\r\nwas drawn in favour of reason, but under the influence of Rousseau and\r\nthe romantic movement instinct was given the preference, first by\r\nthose who rebelled against artificial forms of government and thought,\r\nand then, as the purely rationalistic defence of traditional theology\r\nbecame increasingly difficult, by all who felt in science a menace to\r\ncreeds which they associated with a spiritual outlook on life and the\r\nworld. Bergson, under the name of \"intuition,\" has raised instinct to\r\nthe position of sole \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_13\" id=\"Page_13\"\u003e[13]\u003c/a\u003e\u003c/span\u003earbiter of metaphysical truth. But in fact the\r\nopposition of instinct and reason is mainly illusory. Instinct,\r\nintuition, or insight is what first leads to the beliefs which\r\nsubsequent reason confirms or confutes; but the confirmation, where it\r\nis possible, consists, in the last analysis, of agreement with other\r\nbeliefs no less instinctive. Reason is a harmonising, controlling\r\nforce rather than a creative one. Even in the most purely logical\r\nrealm, it is insight that first arrives at what is new.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhere instinct and reason do sometimes conflict is in regard to single\r\nbeliefs, held instinctively, and held with such determination that no\r\ndegree of inconsistency with other beliefs leads to their abandonment.\r\nInstinct, like all human faculties, is liable to error. Those in whom\r\nreason is weak are often unwilling to admit this as regards\r\nthemselves, though all admit it in regard to others. Where instinct is\r\nleast liable to error is in practical matters as to which right\r\njudgment is a help to survival: friendship and hostility in others,\r\nfor instance, are often felt with extraordinary discrimination through\r\nvery careful disguises. But even in such matters a wrong impression\r\nmay be given by reserve or flattery; and in matters less directly\r\npractical, such as philosophy deals with, very strong instinctive\r\nbeliefs are sometimes wholly mistaken, as we may come to know through\r\ntheir perceived inconsistency with other equally strong beliefs. It is\r\nsuch considerations that necessitate the harmonising mediation of\r\nreason, which tests our beliefs by their mutual compatibility, and\r\nexamines, in doubtful cases, the possible sources of error on the one\r\nside and on the other. In this there is no opposition to instinct as a\r\nwhole, but only to blind reliance upon some one interesting aspect of\r\ninstinct to the exclusion of other more \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_14\" id=\"Page_14\"\u003e[14]\u003c/a\u003e\u003c/span\u003ecommonplace but not less\r\ntrustworthy aspects. It is such one-sidedness, not instinct itself,\r\nthat reason aims at correcting.\u003c/p\u003e\r\n\r\n\u003cp\u003eThese more or less trite maxims may be illustrated by application to\r\nBergson\u0027s advocacy of \"intuition\" as against \"intellect.\" There are,\r\nhe says, \"two profoundly different ways of knowing a thing. The first\r\nimplies that we move round the object: the second that we enter into\r\nit. The first depends on the point of view at which we are placed and\r\non the symbols by which we express ourselves. The second neither\r\ndepends on a point of view nor relies on any symbol. The first kind of\r\nknowledge may be said to stop at the \u003ci\u003erelative\u003c/i\u003e; the second, in those\r\ncases where it is possible, to attain the \u003ci\u003eabsolute\u003c/i\u003e.\"\u003ca name=\"FNanchor_4_4\" id=\"FNanchor_4_4\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_4_4\" class=\"fnanchor\"\u003e[4]\u003c/a\u003e The second\r\nof these, which is intuition, is, he says, \"the kind of \u003ci\u003eintellectual\r\nsympathy\u003c/i\u003e by which one places oneself within an object in order to\r\ncoincide with what is unique in it and therefore inexpressible\" (p.\r\n6). In illustration, he mentions self-knowledge: \"there is one\r\nreality, at least, which we all seize from within, by intuition and\r\nnot by simple analysis. It is our own personality in its flowing\r\nthrough time\u0026mdash;our self which endures\" (p. 8). The rest of Bergson\u0027s\r\nphilosophy consists in reporting, through the imperfect medium of\r\nwords, the knowledge gained by intuition, and the consequent complete\r\ncondemnation of all the pretended knowledge derived from science and\r\ncommon sense.\u003c/p\u003e\r\n\r\n\u003cp\u003eThis procedure, since it takes sides in a conflict of instinctive\r\nbeliefs, stands in need of justification by proving the greater\r\ntrustworthiness of the beliefs on one side than of those on the other.\r\nBergson attempts this justification in two ways, first by explaining\r\nthat intellect is a purely practical faculty to secure biological\r\nsuccess, \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_15\" id=\"Page_15\"\u003e[15]\u003c/a\u003e\u003c/span\u003esecondly by mentioning remarkable feats of instinct in\r\nanimals and by pointing out characteristics of the world which, though\r\nintuition can apprehend them, are baffling to intellect as he\r\ninterprets it.\u003c/p\u003e\r\n\r\n\u003cp\u003eOf Bergson\u0027s theory that intellect is a purely practical faculty,\r\ndeveloped in the struggle for survival, and not a source of true\r\nbeliefs, we may say, first, that it is only through intellect that we\r\nknow of the struggle for survival and of the biological ancestry of\r\nman: if the intellect is misleading, the whole of this merely inferred\r\nhistory is presumably untrue. If, on the other hand, we agree with him\r\nin thinking that evolution took place as Darwin believed, then it is\r\nnot only intellect, but all our faculties, that have been developed\r\nunder the stress of practical utility. Intuition is seen at its best\r\nwhere it is directly useful, for example in regard to other people\u0027s\r\ncharacters and dispositions. Bergson apparently holds that capacity\r\nfor this kind of knowledge is less explicable by the struggle for\r\nexistence than, for example, capacity for pure mathematics. Yet the\r\nsavage deceived by false friendship is likely to pay for his mistake\r\nwith his life; whereas even in the most civilised societies men are\r\nnot put to death for mathematical incompetence. All the most striking\r\nof his instances of intuition in animals have a very direct survival\r\nvalue. The fact is, of course, that both intuition and intellect have\r\nbeen developed because they are useful, and that, speaking broadly,\r\nthey are useful when they give truth and become harmful when they give\r\nfalsehood. Intellect, in civilised man, like artistic capacity, has\r\noccasionally been developed beyond the point where it is useful to the\r\nindividual; intuition, on the other hand, seems on the whole to\r\ndiminish as civilisation increases. It is greater, as a rule, in\r\nchildren than in adults, in the uneducated than in the educated.\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_16\" id=\"Page_16\"\u003e[16]\u003c/a\u003e\u003c/span\u003eProbably in dogs it exceeds anything to be found in human beings. But\r\nthose who see in these facts a recommendation of intuition ought to\r\nreturn to running wild in the woods, dyeing themselves with woad and\r\nliving on hips and haws.\u003c/p\u003e\r\n\r\n\u003cp\u003eLet us next examine whether intuition possesses any such infallibility\r\nas Bergson claims for it. The best instance of it, according to him,\r\nis our acquaintance with ourselves; yet self-knowledge is proverbially\r\nrare and difficult. Most men, for example, have in their nature\r\nmeannesses, vanities, and envies of which they are quite unconscious,\r\nthough even their best friends can perceive them without any\r\ndifficulty. It is true that intuition has a convincingness which is\r\nlacking to intellect: while it is present, it is almost impossible to\r\ndoubt its truth. But if it should appear, on examination, to be at\r\nleast as fallible as intellect, its greater subjective certainty\r\nbecomes a demerit, making it only the more irresistibly deceptive.\r\nApart from self-knowledge, one of the most notable examples of\r\nintuition is the knowledge people believe themselves to possess of\r\nthose with whom they are in love: the wall between different\r\npersonalities seems to become transparent, and people think they see\r\ninto another soul as into their own. Yet deception in such cases is\r\nconstantly practised with success; and even where there is no\r\nintentional deception, experience gradually proves, as a rule, that\r\nthe supposed insight was illusory, and that the slower more groping\r\nmethods of the intellect are in the long run more reliable.\u003c/p\u003e\r\n\r\n\u003cp\u003eBergson maintains that intellect can only deal with things in so far\r\nas they resemble what has been experienced in the past, while\r\nintuition has the power of apprehending the uniqueness and novelty\r\nthat always belong to each fresh moment. That there is something\r\nunique \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_17\" id=\"Page_17\"\u003e[17]\u003c/a\u003e\u003c/span\u003eand new at every moment, is certainly true; it is also true\r\nthat this cannot be fully expressed by means of intellectual concepts.\r\nOnly direct acquaintance can give knowledge of what is unique and new.\r\nBut direct acquaintance of this kind is given fully in sensation, and\r\ndoes not require, so far as I can see, any special faculty of\r\nintuition for its apprehension. It is neither intellect nor intuition,\r\nbut sensation, that supplies new data; but when the data are new in\r\nany remarkable manner, intellect is much more capable of dealing with\r\nthem than intuition would be. The hen with a brood of ducklings no\r\ndoubt has intuition which seems to place her inside them, and not\r\nmerely to know them analytically; but when the ducklings take to the\r\nwater, the whole apparent intuition is seen to be illusory, and the\r\nhen is left helpless on the shore. Intuition, in fact, is an aspect\r\nand development of instinct, and, like all instinct, is admirable in\r\nthose customary surroundings which have moulded the habits of the\r\nanimal in question, but totally incompetent as soon as the\r\nsurroundings are changed in a way which demands some non-habitual mode\r\nof action.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe theoretical understanding of the world, which is the aim of\r\nphilosophy, is not a matter of great practical importance to animals,\r\nor to savages, or even to most civilised men. It is hardly to be\r\nsupposed, therefore, that the rapid, rough and ready methods of\r\ninstinct or intuition will find in this field a favourable ground for\r\ntheir application. It is the older kinds of activity, which bring out\r\nour kinship with remote generations of animal and semi-human\r\nancestors, that show intuition at its best. In such matters as\r\nself-preservation and love, intuition will act sometimes (though not\r\nalways) with a swiftness and precision which are astonishing to the\r\ncritical intellect. But philosophy is not one of the \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_18\" id=\"Page_18\"\u003e[18]\u003c/a\u003e\u003c/span\u003epursuits which\r\nillustrate our affinity with the past: it is a highly refined, highly\r\ncivilised pursuit, demanding, for its success, a certain liberation\r\nfrom the life of instinct, and even, at times, a certain aloofness\r\nfrom all mundane hopes and fears. It is not in philosophy, therefore,\r\nthat we can hope to see intuition at its best. On the contrary, since\r\nthe true objects of philosophy, and the habit of thought demanded for\r\ntheir apprehension, are strange, unusual, and remote, it is here, more\r\nalmost than anywhere else, that intellect proves superior to\r\nintuition, and that quick unanalysed convictions are least deserving\r\nof uncritical acceptance.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn advocating the scientific restraint and balance, as against the\r\nself-assertion of a confident reliance upon intuition, we are only\r\nurging, in the sphere of knowledge, that largeness of contemplation,\r\nthat impersonal disinterestedness, and that freedom from practical\r\npreoccupations which have been inculcated by all the great religions\r\nof the world. Thus our conclusion, however it may conflict with the\r\nexplicit beliefs of many mystics, is, in essence, not contrary to the\r\nspirit which inspires those beliefs, but rather the outcome of this\r\nvery spirit as applied in the realm of thought.\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\u003ch4\u003eII. UNITY AND PLURALITY\u003c/h4\u003e\r\n\r\n\u003cp\u003eOne of the most convincing aspects of the mystic illumination is the\r\napparent revelation of the oneness of all things, giving rise to\r\npantheism in religion and to monism in philosophy. An elaborate logic,\r\nbeginning with Parmenides, and culminating in Hegel and his followers,\r\nhas been gradually developed, to prove that the universe is one\r\nindivisible Whole, and that what seem to be its parts, if considered\r\nas substantial and \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_19\" id=\"Page_19\"\u003e[19]\u003c/a\u003e\u003c/span\u003eself-existing, are mere illusion. The conception\r\nof a Reality quite other than the world of appearance, a reality one,\r\nindivisible, and unchanging, was introduced into Western philosophy by\r\nParmenides, not, nominally at least, for mystical or religious\r\nreasons, but on the basis of a logical argument as to the\r\nimpossibility of not-being, and most subsequent metaphysical systems\r\nare the outcome of this fundamental idea.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe logic used in defence of mysticism seems to be faulty as logic,\r\nand open to technical criticisms, which I have explained elsewhere. I\r\nshall not here repeat these criticisms, since they are lengthy and\r\ndifficult, but shall instead attempt an analysis of the state of mind\r\nfrom which mystical logic has arisen.\u003c/p\u003e\r\n\r\n\u003cp\u003eBelief in a reality quite different from what appears to the senses\r\narises with irresistible force in certain moods, which are the source\r\nof most mysticism, and of most metaphysics. While such a mood is\r\ndominant, the need of logic is not felt, and accordingly the more\r\nthoroughgoing mystics do not employ logic, but appeal directly to the\r\nimmediate deliverance of their insight. But such fully developed\r\nmysticism is rare in the West. When the intensity of emotional\r\nconviction subsides, a man who is in the habit of reasoning will\r\nsearch for logical grounds in favour of the belief which he finds in\r\nhimself. But since the belief already exists, he will be very\r\nhospitable to any ground that suggests itself. The paradoxes\r\napparently proved by his logic are really the paradoxes of mysticism,\r\nand are the goal which he feels his logic must reach if it is to be in\r\naccordance with insight. The resulting logic has rendered most\r\nphilosophers incapable of giving any account of the world of science\r\nand daily life. If they had been anxious to give such an account, they\r\nwould probably have discovered the errors of their \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_20\" id=\"Page_20\"\u003e[20]\u003c/a\u003e\u003c/span\u003elogic; but most of\r\nthem were less anxious to understand the world of science and daily\r\nlife than to convict it of unreality in the interests of a\r\nsuper-sensible \"real\" world.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is in this way that logic has been pursued by those of the great\r\nphilosophers who were mystics. But since they usually took for granted\r\nthe supposed insight of the mystic emotion, their logical doctrines\r\nwere presented with a certain dryness, and were believed by their\r\ndisciples to be quite independent of the sudden illumination from\r\nwhich they sprang. Nevertheless their origin clung to them, and they\r\nremained\u0026mdash;to borrow a useful word from Mr. Santayana\u0026mdash;\"malicious\" in\r\nregard to the world of science and common sense. It is only so that we\r\ncan account for the complacency with which philosophers have accepted\r\nthe inconsistency of their doctrines with all the common and\r\nscientific facts which seem best established and most worthy of\r\nbelief.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe logic of mysticism shows, as is natural, the defects which are\r\ninherent in anything malicious. The impulse to logic, not felt while\r\nthe mystic mood is dominant, reasserts itself as the mood fades, but\r\nwith a desire to retain the vanishing insight, or at least to prove\r\nthat it \u003ci\u003ewas\u003c/i\u003e insight, and that what seems to contradict it is\r\nillusion. The logic which thus arises is not quite disinterested or\r\ncandid, and is inspired by a certain hatred of the daily world to\r\nwhich it is to be applied. Such an attitude naturally does not tend to\r\nthe best results. Everyone knows that to read an author simply in\r\norder to refute him is not the way to understand him; and to read the\r\nbook of Nature with a conviction that it is all illusion is just as\r\nunlikely to lead to understanding. If our logic is to find the common\r\nworld intelligible, it must not be hostile, but must be inspired by a\r\ngenuine \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_21\" id=\"Page_21\"\u003e[21]\u003c/a\u003e\u003c/span\u003eacceptance such as is not usually to be found among\r\nmetaphysicians.\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\u003ch4\u003eIII. TIME\u003c/h4\u003e\r\n\r\n\u003cp\u003eThe unreality of time is a cardinal doctrine of many metaphysical\r\nsystems, often nominally based, as already by Parmenides, upon logical\r\narguments, but originally derived, at any rate in the founders of new\r\nsystems, from the certainty which is born in the moment of mystic\r\ninsight. As a Persian Sufi poet says:\u003c/p\u003e\r\n\r\n\u003cdiv class=\"poem\"\u003e\u003cdiv class=\"stanza\"\u003e\r\n\u003cspan class=\"i0\"\u003e\"Past and future are what veil God from our sight.\u003cbr /\u003e\u003c/span\u003e\r\n\u003cspan class=\"i0\"\u003eBurn up both of them with fire! How long\u003cbr /\u003e\u003c/span\u003e\r\n\u003cspan class=\"i0\"\u003eWilt thou be partitioned by these segments as a reed?\"\u003ca name=\"FNanchor_5_5\" id=\"FNanchor_5_5\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_5_5\" class=\"fnanchor\"\u003e[5]\u003c/a\u003e\u003cbr /\u003e\u003c/span\u003e\r\n\u003c/div\u003e\u003c/div\u003e\r\n\r\n\u003cp\u003eThe belief that what is ultimately real must be immutable is a very\r\ncommon one: it gave rise to the metaphysical notion of substance, and\r\nfinds, even now, a wholly illegitimate satisfaction in such scientific\r\ndoctrines as the conservation of energy and mass.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is difficult to disentangle the truth and the error in this view.\r\nThe arguments for the contention that time is unreal and that the\r\nworld of sense is illusory must, I think, be regarded as fallacious.\r\nNevertheless there is some sense\u0026mdash;easier to feel than to state\u0026mdash;in\r\nwhich time is an unimportant and superficial characteristic of\r\nreality. Past and future must be acknowledged to be as real as the\r\npresent, and a certain emancipation from slavery to time is essential\r\nto philosophic thought. The importance of time is rather practical\r\nthan theoretical, rather in relation to our desires than in relation\r\nto truth. A truer image of the world, I think, is obtained by\r\npicturing things as entering into the stream of time from an eternal\r\nworld outside, than from a view which regards time as the devouring\r\ntyrant of all that is. Both in \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_22\" id=\"Page_22\"\u003e[22]\u003c/a\u003e\u003c/span\u003ethought and in feeling, even though\r\ntime be real, to realise the unimportance of time is the gate of\r\nwisdom.\u003c/p\u003e\r\n\r\n\u003cp\u003eThat this is the case may be seen at once by asking ourselves why our\r\nfeelings towards the past are so different from our feelings towards\r\nthe future. The reason for this difference is wholly practical: our\r\nwishes can affect the future but not the past, the future is to some\r\nextent subject to our power, while the past is unalterably fixed. But\r\nevery future will some day be past: if we see the past truly now, it\r\nmust, when it was still future, have been just what we now see it to\r\nbe, and what is now future must be just what we shall see it to be\r\nwhen it has become past. The felt difference of quality between past\r\nand future, therefore, is not an intrinsic difference, but only a\r\ndifference in relation to us: to impartial contemplation, it ceases to\r\nexist. And impartiality of contemplation is, in the intellectual\r\nsphere, that very same virtue of disinterestedness which, in the\r\nsphere of action, appears as justice and unselfishness. Whoever wishes\r\nto see the world truly, to rise in thought above the tyranny of\r\npractical desires, must learn to overcome the difference of attitude\r\ntowards past and future, and to survey the whole stream of time in one\r\ncomprehensive vision.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe kind of way in which, as it seems to me, time ought not to enter\r\ninto our theoretic philosophical thought, may be illustrated by the\r\nphilosophy which has become associated with the idea of evolution, and\r\nwhich is exemplified by Nietzsche, pragmatism, and Bergson. This\r\nphilosophy, on the basis of the development which has led from the\r\nlowest forms of life up to man, sees in \u003ci\u003eprogress\u003c/i\u003e the fundamental law\r\nof the universe, and thus admits the difference between \u003ci\u003eearlier\u003c/i\u003e and\r\n\u003ci\u003elater\u003c/i\u003e into the very citadel of its contemplative outlook. With its\r\npast and future \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_23\" id=\"Page_23\"\u003e[23]\u003c/a\u003e\u003c/span\u003ehistory of the world, conjectural as it is, I do not\r\nwish to quarrel. But I think that, in the intoxication of a quick\r\nsuccess, much that is required for a true understanding of the\r\nuniverse has been forgotten. Something of Hellenism, something, too,\r\nof Oriental resignation, must be combined with its hurrying Western\r\nself-assertion before it can emerge from the ardour of youth into the\r\nmature wisdom of manhood. In spite of its appeals to science, the true\r\nscientific philosophy, I think, is something more arduous and more\r\naloof, appealing to less mundane hopes, and requiring a severer\r\ndiscipline for its successful practice.\u003c/p\u003e\r\n\r\n\u003cp\u003eDarwin\u0027s \u003ci\u003eOrigin of Species\u003c/i\u003e persuaded the world that the difference\r\nbetween different species of animals and plants is not the fixed\r\nimmutable difference that it appears to be. The doctrine of natural\r\nkinds, which had rendered classification easy and definite, which was\r\nenshrined in the Aristotelian tradition, and protected by its supposed\r\nnecessity for orthodox dogma, was suddenly swept away for ever out of\r\nthe biological world. The difference between man and the lower\r\nanimals, which to our human conceit appears enormous, was shown to be\r\na gradual achievement, involving intermediate being who could not with\r\ncertainty be placed either within or without the human family. The sun\r\nand the planets had already been shown by Laplace to be very probably\r\nderived from a primitive more or less undifferentiated nebula. Thus\r\nthe old fixed landmarks became wavering and indistinct, and all sharp\r\noutlines were blurred. Things and species lost their boundaries, and\r\nnone could say where they began or where they ended.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut if human conceit was staggered for a moment by its kinship with\r\nthe ape, it soon found a way to reassert itself, and that way is the\r\n\"philosophy\" of evolution. \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_24\" id=\"Page_24\"\u003e[24]\u003c/a\u003e\u003c/span\u003eA process which led from the am[oe]ba to\r\nMan appeared to the philosophers to be obviously a progress\u0026mdash;though\r\nwhether the am[oe]ba would agree with this opinion is not known. Hence\r\nthe cycle of changes which science had shown to be the probable\r\nhistory of the past was welcomed as revealing a law of development\r\ntowards good in the universe\u0026mdash;an evolution or unfolding of an idea\r\nslowly embodying itself in the actual. But such a view, though it\r\nmight satisfy Spencer and those whom we may call Hegelian\r\nevolutionists, could not be accepted as adequate by the more\r\nwhole-hearted votaries of change. An ideal to which the world\r\ncontinuously approaches is, to these minds, too dead and static to be\r\ninspiring. Not only the aspiration, but the ideal too, must change and\r\ndevelop with the course of evolution: there must be no fixed goal, but\r\na continual fashioning of fresh needs by the impulse which is life and\r\nwhich alone gives unity to the process.\u003c/p\u003e\r\n\r\n\u003cp\u003eLife, in this philosophy, is a continuous stream, in which all\r\ndivisions are artificial and unreal. Separate things, beginnings and\r\nendings, are mere convenient fictions: there is only smooth unbroken\r\ntransition. The beliefs of to-day may count as true to-day, if they\r\ncarry us along the stream; but to-morrow they will be false, and must\r\nbe replaced by new beliefs to meet the new situation. All our thinking\r\nconsists of convenient fictions, imaginary congealings of the stream:\r\nreality flows on in spite of all our fictions, and though it can be\r\nlived, it cannot be conceived in thought. Somehow, without explicit\r\nstatement, the assurance is slipped in that the future, though we\r\ncannot foresee it, will be better than the past or the present: the\r\nreader is like the child which expects a sweet because it has been\r\ntold to open its mouth and shut its eyes. Logic, mathematics, \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_25\" id=\"Page_25\"\u003e[25]\u003c/a\u003e\u003c/span\u003ephysics\r\ndisappear in this philosophy, because they are too \"static\"; what is\r\nreal is no impulse and movement towards a goal which, like the\r\nrainbow, recedes as we advance, and makes every place different when\r\nit reaches it from what it appeared to be at a distance.\u003c/p\u003e\r\n\r\n\u003cp\u003eI do not propose to enter upon a technical examination of this\r\nphilosophy. I wish only to maintain that the motives and interests\r\nwhich inspire it are so exclusively practical, and the problems with\r\nwhich it deals are so special, that it can hardly be regarded as\r\ntouching any of the questions that, to my mind, constitute genuine\r\nphilosophy.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe predominant interest of evolutionism is in the question of human\r\ndestiny, or at least of the destiny of Life. It is more interested in\r\nmorality and happiness than in knowledge for its own sake. It must be\r\nadmitted that the same may be said of many other philosophies, and\r\nthat a desire for the kind of knowledge which philosophy can give is\r\nvery rare. But if philosophy is to attain truth, it is necessary first\r\nand foremost that philosophers should acquire the disinterested\r\nintellectual curiosity which characterises the genuine man of science.\r\nKnowledge concerning the future\u0026mdash;which is the kind of knowledge that\r\nmust be sought if we are to know about human destiny\u0026mdash;is possible\r\nwithin certain narrow limits. It is impossible to say how much the\r\nlimits may be enlarged with the progress of science. But what is\r\nevident is that any proposition about the future belongs by its\r\nsubject-matter to some particular science, and is to be ascertained,\r\nif at all, by the methods of that science. Philosophy is not a short\r\ncut to the same kind of results as those of the other sciences: if it\r\nis to be a genuine study, it must have a province of its own, and aim\r\nat results which the other sciences can neither prove nor disprove.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_26\" id=\"Page_26\"\u003e[26]\u003c/a\u003e\u003c/span\u003eEvolutionism, in basing itself upon the notion of \u003ci\u003eprogress\u003c/i\u003e, which is\r\nchange from the worse to the better, allows the notion of time, as it\r\nseems to me, to become its tyrant rather than its servant, and thereby\r\nloses that impartiality of contemplation which is the source of all\r\nthat is best in philosophic thought and feeling. Metaphysicians, as we\r\nsaw, have frequently denied altogether the reality of time. I do not\r\nwish to do this; I wish only to preserve the mental outlook which\r\ninspired the denial, the attitude which, in thought, regards the past\r\nas having the same reality as the present and the same importance as\r\nthe future. \"In so far,\" says Spinoza,\u003ca name=\"FNanchor_6_6\" id=\"FNanchor_6_6\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_6_6\" class=\"fnanchor\"\u003e[6]\u003c/a\u003e \"as the mind conceives a\r\nthing according to the dictate of reason, it will be equally affected\r\nwhether the idea is that of a future, past, or present thing.\" It is\r\nthis \"conceiving according to the dictate of reason\" that I find\r\nlacking in the philosophy which is based on evolution.\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\u003ch4\u003eIV. GOOD AND EVIL\u003c/h4\u003e\r\n\r\n\u003cp\u003eMysticism maintains that all evil is illusory, and sometimes maintains\r\nthe same view as regards good, but more often holds that all Reality\r\nis good. Both views are to be found in Heraclitus: \"Good and ill are\r\none,\" he says, but again, \"To God all things are fair and good and\r\nright, but men hold some things wrong and some right.\" A similar\r\ntwofold position is to be found in Spinoza, but he uses the word\r\n\"perfection\" when he means to speak of the good that is not merely\r\nhuman. \"By reality and perfection I mean the same thing,\" he says;\u003ca name=\"FNanchor_7_7\" id=\"FNanchor_7_7\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_7_7\" class=\"fnanchor\"\u003e[7]\u003c/a\u003e\r\nbut elsewhere we find the definition: \"By \u003ci\u003egood\u003c/i\u003e I shall mean that\r\nwhich we certainly know to be useful to us.\"\u003ca name=\"FNanchor_8_8\" id=\"FNanchor_8_8\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_8_8\" class=\"fnanchor\"\u003e[8]\u003c/a\u003e Thus perfection\r\nbelongs to Reality in its own nature, but \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_27\" id=\"Page_27\"\u003e[27]\u003c/a\u003e\u003c/span\u003egoodness is relative to\r\nourselves and our needs, and disappears in an impartial survey. Some\r\nsuch distinction, I think, is necessary in order to understand the\r\nethical outlook of mysticism: there is a lower mundane kind of good\r\nand evil, which divides the world of appearance into what seem to be\r\nconflicting parts; but there is also a higher, mystical kind of good,\r\nwhich belongs to Reality and is not opposed by any correlative kind of\r\nevil.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is difficult to give a logically tenable account of this position\r\nwithout recognising that good and evil are subjective, that what is\r\ngood is merely that towards which we have one kind of feeling, and\r\nwhat is evil is merely that towards which we have another kind of\r\nfeeling. In our active life, where we have to exercise choice, and to\r\nprefer this to that of two possible acts, it is necessary to have a\r\ndistinction of good and evil, or at least of better and worse. But\r\nthis distinction, like everything pertaining to action, belongs to\r\nwhat mysticism regards as the world of illusion, if only because it is\r\nessentially concerned with time. In our contemplative life, where\r\naction is not called for, it is possible to be impartial, and to\r\novercome the ethical dualism which action requires. So long as we\r\nremain \u003ci\u003emerely\u003c/i\u003e impartial, we may be content to say that both the good\r\nand the evil of action are illusions. But if, as we must do if we have\r\nthe mystic vision, we find the whole world worthy of love and worship,\r\nif we see\u003c/p\u003e\r\n\r\n\u003cdiv class=\"poem\"\u003e\u003cdiv class=\"stanza\"\u003e\r\n\u003cspan class=\"i0\"\u003e\"The earth, and every common sight….\u003cbr /\u003e\u003c/span\u003e\r\n\u003cspan class=\"i0\"\u003eApparell\u0027d in celestial light,\"\u003cbr /\u003e\u003c/span\u003e\r\n\u003c/div\u003e\u003c/div\u003e\r\n\r\n\u003cp class=\"noin\"\u003ewe shall say that there is a higher good than that of action, and that\r\nthis higher good belongs to the whole world as it is in reality. In\r\nthis way the twofold attitude and the apparent vacillation of\r\nmysticism are explained and justified.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_28\" id=\"Page_28\"\u003e[28]\u003c/a\u003e\u003c/span\u003eThe possibility of this universal love and joy in all that exists is\r\nof supreme importance for the conduct and happiness of life, and gives\r\ninestimable value to the mystic emotion, apart from any creeds which\r\nmay be built upon it. But if we are not to be led into false beliefs,\r\nit is necessary to realise exactly \u003ci\u003ewhat\u003c/i\u003e the mystic emotion reveals.\r\nIt reveals a possibility of human nature\u0026mdash;a possibility of a nobler,\r\nhappier, freer life than any that can be otherwise achieved. But it\r\ndoes not reveal anything about the non-human, or about the nature of\r\nthe universe in general. Good and bad, and even the higher good that\r\nmysticism finds everywhere, are the reflections of our own emotions on\r\nother things, not part of the substance of things as they are in\r\nthemselves. And therefore an impartial contemplation, freed from all\r\npre-occupation with Self, will not judge things good or bad, although\r\nit is very easily combined with that feeling of universal love which\r\nleads the mystic to say that the whole world is good.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe philosophy of evolution, through the notion of progress, is bound\r\nup with the ethical dualism of the worse and the better, and is thus\r\nshut out, not only from the kind of survey which discards good and\r\nevil altogether from its view, but also from the mystical belief in\r\nthe goodness of everything. In this way the distinction of good and\r\nevil, like time, becomes a tyrant in this philosophy, and introduces\r\ninto thought the restless selectiveness of action. Good and evil, like\r\ntime, are, it would seem, not general or fundamental in the world of\r\nthought, but late and highly specialised members of the intellectual\r\nhierarchy.\u003c/p\u003e\r\n\r\n\u003cp\u003eAlthough, as we saw, mysticism can be interpreted so as to agree with\r\nthe view that good and evil are not intellectually fundamental, it\r\nmust be admitted that here \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_29\" id=\"Page_29\"\u003e[29]\u003c/a\u003e\u003c/span\u003ewe are no longer in verbal agreement with\r\nmost of the great philosophers and religious teachers of the past. I\r\nbelieve, however, that the elimination of ethical considerations from\r\nphilosophy is both scientifically necessary and\u0026mdash;though this may seem\r\na paradox\u0026mdash;an ethical advance. Both these contentions must be briefly\r\ndefended.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe hope of satisfaction to our more human desires\u0026mdash;the hope of\r\ndemonstrating that the world has this or that desirable ethical\r\ncharacteristic\u0026mdash;is not one which, so far as I can see, a scientific\r\nphilosophy can do anything whatever to satisfy. The difference between\r\na good world and a bad one is a difference in the particular\r\ncharacteristics of the particular things that exist in these worlds:\r\nit is not a sufficiently abstract difference to come within the\r\nprovince of philosophy. Love and hate, for example, are ethical\r\nopposites, but to philosophy they are closely analogous attitudes\r\ntowards objects. The general form and structure of those attitudes\r\ntowards objects which constitute mental phenomena is a problem for\r\nphilosophy, but the difference between love and hate is not a\r\ndifference of form or structure, and therefore belongs rather to the\r\nspecial science of psychology than to philosophy. Thus the ethical\r\ninterests which have often inspired philosophers must remain in the\r\nbackground: some kind of ethical interest may inspire the whole study,\r\nbut none must obtrude in the detail or be expected in the special\r\nresults which are sought.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf this view seems at first sight disappointing, we may remind\r\nourselves that a similar change has been found necessary in all the\r\nother sciences. The physicist or chemist is not now required to prove\r\nthe ethical importance of his ions or atoms; the biologist is not\r\nexpected to prove the utility of the plants or animals \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_30\" id=\"Page_30\"\u003e[30]\u003c/a\u003e\u003c/span\u003ewhich he\r\ndissects. In pre-scientific ages this was not the case. Astronomy, for\r\nexample, was studied because men believed in astrology: it was thought\r\nthat the movements of the planets had the most direct and important\r\nbearing upon the lives of human beings. Presumably, when this belief\r\ndecayed and the disinterested study of astronomy began, many who had\r\nfound astrology absorbingly interesting decided that astronomy had too\r\nlittle human interest to be worthy of study. Physics, as it appears in\r\nPlato\u0027s Tim\u0026aelig;us for example, is full of ethical notions: it is an\r\nessential part of its purpose to show that the earth is worthy of\r\nadmiration. The modern physicist, on the contrary, though he has no\r\nwish to deny that the earth is admirable, is not concerned, as\r\nphysicist, with its ethical attributes: he is merely concerned to find\r\nout facts, not to consider whether they are good or bad. In\r\npsychology, the scientific attitude is even more recent and more\r\ndifficult than in the physical sciences: it is natural to consider\r\nthat human nature is either good or bad, and to suppose that the\r\ndifference between good and bad, so all-important in practice, must be\r\nimportant in theory also. It is only during the last century that an\r\nethically neutral psychology has grown up; and here too, ethical\r\nneutrality has been essential to scientific success.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn philosophy, hitherto, ethical neutrality has been seldom sought and\r\nhardly ever achieved. Men have remembered their wishes, and have\r\njudged philosophies in relation to their wishes. Driven from the\r\nparticular sciences, the belief that the notions of good and evil must\r\nafford a key to the understanding of the world has sought a refuge in\r\nphilosophy. But even from this last refuge, if philosophy is not to\r\nremain a set of pleasing dreams, this belief must be driven forth. It\r\nis a commonplace that \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_31\" id=\"Page_31\"\u003e[31]\u003c/a\u003e\u003c/span\u003ehappiness is not best achieved by those who\r\nseek it directly; and it would seem that the same is true of the good.\r\nIn thought, at any rate, those who forget good and evil and seek only\r\nto know the facts are more likely to achieve good than those who view\r\nthe world through the distorting medium of their own desires.\u003c/p\u003e\r\n\r\n\u003cp\u003eWe are thus brought back to our seeming paradox, that a philosophy\r\nwhich does not seek to impose upon the world its own conceptions of\r\ngood and evil is not only more likely to achieve truth, but is also\r\nthe outcome of a higher ethical standpoint than one which, like\r\nevolutionism and most traditional systems, is perpetually appraising\r\nthe universe and seeking to find in it an embodiment of present\r\nideals. In religion, and in every deeply serious view of the world and\r\nof human destiny, there is an element of submission, a realisation of\r\nthe limits of human power, which is somewhat lacking in the modern\r\nworld, with its quick material successes and its insolent belief in\r\nthe boundless possibilities of progress. \"He that loveth his life\r\nshall lose it\"; and there is danger lest, through a too confident love\r\nof life, life itself should lose much of what gives it its highest\r\nworth. The submission which religion inculcates in action is\r\nessentially the same in spirit as that which science teaches in\r\nthought; and the ethical neutrality by which its victories have been\r\nachieved is the outcome of that submission.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe good which it concerns us to remember is the good which it lies in\r\nour power to create\u0026mdash;the good in our own lives and in our attitude\r\ntowards the world. Insistence on belief in an external realisation of\r\nthe good is a form of self-assertion, which, while it cannot secure\r\nthe external good which it desires, can seriously impair the inward\r\ngood which lies within our power, and destroy that reverence towards\r\nfact which constitutes both what is \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_32\" id=\"Page_32\"\u003e[32]\u003c/a\u003e\u003c/span\u003evaluable in humility and what is\r\nfruitful in the scientific temper.\u003c/p\u003e\r\n\r\n\u003cp\u003eHuman beings cannot, of course, wholly transcend human nature;\r\nsomething subjective, if only the interest that determines the\r\ndirection of our attention, must remain in all our thought. But\r\nscientific philosophy comes nearer to objectivity than any other human\r\npursuit, and gives us, therefore, the closest constant and the most\r\nintimate relation with the outer world that it is possible to achieve.\r\nTo the primitive mind, everything is either friendly or hostile; but\r\nexperience has shown that friendliness and hostility are not the\r\nconceptions by which the world is to be understood. Scientific\r\nphilosophy thus represents, though as yet only in a nascent condition,\r\na higher form of thought than any pre-scientific belief or\r\nimagination, and, like every approach to self-transcendence, it brings\r\nwith it a rich reward in increase of scope and breadth and\r\ncomprehension. Evolutionism, in spite of its appeals to particular\r\nscientific facts, fails to be a truly scientific philosophy because of\r\nits slavery to time, its ethical preoccupations, and its predominant\r\ninterest in our mundane concerns and destiny. A truly scientific\r\nphilosophy will be more humble, more piecemeal, more arduous, offering\r\nless glitter of outward mirage to flatter fallacious hopes, but more\r\nindifferent to fate, and more capable of accepting the world without\r\nthe tyrannous imposition of our human and temporary demands.\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\u003chr style=\"width: 15%;\" /\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003ch4\u003eFOOTNOTES:\u003c/h4\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_1_1\" id=\"Footnote_1_1\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_1_1\"\u003e\u003cspan class=\"label\"\u003e[1]\u003c/span\u003e\u003c/a\u003e All the above quotations are from Burnet\u0027s \u003ci\u003eEarly Greek\r\nPhilosophy\u003c/i\u003e, (2nd ed., 1908), pp. 146-156.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_2_2\" id=\"Footnote_2_2\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_2_2\"\u003e\u003cspan class=\"label\"\u003e[2]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eRepublic\u003c/i\u003e, 514, translated by Davies and Vaughan.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_3_3\" id=\"Footnote_3_3\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_3_3\"\u003e\u003cspan class=\"label\"\u003e[3]\u003c/span\u003e\u003c/a\u003e This section, and also one or two pages in later\r\nsections, have been printed in a course of Lowell lectures \u003ci\u003eOn our\r\nknowledge of the external world\u003c/i\u003e, published by the Open Court\r\nPublishing Company. But I have left them here, as this is the context\r\nfor which they were originally written.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_4_4\" id=\"Footnote_4_4\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_4_4\"\u003e\u003cspan class=\"label\"\u003e[4]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eIntroduction to Metaphysics\u003c/i\u003e, p. 1.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_5_5\" id=\"Footnote_5_5\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_5_5\"\u003e\u003cspan class=\"label\"\u003e[5]\u003c/span\u003e\u003c/a\u003e Whinfield\u0027s translation of the \u003ci\u003eMasnavi\u003c/i\u003e (Tr\u0026uuml;bner, 1887),\r\np. 34.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_6_6\" id=\"Footnote_6_6\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_6_6\"\u003e\u003cspan class=\"label\"\u003e[6]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eEthics\u003c/i\u003e, Bk. IV, Prop. LXII.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_7_7\" id=\"Footnote_7_7\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_7_7\"\u003e\u003cspan class=\"label\"\u003e[7]\u003c/span\u003e\u003c/a\u003e Ib., Pt. IV, Df. I.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_8_8\" id=\"Footnote_8_8\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_8_8\"\u003e\u003cspan class=\"label\"\u003e[8]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eEthics\u003c/i\u003e. Pt. II. Df. VI.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003ca name=\"II\" id=\"II\"\u003e\u003c/a\u003e\u003chr /\u003e\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_33\" id=\"Page_33\"\u003e[33]\u003c/a\u003e\u003c/span\u003e\u003cbr /\u003e\r\n\r\n\u003ch3\u003eII\u003cspan class=\"totoc\"\u003e\u003ca href=\"#toc\"\u003eToC\u003c/a\u003e\u003c/span\u003e\u003c/h3\u003e\r\n\r\n\u003ch4\u003eTHE PLACE OF SCIENCE IN A LIBERAL EDUCATION\u003c/h4\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003ch4\u003eI\u003c/h4\u003e\r\n\r\n\u003cp\u003eScience, to the ordinary reader of newspapers, is represented by a\r\nvarying selection of sensational triumphs, such as wireless telegraphy\r\nand aeroplanes, radio-activity and the marvels of modern alchemy. It is\r\nnot of this aspect of science that I wish to speak. Science, in this\r\naspect, consists of detached up-to-date fragments, interesting only\r\nuntil they are replaced by something newer and more up-to-date,\r\ndisplaying nothing of the systems of patiently constructed knowledge\r\nout of which, almost as a casual incident, have come the practically\r\nuseful results which interest the man in the street. The increased\r\ncommand over the forces of nature which is derived from science is\r\nundoubtedly an amply sufficient reason for encouraging scientific\r\nresearch, but this reason has been so often urged and is so easily\r\nappreciated that other reasons, to my mind quite as important, are apt\r\nto be overlooked. It is with these other reasons, especially with the\r\nintrinsic value of a scientific habit of mind in forming our outlook\r\non the world, that I shall be concerned in what follows.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe instance of wireless telegraphy will serve to illustrate the\r\ndifference between the two points of view. Almost all the serious\r\nintellectual labour required for the \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_34\" id=\"Page_34\"\u003e[34]\u003c/a\u003e\u003c/span\u003epossibility of this invention is\r\ndue to three men\u0026mdash;Faraday, Maxwell, and Hertz. In alternating layers\r\nof experiment and theory these three men built up the modern theory of\r\nelectromagnetism, and demonstrated the identity of light with\r\nelectromagnetic waves. The system which they discovered is one of\r\nprofound intellectual interest, bringing together and unifying an\r\nendless variety of apparently detached phenomena, and displaying a\r\ncumulative mental power which cannot but afford delight to every\r\ngenerous spirit. The mechanical details which remained to be adjusted\r\nin order to utilise their discoveries for a practical system of\r\ntelegraphy demanded, no doubt, very considerable ingenuity, but had\r\nnot that broad sweep and that universality which could give them\r\nintrinsic interest as an object of disinterested contemplation.\u003c/p\u003e\r\n\r\n\u003cp\u003eFrom the point of view of training the mind, of giving that\r\nwell-informed, impersonal outlook which constitutes culture in the\r\ngood sense of this much-misused word, it seems to be generally held\r\nindisputable that a literary education is superior to one based on\r\nscience. Even the warmest advocates of science are apt to rest their\r\nclaims on the contention that culture ought to be sacrificed to\r\nutility. Those men of science who respect culture, when they associate\r\nwith men learned in the classics, are apt to admit, not merely\r\npolitely, but sincerely, a certain inferiority on their side,\r\ncompensated doubtless by the services which science renders to\r\nhumanity, but none the less real. And so long as this attitude exists\r\namong men of science, it tends to verify itself: the intrinsically\r\nvaluable aspects of science tend to be sacrificed to the merely\r\nuseful, and little attempt is made to preserve that leisurely,\r\nsystematic survey by which the finer quality of mind is formed and\r\nnourished.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_35\" id=\"Page_35\"\u003e[35]\u003c/a\u003e\u003c/span\u003eBut even if there be, in present fact, any such inferiority as is\r\nsupposed in the educational value of science, this is, I believe, not\r\nthe fault of science itself, but the fault of the spirit in which\r\nscience is taught. If its full possibilities were realised by those\r\nwho teach it, I believe that its capacity of producing those habits of\r\nmind which constitute the highest mental excellence would be at least\r\nas great as that of literature, and more particularly of Greek and\r\nLatin literature. In saying this I have no wish whatever to disparage\r\na classical education. I have not myself enjoyed its benefits, and my\r\nknowledge of Greek and Latin authors is derived almost wholly from\r\ntranslations. But I am firmly persuaded that the Greeks fully deserve\r\nall the admiration that is bestowed upon them, and that it is a very\r\ngreat and serious loss to be unacquainted with their writings. It is\r\nnot by attacking them, but by drawing attention to neglected\r\nexcellences in science, that I wish to conduct my argument.\u003c/p\u003e\r\n\r\n\u003cp\u003eOne defect, however, does seem inherent in a purely classical\r\neducation\u0026mdash;namely, a too exclusive emphasis on the past. By the study\r\nof what is absolutely ended and can never be renewed, a habit of\r\ncriticism towards the present and the future is engendered. The\r\nqualities in which the present excels are qualities to which the study\r\nof the past does not direct attention, and to which, therefore, the\r\nstudent of Greek civilisation may easily become blind. In what is new\r\nand growing there is apt to be something crude, insolent, even a\r\nlittle vulgar, which is shocking to the man of sensitive taste;\r\nquivering from the rough contact, he retires to the trim gardens of a\r\npolished past, forgetting that they were reclaimed from the wilderness\r\nby men as rough and earth-soiled as those from whom he shrinks in his\r\nown day. The habit of being unable to recognise merit \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_36\" id=\"Page_36\"\u003e[36]\u003c/a\u003e\u003c/span\u003euntil it is\r\ndead is too apt to be the result of a purely bookish life, and a\r\nculture based wholly on the past will seldom be able to pierce through\r\neveryday surroundings to the essential splendour of contemporary\r\nthings, or to the hope of still greater splendour in the future.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"poem\"\u003e\u003cdiv class=\"stanza\"\u003e\r\n\u003cspan class=\"i0\"\u003e\"My eyes saw not the men of old;\u003cbr /\u003e\u003c/span\u003e\r\n\u003cspan class=\"i0\"\u003eAnd now their age away has rolled.\u003cbr /\u003e\u003c/span\u003e\r\n\u003cspan class=\"i0\"\u003eI weep\u0026mdash;to think I shall not see\u003cbr /\u003e\u003c/span\u003e\r\n\u003cspan class=\"i0\"\u003eThe heroes of posterity.\"\u003cbr /\u003e\u003c/span\u003e\r\n\u003c/div\u003e\u003c/div\u003e\r\n\r\n\u003cp class=\"noin\"\u003eSo says the Chinese poet; but such impartiality is rare in the more\r\npugnacious atmosphere of the West, where the champions of past and\r\nfuture fight a never-ending battle, instead of combining to seek out\r\nthe merits of both.\u003c/p\u003e\r\n\r\n\u003cp\u003eThis consideration, which militates not only against the exclusive\r\nstudy of the classics, but against every form of culture which has\r\nbecome static, traditional, and academic, leads inevitably to the\r\nfundamental question: What is the true end of education? But before\r\nattempting to answer this question it will be well to define the sense\r\nin which we are to use the word \"education.\" For this purpose I shall\r\ndistinguish the sense in which I mean to use it from two others, both\r\nperfectly legitimate, the one broader and the other narrower than the\r\nsense in which I mean to use the word.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn the broader sense, education will include not only what we learn\r\nthrough instruction, but all that we learn through personal\r\nexperience\u0026mdash;the formation of character through the education of life.\r\nOf this aspect of education, vitally important as it is, I will say\r\nnothing, since its consideration would introduce topics quite foreign\r\nto the question with which we are concerned.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn the narrower sense, education may be confined to instruction, the\r\nimparting of definite information on \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_37\" id=\"Page_37\"\u003e[37]\u003c/a\u003e\u003c/span\u003evarious subjects, because such\r\ninformation, in and for itself, is useful in daily life. Elementary\r\neducation\u0026mdash;reading, writing, and arithmetic\u0026mdash;is almost wholly of this\r\nkind. But instruction, necessary as it is, does not \u003ci\u003eper se\u003c/i\u003e\r\nconstitute education in the sense in which I wish to consider it.\u003c/p\u003e\r\n\r\n\u003cp\u003eEducation, in the sense in which I mean it, may be defined as \u003ci\u003ethe\r\nformation, by means of instruction, of certain mental habits and a\r\ncertain outlook on life and the world\u003c/i\u003e. It remains to ask ourselves,\r\nwhat mental habits, and what sort of outlook, can be hoped for as the\r\nresult of instruction? When we have answered this question we can\r\nattempt to decide what science has to contribute to the formation of\r\nthe habits and outlook which we desire.\u003c/p\u003e\r\n\r\n\u003cp\u003eOur whole life is built about a certain number\u0026mdash;not a very small\r\nnumber\u0026mdash;of primary instincts and impulses. Only what is in some way\r\nconnected with these instincts and impulses appears to us desirable or\r\nimportant; there is no faculty, whether \"reason\" or \"virtue\" or\r\nwhatever it may be called, that can take our active life and our hopes\r\nand fears outside the region controlled by these first movers of all\r\ndesire. Each of them is like a queen-bee, aided by a hive of workers\r\ngathering honey; but when the queen is gone the workers languish and\r\ndie, and the cells remain empty of their expected sweetness. So with\r\neach primary impulse in civilised man: it is surrounded and protected\r\nby a busy swarm of attendant derivative desires, which store up in its\r\nservice whatever honey the surrounding world affords. But if the\r\nqueen-impulse dies, the death-dealing influence, though retarded a\r\nlittle by habit, spreads slowly through all the subsidiary impulses,\r\nand a whole tract of life becomes inexplicably colourless. What was\r\nformerly full of zest, and so obviously worth doing that it raised \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_38\" id=\"Page_38\"\u003e[38]\u003c/a\u003e\u003c/span\u003eno\r\nquestions, has now grown dreary and purposeless: with a sense of\r\ndisillusion we inquire the meaning of life, and decide, perhaps, that\r\nall is vanity. The search for an outside meaning that can \u003ci\u003ecompel\u003c/i\u003e an\r\ninner response must always be disappointed: all \"meaning\" must be at\r\nbottom related to our primary desires, and when they are extinct no\r\nmiracle can restore to the world the value which they reflected upon\r\nit.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe purpose of education, therefore, cannot be to create any primary\r\nimpulse which is lacking in the uneducated; the purpose can only be to\r\nenlarge the scope of those that human nature provides, by increasing\r\nthe number and variety of attendant thoughts, and by showing where the\r\nmost permanent satisfaction is to be found. Under the impulse of a\r\nCalvinistic horror of the \"natural man,\" this obvious truth has been\r\ntoo often misconceived in the training of the young; \"nature\" has been\r\nfalsely regarded as excluding all that is best in what is natural, and\r\nthe endeavour to teach virtue has led to the production of stunted and\r\ncontorted hypocrites instead of full-grown human beings. From such\r\nmistakes in education a better psychology or a kinder heart is\r\nbeginning to preserve the present generation; we need, therefore,\r\nwaste no more words on the theory that the purpose of education is to\r\nthwart or eradicate nature.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut although nature must supply the initial force of desire, nature is\r\nnot, in the civilised man, the spasmodic, fragmentary, and yet violent\r\nset of impulses that it is in the savage. Each impulse has its\r\nconstitutional ministry of thought and knowledge and reflection,\r\nthrough which possible conflicts of impulses are foreseen, and\r\ntemporary impulses are controlled by the unifying impulse which may be\r\ncalled wisdom. In this way \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_39\" id=\"Page_39\"\u003e[39]\u003c/a\u003e\u003c/span\u003eeducation destroys the crudity of\r\ninstinct, and increases through knowledge the wealth and variety of\r\nthe individual\u0027s contacts with the outside world, making him no longer\r\nan isolated fighting unit, but a citizen of the universe, embracing\r\ndistant countries, remote regions of space, and vast stretches of past\r\nand future within the circle of his interests. It is this simultaneous\r\nsoftening in the insistence of desire and enlargement of its scope\r\nthat is the chief moral end of education.\u003c/p\u003e\r\n\r\n\u003cp\u003eClosely connected with this moral end is the more purely intellectual\r\naim of education, the endeavour to make us see and imagine the world\r\nin an objective manner, as far as possible as it is in itself, and not\r\nmerely through the distorting medium of personal desire. The complete\r\nattainment of such an objective view is no doubt an ideal,\r\nindefinitely approachable, but not actually and fully realisable.\r\nEducation, considered as a process of forming our mental habits and\r\nour outlook on the world, is to be judged successful in proportion as\r\nits outcome approximates to this ideal; in proportion, that is to say,\r\nas it gives us a true view of our place in society, of the relation of\r\nthe whole human society to its non-human environment, and of the\r\nnature of the non-human world as it is in itself apart from our\r\ndesires and interests. If this standard is admitted, we can return to\r\nthe consideration of science, inquiring how far science contributes to\r\nsuch an aim, and whether it is in any respect superior to its rivals\r\nin educational practice.\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\r\n\u003ch4\u003eII\u003c/h4\u003e\r\n\r\n\u003cp\u003eTwo opposite and at first sight conflicting merits belong to science\r\nas against literature and art. The one, which is not inherently\r\nnecessary, but is certainly true \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_40\" id=\"Page_40\"\u003e[40]\u003c/a\u003e\u003c/span\u003eat the present day, is hopefulness\r\nas to the future of human achievement, and in particular as to the\r\nuseful work that may be accomplished by any intelligent student. This\r\nmerit and the cheerful outlook which it engenders prevent what might\r\notherwise be the depressing effect of another aspect of science, to my\r\nmind also a merit, and perhaps its greatest merit\u0026mdash;I mean the\r\nirrelevance of human passions and of the whole subjective apparatus\r\nwhere scientific truth is concerned. Each of these reasons for\r\npreferring the study of science requires some amplification. Let us\r\nbegin with the first.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn the study of literature or art our attention is perpetually riveted\r\nupon the past: the men of Greece or of the Renaissance did better than\r\nany men do now; the triumphs of former ages, so far from facilitating\r\nfresh triumphs in our own age, actually increase the difficulty of\r\nfresh triumphs by rendering originality harder of attainment; not only\r\nis artistic achievement not cumulative, but it seems even to depend\r\nupon a certain freshness and \u003ci\u003ena\u0026iuml;vet\u0026eacute;\u003c/i\u003e of impulse and vision which\r\ncivilisation tends to destroy. Hence comes, to those who have been\r\nnourished on the literary and artistic productions of former ages, a\r\ncertain peevishness and undue fastidiousness towards the present, from\r\nwhich there seems no escape except into the deliberate vandalism which\r\nignores tradition and in the search after originality achieves only\r\nthe eccentric. But in such vandalism there is none of the simplicity\r\nand spontaneity out of which great art springs: theory is still the\r\ncanker in its core, and insincerity destroys the advantages of a\r\nmerely pretended ignorance.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe despair thus arising from an education which suggests no\r\npre-eminent mental activity except that of artistic creation is wholly\r\nabsent from an education \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_41\" id=\"Page_41\"\u003e[41]\u003c/a\u003e\u003c/span\u003ewhich gives the knowledge of scientific\r\nmethod. The discovery of scientific method, except in pure\r\nmathematics, is a thing of yesterday; speaking broadly, we may say\r\nthat it dates from Galileo. Yet already it has transformed the world,\r\nand its success proceeds with ever-accelerating velocity. In science\r\nmen have discovered an activity of the very highest value in which\r\nthey are no longer, as in art, dependent for progress upon the\r\nappearance of continually greater genius, for in science the\r\nsuccessors stand upon the shoulders of their predecessors; where one\r\nman of supreme genius has invented a method, a thousand lesser men can\r\napply it. No transcendent ability is required in order to make useful\r\ndiscoveries in science; the edifice of science needs its masons,\r\nbricklayers, and common labourers as well as its foremen,\r\nmaster-builders, and architects. In art nothing worth doing can be\r\ndone without genius; in science even a very moderate capacity can\r\ncontribute to a supreme achievement.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn science the man of real genius is the man who invents a new method.\r\nThe notable discoveries are often made by his successors, who can\r\napply the method with fresh vigour, unimpaired by the previous labour\r\nof perfecting it; but the mental calibre of the thought required for\r\ntheir work, however brilliant, is not so great as that required by the\r\nfirst inventor of the method. There are in science immense numbers of\r\ndifferent methods, appropriate to different classes of problems; but\r\nover and above them all, there is something not easily definable,\r\nwhich may be called \u003ci\u003ethe\u003c/i\u003e method of science. It was formerly customary\r\nto identify this with the inductive method, and to associate it with\r\nthe name of Bacon. But the true inductive method was not discovered by\r\nBacon, and the true method of science \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_42\" id=\"Page_42\"\u003e[42]\u003c/a\u003e\u003c/span\u003eis something which includes\r\ndeduction as much as induction, logic and mathematics as much as\r\nbotany and geology. I shall not attempt the difficult task of stating\r\nwhat the scientific method is, but I will try to indicate the temper\r\nof mind out of which the scientific method grows, which is the second\r\nof the two merits that were mentioned above as belonging to a\r\nscientific education.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe kernel of the scientific outlook is a thing so simple, so obvious,\r\nso seemingly trivial, that the mention of it may almost excite\r\nderision. The kernel of the scientific outlook is the refusal to\r\nregard our own desires, tastes, and interests as affording a key to\r\nthe understanding of the world. Stated thus baldly, this may seem no\r\nmore than a trite truism. But to remember it consistently in matters\r\narousing our passionate partisanship is by no means easy, especially\r\nwhere the available evidence is uncertain and inconclusive. A few\r\nillustrations will make this clear.\u003c/p\u003e\r\n\r\n\u003cp\u003eAristotle, I understand, considered that the stars must move in\r\ncircles because the circle is the most perfect curve. In the absence\r\nof evidence to the contrary, he allowed himself to decide a question\r\nof fact by an appeal to \u0026aelig;sthetico-moral considerations. In such a case\r\nit is at once obvious to us that this appeal was unjustifiable. We\r\nknow now how to ascertain as a fact the way in which the heavenly\r\nbodies move, and we know that they do not move in circles, or even in\r\naccurate ellipses, or in any other kind of simply describable curve.\r\nThis may be painful to a certain hankering after simplicity of pattern\r\nin the universe, but we know that in astronomy such feelings are\r\nirrelevant. Easy as this knowledge seems now, we owe it to the courage\r\nand insight of the first inventors of scientific method, and more\r\nespecially of Galileo.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_43\" id=\"Page_43\"\u003e[43]\u003c/a\u003e\u003c/span\u003eWe may take as another illustration Malthus\u0027s doctrine of population.\r\nThis illustration is all the better for the fact that his actual\r\ndoctrine is now known to be largely erroneous. It is not his\r\nconclusions that are valuable, but the temper and method of his\r\ninquiry. As everyone knows, it was to him that Darwin owed an\r\nessential part of his theory of natural selection, and this was only\r\npossible because Malthus\u0027s outlook was truly scientific. His great\r\nmerit lies in considering man not as the object of praise or blame,\r\nbut as a part of nature, a thing with a certain characteristic\r\nbehaviour from which certain consequences must follow. If the\r\nbehaviour is not quite what Malthus supposed, if the consequences are\r\nnot quite what he inferred, that may falsify his conclusions, but does\r\nnot impair the value of his method. The objections which were made\r\nwhen his doctrine was new\u0026mdash;that it was horrible and depressing, that\r\npeople ought not to act as he said they did, and so on\u0026mdash;were all such\r\nas implied an unscientific attitude of mind; as against all of them,\r\nhis calm determination to treat man as a natural phenomenon marks an\r\nimportant advance over the reformers of the eighteenth century and the\r\nRevolution.\u003c/p\u003e\r\n\r\n\u003cp\u003eUnder the influence of Darwinism the scientific attitude towards man\r\nhas now become fairly common, and is to some people quite natural,\r\nthough to most it is still a difficult and artificial intellectual\r\ncontortion. There is however, one study which is as yet almost wholly\r\nuntouched by the scientific spirit\u0026mdash;I mean the study of philosophy.\r\nPhilosophers and the public imagine that the scientific spirit must\r\npervade pages that bristle with allusions to ions, germ-plasms, and\r\nthe eyes of shell-fish. But as the devil can quote Scripture, so the\r\nphilosopher can quote science. The scientific spirit is not an affair\r\nof \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_44\" id=\"Page_44\"\u003e[44]\u003c/a\u003e\u003c/span\u003equotation, of externally acquired information, any more than\r\nmanners are an affair of the etiquette-book. The scientific attitude\r\nof mind involves a sweeping away of all other desires in the interests\r\nof the desire to know\u0026mdash;it involves suppression of hopes and fears,\r\nloves and hates, and the whole subjective emotional life, until we\r\nbecome subdued to the material, able to see it frankly, without\r\npreconceptions, without bias, without any wish except to see it as it\r\nis, and without any belief that what it is must be determined by some\r\nrelation, positive or negative, to what we should like it to be, or to\r\nwhat we can easily imagine it to be.\u003c/p\u003e\r\n\r\n\u003cp\u003eNow in philosophy this attitude of mind has not as yet been achieved.\r\nA certain self-absorption, not personal, but human, has marked almost\r\nall attempts to conceive the universe as a whole. Mind, or some aspect\r\nof it\u0026mdash;thought or will or sentience\u0026mdash;has been regarded as the pattern\r\nafter which the universe is to be conceived, for no better reason, at\r\nbottom, than that such a universe would not seem strange, and would\r\ngive us the cosy feeling that every place is like home. To conceive\r\nthe universe as essentially progressive or essentially deteriorating,\r\nfor example, is to give to our hopes and fears a cosmic importance\r\nwhich \u003ci\u003emay\u003c/i\u003e, of course, be justified, but which we have as yet no\r\nreason to suppose justified. Until we have learnt to think of it in\r\nethically neutral terms, we have not arrived at a scientific attitude\r\nin philosophy; and until we have arrived at such an attitude, it is\r\nhardly to be hoped that philosophy will achieve any solid results.\u003c/p\u003e\r\n\r\n\u003cp\u003eI have spoken so far largely of the negative aspect of the scientific\r\nspirit, but it is from the positive aspect that its value is derived.\r\nThe instinct of constructiveness, which is one of the chief incentives\r\nto artistic creation, can find \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_45\" id=\"Page_45\"\u003e[45]\u003c/a\u003e\u003c/span\u003ein scientific systems a satisfaction\r\nmore massive than any epic poem. Disinterested curiosity, which is the\r\nsource of almost all intellectual effort, finds with astonished\r\ndelight that science can unveil secrets which might well have seemed\r\nfor ever undiscoverable. The desire for a larger life and wider\r\ninterests, for an escape from private circumstances, and even from the\r\nwhole recurring human cycle of birth and death, is fulfilled by the\r\nimpersonal cosmic outlook of science as by nothing else. To all these\r\nmust be added, as contributing to the happiness of the man of science,\r\nthe admiration of splendid achievement, and the consciousness of\r\ninestimable utility to the human race. A life devoted to science is\r\ntherefore a happy life, and its happiness is derived from the very\r\nbest sources that are open to dwellers on this troubled and passionate\r\nplanet.\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003ca name=\"III\" id=\"III\"\u003e\u003c/a\u003e\u003chr /\u003e\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_46\" id=\"Page_46\"\u003e[46]\u003c/a\u003e\u003c/span\u003e\u003cbr /\u003e\r\n\r\n\u003ch3\u003eIII\u003cspan class=\"totoc\"\u003e\u003ca href=\"#toc\"\u003eToC\u003c/a\u003e\u003c/span\u003e\u003c/h3\u003e\r\n\r\n\u003ch4\u003eA FREE MAN\u0027S WORSHIP\u003ca name=\"FNanchor_9_9\" id=\"FNanchor_9_9\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_9_9\" class=\"fnanchor\"\u003e[9]\u003c/a\u003e\u003c/h4\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003cp\u003eTo Dr. Faustus in his study Mephistopheles told the history of the\r\nCreation, saying:\u003c/p\u003e\r\n\r\n\u003cp\u003e\"The endless praises of the choirs of angels had begun to grow\r\nwearisome; for, after all, did he not deserve their praise? Had he not\r\ngiven them endless joy? Would it not be more amusing to obtain\r\nundeserved praise, to be worshipped by beings whom he tortured? He\r\nsmiled inwardly, and resolved that the great drama should be\r\nperformed.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"For countless ages the hot nebula whirled aimlessly through space. At\r\nlength it began to take shape, the central mass threw off planets, the\r\nplanets cooled, boiling seas and burning mountains heaved and tossed,\r\nfrom black masses of cloud hot sheets of rain deluged the barely solid\r\ncrust. And now the first germ of life grew in the depths of the ocean,\r\nand developed rapidly in the fructifying warmth into vast forest\r\ntrees, huge ferns springing from the damp mould, sea monsters\r\nbreeding, fighting, devouring, and passing away. And from the\r\nmonsters, as the play unfolded itself, Man was born, with the power of\r\nthought, the knowledge of good and evil, and the cruel thirst for\r\nworship. And Man saw that all is passing in this mad, monstrous world,\r\nthat all is struggling to snatch, at any cost, a few brief moments of\r\nlife before Death\u0027s inexorable decree. And \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_47\" id=\"Page_47\"\u003e[47]\u003c/a\u003e\u003c/span\u003eMan said: \u0027There is a\r\nhidden purpose, could we but fathom it, and the purpose is good; for\r\nwe must reverence something, and in the visible world there is nothing\r\nworthy of reverence.\u0027 And Man stood aside from the struggle, resolving\r\nthat God intended harmony to come out of chaos by human efforts. And\r\nwhen he followed the instincts which God had transmitted to him from\r\nhis ancestry of beasts of prey, he called it Sin, and asked God to\r\nforgive him. But he doubted whether he could be justly forgiven, until\r\nhe invented a divine Plan by which God\u0027s wrath was to have been\r\nappeased. And seeing the present was bad, he made it yet worse, that\r\nthereby the future might be better. And he gave God thanks for the\r\nstrength that enabled him to forgo even the joys that were possible.\r\nAnd God smiled; and when he saw that Man had become perfect in\r\nrenunciation and worship, he sent another sun through the sky, which\r\ncrashed into Man\u0027s sun; and all returned again to nebula.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"\u0027Yes,\u0027 he murmured, \u0027it was a good play; I will have it performed\r\nagain.\u0027\"\u003c/p\u003e\r\n\r\n\u003cp\u003eSuch, in outline, but even more purposeless, more void of meaning, is\r\nthe world which Science presents for our belief. Amid such a world, if\r\nanywhere, our ideals henceforward must find a home. That Man is the\r\nproduct of causes which had no prevision of the end they were\r\nachieving; that his origin, his growth, his hopes and fears, his loves\r\nand his beliefs, are but the outcome of accidental collocations of\r\natoms; that no fire, no heroism, no intensity of thought and feeling,\r\ncan preserve an individual life beyond the grave; that all the labours\r\nof the ages, all the devotion, all the inspiration, all the noonday\r\nbrightness of human genius, are destined to extinction in the vast\r\ndeath of the solar \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_48\" id=\"Page_48\"\u003e[48]\u003c/a\u003e\u003c/span\u003esystem, and that the whole temple of Man\u0027s\r\nachievement must inevitably be buried beneath the d\u0026eacute;bris of a universe\r\nin ruins\u0026mdash;all these things, if not quite beyond dispute, are yet so\r\nnearly certain, that no philosophy which rejects them can hope to\r\nstand. Only within the scaffolding of these truths, only on the firm\r\nfoundation of unyielding despair, can the soul\u0027s habitation henceforth\r\nbe safely built.\u003c/p\u003e\r\n\r\n\u003cp\u003eHow, in such an alien and inhuman world, can so powerless a creature\r\nas Man preserve his aspirations untarnished? A strange mystery it is\r\nthat Nature, omnipotent but blind, in the revolutions of her secular\r\nhurryings through the abysses of space, has brought forth at last a\r\nchild, subject still to her power, but gifted with sight, with\r\nknowledge of good and evil, with the capacity of judging all the works\r\nof his unthinking Mother. In spite of Death, the mark and seal of the\r\nparental control, Man is yet free, during his brief years, to examine,\r\nto criticise, to know, and in imagination to create. To him alone, in\r\nthe world with which he is acquainted, this freedom belongs; and in\r\nthis lies his superiority to the resistless forces that control his\r\noutward life.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe savage, like ourselves, feels the oppression of his impotence\r\nbefore the powers of Nature; but having in himself nothing that he\r\nrespects more than Power, he is willing to prostrate himself before\r\nhis gods, without inquiring whether they are worthy of his worship.\r\nPathetic and very terrible is the long history of cruelty and torture,\r\nof degradation and human sacrifice, endured in the hope of placating\r\nthe jealous gods: surely, the trembling believer thinks, when what is\r\nmost precious has been freely given, their lust for blood must be\r\nappeased, and more will not be required. The religion of \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_49\" id=\"Page_49\"\u003e[49]\u003c/a\u003e\u003c/span\u003eMoloch\u0026mdash;as\r\nsuch creeds may be generically called\u0026mdash;is in essence the cringing\r\nsubmission of the slave, who dare not, even in his heart, allow the\r\nthought that his master deserves no adulation. Since the independence\r\nof ideals is not yet acknowledged, Power may be freely worshipped, and\r\nreceive an unlimited respect, despite its wanton infliction of pain.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut gradually, as morality grows bolder, the claim of the ideal world\r\nbegins to be felt; and worship, if it is not to cease, must be given\r\nto gods of another kind than those created by the savage. Some, though\r\nthey feel the demands of the ideal, will still consciously reject\r\nthem, still urging that naked Power is worthy of worship. Such is the\r\nattitude inculcated in God\u0027s answer to Job out of the whirlwind: the\r\ndivine power and knowledge are paraded, but of the divine goodness\r\nthere is no hint. Such also is the attitude of those who, in our own\r\nday, base their morality upon the struggle for survival, maintaining\r\nthat the survivors are necessarily the fittest. But others, not\r\ncontent with an answer so repugnant to the moral sense, will adopt the\r\nposition which we have become accustomed to regard as specially\r\nreligious, maintaining that, in some hidden manner, the world of fact\r\nis really harmonious with the world of ideals. Thus Man creates God,\r\nall-powerful and all-good, the mystic unity of what is and what should\r\nbe.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut the world of fact, after all, is not good; and, in submitting our\r\njudgment to it, there is an element of slavishness from which our\r\nthoughts must be purged. For in all things it is well to exalt the\r\ndignity of Man, by freeing him as far as possible from the tyranny of\r\nnon-human Power. When we have realised that Power is largely bad, that\r\nman, with his knowledge of good and evil, is but a helpless atom in a\r\nworld which has no such \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_50\" id=\"Page_50\"\u003e[50]\u003c/a\u003e\u003c/span\u003eknowledge, the choice is again presented to\r\nus: Shall we worship Force, or shall we worship Goodness? Shall our\r\nGod exist and be evil, or shall he be recognised as the creation of\r\nour own conscience?\u003c/p\u003e\r\n\r\n\u003cp\u003eThe answer to this question is very momentous, and affects profoundly\r\nour whole morality. The worship of Force, to which Carlyle and\r\nNietzsche and the creed of Militarism have accustomed us, is the\r\nresult of failure to maintain our own ideals against a hostile\r\nuniverse: it is itself a prostrate submission to evil, a sacrifice of\r\nour best to Moloch. If strength indeed is to be respected, let us\r\nrespect rather the strength of those who refuse that false\r\n\"recognition of facts\" which fails to recognise that facts are often\r\nbad. Let us admit that, in the world we know, there are many things\r\nthat would be better otherwise, and that the ideals to which we do and\r\nmust adhere are not realised in the realm of matter. Let us preserve\r\nour respect for truth, for beauty, for the ideal of perfection which\r\nlife does not permit us to attain, though none of these things meet\r\nwith the approval of the unconscious universe. If Power is bad, as it\r\nseems to be, let us reject it from our hearts. In this lies Man\u0027s true\r\nfreedom: in determination to worship only the God created by our own\r\nlove of the good, to respect only the heaven which inspires the\r\ninsight of our best moments. In action, in desire, we must submit\r\nperpetually to the tyranny of outside forces; but in thought, in\r\naspiration, we are free, free from our fellow-men, free from the petty\r\nplanet on which our bodies impotently crawl, free even, while we live,\r\nfrom the tyranny of death. Let us learn, then, that energy of faith\r\nwhich enables us to live constantly in the vision of the good; and let\r\nus descend, in action, into the world of fact, with that vision always\r\nbefore us.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_51\" id=\"Page_51\"\u003e[51]\u003c/a\u003e\u003c/span\u003eWhen first the opposition of fact and ideal grows fully visible, a\r\nspirit of fiery revolt, of fierce hatred of the gods, seems necessary\r\nto the assertion of freedom. To defy with Promethean constancy a\r\nhostile universe, to keep its evil always in view, always actively\r\nhated, to refuse no pain that the malice of Power can invent, appears\r\nto be the duty of all who will not bow before the inevitable. But\r\nindignation is still a bondage, for it compels our thoughts to be\r\noccupied with an evil world; and in the fierceness of desire from\r\nwhich rebellion springs there is a kind of self-assertion which it is\r\nnecessary for the wise to overcome. Indignation is a submission of our\r\nthoughts, but not of our desires; the Stoic freedom in which wisdom\r\nconsists is found in the submission of our desires, but not of our\r\nthoughts. From the submission of our desires springs the virtue of\r\nresignation; from the freedom of our thoughts springs the whole world\r\nof art and philosophy, and the vision of beauty by which, at last, we\r\nhalf reconquer the reluctant world. But the vision of beauty is\r\npossible only to unfettered contemplation, to thoughts not weighted by\r\nthe load of eager wishes; and thus Freedom comes only to those who no\r\nlonger ask of life that it shall yield them any of those personal\r\ngoods that are subject to the mutations of Time.\u003c/p\u003e\r\n\r\n\u003cp\u003eAlthough the necessity of renunciation is evidence of the existence of\r\nevil, yet Christianity, in preaching it, has shown a wisdom exceeding\r\nthat of the Promethean philosophy of rebellion. It must be admitted\r\nthat, of the things we desire, some, though they prove impossible, are\r\nyet real goods; others, however, as ardently longed for, do not form\r\npart of a fully purified ideal. The belief that what must be renounced\r\nis bad, though sometimes false, is far less often false than untamed\r\npassion supposes; and the creed of religion, by providing a reason\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_52\" id=\"Page_52\"\u003e[52]\u003c/a\u003e\u003c/span\u003efor proving that it is never false, has been the means of purifying\r\nour hopes by the discovery of many austere truths.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut there is in resignation a further good element: even real goods,\r\nwhen they are unattainable, ought not to be fretfully desired. To\r\nevery man comes, sooner or later, the great renunciation. For the\r\nyoung, there is nothing unattainable; a good thing desired with the\r\nwhole force of a passionate will, and yet impossible, is to them not\r\ncredible. Yet, by death, by illness, by poverty, or by the voice of\r\nduty, we must learn, each one of us, that the world was not made for\r\nus, and that, however beautiful may be the things we crave, Fate may\r\nnevertheless forbid them. It is the part of courage, when misfortune\r\ncomes, to bear without repining the ruin of our hopes, to turn away\r\nour thoughts from vain regrets. This degree of submission to Power is\r\nnot only just and right: it is the very gate of wisdom.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut passive renunciation is not the whole of wisdom; for not by\r\nrenunciation alone can we build a temple for the worship of our own\r\nideals. Haunting foreshadowings of the temple appear in the realm of\r\nimagination, in music, in architecture, in the untroubled kingdom of\r\nreason, and in the golden sunset magic of lyrics, where beauty shines\r\nand glows, remote from the touch of sorrow, remote from the fear of\r\nchange, remote from the failures and disenchantments of the world of\r\nfact. In the contemplation of these things the vision of heaven will\r\nshape itself in our hearts, giving at once a touchstone to judge the\r\nworld about us, and an inspiration by which to fashion to our needs\r\nwhatever is not incapable of serving as a stone in the sacred temple.\u003c/p\u003e\r\n\r\n\u003cp\u003eExcept for those rare spirits that are born without sin, there is a\r\ncavern of darkness to be traversed before that \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_53\" id=\"Page_53\"\u003e[53]\u003c/a\u003e\u003c/span\u003etemple can be entered.\r\nThe gate of the cavern is despair, and its floor is paved with the\r\ngravestones of abandoned hopes. There Self must die; there the\r\neagerness, the greed of untamed desire must be slain, for only so can\r\nthe soul be freed from the empire of Fate. But out of the cavern the\r\nGate of Renunciation leads again to the daylight of wisdom, by whose\r\nradiance a new insight, a new joy, a new tenderness, shine forth to\r\ngladden the pilgrim\u0027s heart.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhen, without the bitterness of impotent rebellion, we have learnt\r\nboth to resign ourselves to the outward rule of Fate and to recognise\r\nthat the non-human world is unworthy of our worship, it becomes\r\npossible at last so to transform and refashion the unconscious\r\nuniverse, so to transmute it in the crucible of imagination, that a\r\nnew image of shining gold replaces the old idol of clay. In all the\r\nmultiform facts of the world\u0026mdash;in the visual shapes of trees and\r\nmountains and clouds, in the events of the life of man, even in the\r\nvery omnipotence of Death\u0026mdash;the insight of creative idealism can find\r\nthe reflection of a beauty which its own thoughts first made. In this\r\nway mind asserts its subtle mastery over the thoughtless forces of\r\nNature. The more evil the material with which it deals, the more\r\nthwarting to untrained desire, the greater is its achievement in\r\ninducing the reluctant rock to yield up its hidden treasures, the\r\nprouder its victory in compelling the opposing forces to swell the\r\npageant of its triumph. Of all the arts, Tragedy is the proudest, the\r\nmost triumphant; for it builds its shining citadel in the very centre\r\nof the enemy\u0027s country, on the very summit of his highest mountain;\r\nfrom its impregnable watchtowers, his camps and arsenals, his columns\r\nand forts, are all revealed; within its walls the free life continues,\r\nwhile the legions of Death and Pain and Despair, and all \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_54\" id=\"Page_54\"\u003e[54]\u003c/a\u003e\u003c/span\u003ethe servile\r\ncaptains of tyrant Fate, afford the burghers of that dauntless city\r\nnew spectacles of beauty. Happy those sacred ramparts, thrice happy\r\nthe dwellers on that all-seeing eminence. Honour to those brave\r\nwarriors who, through countless ages of warfare, have preserved for us\r\nthe priceless heritage of liberty, and have kept undefiled by\r\nsacrilegious invaders the home of the unsubdued.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut the beauty of Tragedy does but make visible a quality which, in\r\nmore or less obvious shapes, is present always and everywhere in life.\r\nIn the spectacle of Death, in the endurance of intolerable pain, and\r\nin the irrevocableness of a vanished past, there is a sacredness, an\r\noverpowering awe, a feeling of the vastness, the depth, the\r\ninexhaustible mystery of existence, in which, as by some strange\r\nmarriage of pain, the sufferer is bound to the world by bonds of\r\nsorrow. In these moments of insight, we lose all eagerness of\r\ntemporary desire, all struggling and striving for petty ends, all care\r\nfor the little trivial things that, to a superficial view, make up the\r\ncommon life of day by day; we see, surrounding the narrow raft\r\nillumined by the flickering light of human comradeship, the dark ocean\r\non whose rolling waves we toss for a brief hour; from the great night\r\nwithout, a chill blast breaks in upon our refuge; all the loneliness\r\nof humanity amid hostile forces is concentrated upon the individual\r\nsoul, which must struggle alone, with what of courage it can command,\r\nagainst the whole weight of a universe that cares nothing for its\r\nhopes and fears. Victory, in this struggle with the powers of\r\ndarkness, is the true baptism into the glorious company of heroes, the\r\ntrue initiation into the overmastering beauty of human existence. From\r\nthat awful encounter of the soul with the outer world, renunciation,\r\nwisdom, and charity are born; and with \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_55\" id=\"Page_55\"\u003e[55]\u003c/a\u003e\u003c/span\u003etheir birth a new life begins.\r\nTo take into the inmost shrine of the soul the irresistible forces\r\nwhose puppets we seem to be\u0026mdash;Death and change, the irrevocableness of\r\nthe past, and the powerlessness of man before the blind hurry of the\r\nuniverse from vanity to vanity\u0026mdash;to feel these things and know them is\r\nto conquer them.\u003c/p\u003e\r\n\r\n\u003cp\u003eThis is the reason why the Past has such magical power. The beauty of\r\nits motionless and silent pictures is like the enchanted purity of\r\nlate autumn, when the leaves, though one breath would make them fall,\r\nstill glow against the sky in golden glory. The Past does not change\r\nor strive; like Duncan, after life\u0027s fitful fever it sleeps well; what\r\nwas eager and grasping, what was petty and transitory, has faded away,\r\nthe things that were beautiful and eternal shine out of it like stars\r\nin the night. Its beauty, to a soul not worthy of it, is unendurable;\r\nbut to a soul which has conquered Fate it is the key of religion.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe life of Man, viewed outwardly, is but a small thing in comparison\r\nwith the forces of Nature. The slave is doomed to worship Time and\r\nFate and Death, because they are greater than anything he finds in\r\nhimself, and because all his thoughts are of things which they devour.\r\nBut, great as they are, to think of them greatly, to feel their\r\npassionless splendour, is greater still. And such thought makes us\r\nfree men; we no longer bow before the inevitable in Oriental\r\nsubjection, but we absorb it, and make it a part of ourselves. To\r\nabandon the struggle for private happiness, to expel all eagerness of\r\ntemporary desire, to burn with passion for eternal things\u0026mdash;this is\r\nemancipation, and this is the free man\u0027s worship. And this liberation\r\nis effected by a contemplation of Fate; for Fate itself is subdued by\r\nthe \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_56\" id=\"Page_56\"\u003e[56]\u003c/a\u003e\u003c/span\u003emind which leaves nothing to be purged by the purifying fire of\r\nTime.\u003c/p\u003e\r\n\r\n\u003cp\u003eUnited with his fellow-men by the strongest of all ties, the tie of a\r\ncommon doom, the free man finds that a new vision is with him always,\r\nshedding over every daily task the light of love. The life of Man is a\r\nlong march through the night, surrounded by invisible foes, tortured\r\nby weariness and pain, towards a goal that few can hope to reach, and\r\nwhere none may tarry long. One by one, as they march, our comrades\r\nvanish from our sight, seized by the silent orders of omnipotent\r\nDeath. Very brief is the time in which we can help them, in which\r\ntheir happiness or misery is decided. Be it ours to shed sunshine on\r\ntheir path, to lighten their sorrows by the balm of sympathy, to give\r\nthem the pure joy of a never-tiring affection, to strengthen failing\r\ncourage, to instil faith in hours of despair. Let us not weigh in\r\ngrudging scales their merits and demerits, but let us think only of\r\ntheir need\u0026mdash;of the sorrows, the difficulties, perhaps the blindnesses,\r\nthat make the misery of their lives; let us remember that they are\r\nfellow-sufferers in the same darkness, actors in the same tragedy with\r\nourselves. And so, when their day is over, when their good and their\r\nevil have become eternal by the immortality of the past, be it ours to\r\nfeel that, where they suffered, where they failed, no deed of ours was\r\nthe cause; but wherever a spark of the divine fire kindled in their\r\nhearts, we were ready with encouragement, with sympathy, with brave\r\nwords in which high courage glowed.\u003c/p\u003e\r\n\r\n\u003cp\u003eBrief and powerless is Man\u0027s life; on him and all his race the slow,\r\nsure doom falls pitiless and dark. Blind to good and evil, reckless of\r\ndestruction, omnipotent matter rolls on its relentless way; for Man,\r\ncondemned to-day to lose his dearest, to-morrow himself to pass\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_57\" id=\"Page_57\"\u003e[57]\u003c/a\u003e\u003c/span\u003ethrough the gate of darkness, it remains only to cherish, ere yet the\r\nblow falls, the lofty thoughts that ennoble his little day; disdaining\r\nthe coward terrors of the slave of Fate, to worship at the shrine that\r\nhis own hands have built; undismayed by the empire of chance, to\r\npreserve a mind free from the wanton tyranny that rules his outward\r\nlife; proudly defiant of the irresistible forces that tolerate, for a\r\nmoment, his knowledge and his condemnation, to sustain alone, a weary\r\nbut unyielding Atlas, the world that his own ideals have fashioned\r\ndespite the trampling march of unconscious power.\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\u003chr style=\"width: 15%;\" /\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003ch4\u003eFOOTNOTES:\u003c/h4\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_9_9\" id=\"Footnote_9_9\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_9_9\"\u003e\u003cspan class=\"label\"\u003e[9]\u003c/span\u003e\u003c/a\u003e Reprinted from the \u003ci\u003eIndependent Review\u003c/i\u003e, December,\r\n1903.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003ca name=\"IV\" id=\"IV\"\u003e\u003c/a\u003e\u003chr /\u003e\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_58\" id=\"Page_58\"\u003e[58]\u003c/a\u003e\u003c/span\u003e\u003cbr /\u003e\r\n\r\n\u003ch3\u003eIV\u003cspan class=\"totoc\"\u003e\u003ca href=\"#toc\"\u003eToC\u003c/a\u003e\u003c/span\u003e\u003c/h3\u003e\r\n\r\n\u003ch4\u003eTHE STUDY OF MATHEMATICS\u003c/h4\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003cp\u003eIn regard to every form of human activity it is necessary that the\r\nquestion should be asked from time to time, What is its purpose and\r\nideal? In what way does it contribute to the beauty of human\r\nexistence? As respects those pursuits which contribute only remotely,\r\nby providing the mechanism of life, it is well to be reminded that not\r\nthe mere fact of living is to be desired, but the art of living in the\r\ncontemplation of great things. Still more in regard to those\r\navocations which have no end outside themselves, which are to be\r\njustified, if at all, as actually adding to the sum of the world\u0027s\r\npermanent possessions, it is necessary to keep alive a knowledge of\r\ntheir aims, a clear prefiguring vision of the temple in which creative\r\nimagination is to be embodied.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe fulfilment of this need, in what concerns the studies forming the\r\nmaterial upon which custom has decided to train the youthful mind, is\r\nindeed sadly remote\u0026mdash;so remote as to make the mere statement of such a\r\nclaim appear preposterous. Great men, fully alive to the beauty of the\r\ncontemplations to whose service their lives are devoted, desiring that\r\nothers may share in their joys, persuade mankind to impart to the\r\nsuccessive generations the mechanical knowledge without which it is\r\nimpossible to cross the threshold. Dry pedants possess themselves of\r\nthe privilege of instilling this knowledge: they forget that it is to\r\nserve but as a \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_59\" id=\"Page_59\"\u003e[59]\u003c/a\u003e\u003c/span\u003ekey to open the doors of the temple; though they spend\r\ntheir lives on the steps leading up to those sacred doors, they turn\r\ntheir backs upon the temple so resolutely that its very existence is\r\nforgotten, and the eager youth, who would press forward to be\r\ninitiated to its domes and arches, is bidden to turn back and count\r\nthe steps.\u003c/p\u003e\r\n\r\n\u003cp\u003eMathematics, perhaps more even than the study of Greece and Rome, has\r\nsuffered from this oblivion of its due place in civilisation. Although\r\ntradition has decreed that the great bulk of educated men shall know\r\nat least the elements of the subject, the reasons for which the\r\ntradition arose are forgotten, buried beneath a great rubbish-heap of\r\npedantries and trivialities. To those who inquire as to the purpose of\r\nmathematics, the usual answer will be that it facilitates the making\r\nof machines, the travelling from place to place, and the victory over\r\nforeign nations, whether in war or commerce. If it be objected that\r\nthese ends\u0026mdash;all of which are of doubtful value\u0026mdash;are not furthered by\r\nthe merely elementary study imposed upon those who do not become\r\nexpert mathematicians, the reply, it is true, will probably be that\r\nmathematics trains the reasoning faculties. Yet the very men who make\r\nthis reply are, for the most part, unwilling to abandon the teaching\r\nof definite fallacies, known to be such, and instinctively rejected by\r\nthe unsophisticated mind of every intelligent learner. And the\r\nreasoning faculty itself is generally conceived, by those who urge its\r\ncultivation, as merely a means for the avoidance of pitfalls and a\r\nhelp in the discovery of rules for the guidance of practical life. All\r\nthese are undeniably important achievements to the credit of\r\nmathematics; yet it is none of these that entitles mathematics to a\r\nplace in every liberal education. Plato, we know, regarded the\r\ncontemplation of mathematical truths as worthy of the \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_60\" id=\"Page_60\"\u003e[60]\u003c/a\u003e\u003c/span\u003eDeity; and\r\nPlato realised, more perhaps than any other single man, what those\r\nelements are in human life which merit a place in heaven. There is in\r\nmathematics, he says, \"something which is \u003ci\u003enecessary\u003c/i\u003e and cannot be\r\nset aside … and, if I mistake not, of divine necessity; for as to\r\nthe human necessities of which the Many talk in this connection,\r\nnothing can be more ridiculous than such an application of the words.\r\n\u003ci\u003eCleinias.\u003c/i\u003e And what are these necessities of knowledge, Stranger,\r\nwhich are divine and not human? \u003ci\u003eAthenian.\u003c/i\u003e Those things without some\r\nuse or knowledge of which a man cannot become a God to the world, nor\r\na spirit, nor yet a hero, nor able earnestly to think and care for\r\nman\" (\u003ci\u003eLaws\u003c/i\u003e, p. 818).\u003ca name=\"FNanchor_10_10\" id=\"FNanchor_10_10\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_10_10\" class=\"fnanchor\"\u003e[10]\u003c/a\u003e Such was Plato\u0027s judgment of mathematics;\r\nbut the mathematicians do not read Plato, while those who read him\r\nknow no mathematics, and regard his opinion upon this question as\r\nmerely a curious aberration.\u003c/p\u003e\r\n\r\n\u003cp\u003eMathematics, rightly viewed, possesses not only truth, but supreme\r\nbeauty\u0026mdash;a beauty cold and austere, like that of sculpture, without\r\nappeal to any part of our weaker nature, without the gorgeous\r\ntrappings of painting or music, yet sublimely pure, and capable of a\r\nstern perfection such as only the greatest art can show. The true\r\nspirit of delight, the exaltation, the sense of being more than man,\r\nwhich is the touchstone of the highest excellence, is to be found in\r\nmathematics as surely as in poetry. What is best in mathematics\r\ndeserves not merely to be learnt as a task, but to be assimilated as a\r\npart of daily thought, and brought again and again before the mind\r\nwith ever-renewed encouragement. Real life is, to most men, a long\r\nsecond-best, a perpetual compromise between the ideal and the\r\npossible; but the world of pure reason knows no compromise, no\r\npractical \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_61\" id=\"Page_61\"\u003e[61]\u003c/a\u003e\u003c/span\u003elimitations, no barrier to the creative activity embodying\r\nin splendid edifices the passionate aspiration after the perfect from\r\nwhich all great work springs. Remote from human passions, remote even\r\nfrom the pitiful facts of nature, the generations have gradually\r\ncreated an ordered cosmos, where pure thought can dwell as in its\r\nnatural home, and where one, at least, of our nobler impulses can\r\nescape from the dreary exile of the actual world.\u003c/p\u003e\r\n\r\n\u003cp\u003eSo little, however, have mathematicians aimed at beauty, that hardly\r\nanything in their work has had this conscious purpose. Much, owing to\r\nirrepressible instincts, which were better than avowed beliefs, has\r\nbeen moulded by an unconscious taste; but much also has been spoilt by\r\nfalse notions of what was fitting. The characteristic excellence of\r\nmathematics is only to be found where the reasoning is rigidly\r\nlogical: the rules of logic are to mathematics what those of structure\r\nare to architecture. In the most beautiful work, a chain of argument\r\nis presented in which every link is important on its own account, in\r\nwhich there is an air of ease and lucidity throughout, and the\r\npremises achieve more than would have been thought possible, by means\r\nwhich appear natural and inevitable. Literature embodies what is\r\ngeneral in particular circumstances whose universal significance\r\nshines through their individual dress; but mathematics endeavours to\r\npresent whatever is most general in its purity, without any irrelevant\r\ntrappings.\u003c/p\u003e\r\n\r\n\u003cp\u003eHow should the teaching of mathematics be conducted so as to\r\ncommunicate to the learner as much as possible of this high ideal?\r\nHere experience must, in a great measure, be our guide; but some\r\nmaxims may result from our consideration of the ultimate purpose to be\r\nachieved.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_62\" id=\"Page_62\"\u003e[62]\u003c/a\u003e\u003c/span\u003eOne of the chief ends served by mathematics, when rightly taught, is\r\nto awaken the learner\u0027s belief in reason, his confidence in the truth\r\nof what has been demonstrated, and in the value of demonstration. This\r\npurpose is not served by existing instruction; but it is easy to see\r\nways in which it might be served. At present, in what concerns\r\narithmetic, the boy or girl is given a set of rules, which present\r\nthemselves as neither true nor false, but as merely the will of the\r\nteacher, the way in which, for some unfathomable reason, the teacher\r\nprefers to have the game played. To some degree, in a study of such\r\ndefinite practical utility, this is no doubt unavoidable; but as soon\r\nas possible, the reasons of rules should be set forth by whatever\r\nmeans most readily appeal to the childish mind. In geometry, instead\r\nof the tedious apparatus of fallacious proofs for obvious truisms\r\nwhich constitutes the beginning of Euclid, the learner should be\r\nallowed at first to assume the truth of everything obvious, and should\r\nbe instructed in the demonstrations of theorems which are at once\r\nstartling and easily verifiable by actual drawing, such as those in\r\nwhich it is shown that three or more lines meet in a point. In this\r\nway belief is generated; it is seen that reasoning may lead to\r\nstartling conclusions, which nevertheless the facts will verify; and\r\nthus the instinctive distrust of whatever is abstract or rational is\r\ngradually overcome. Where theorems are difficult, they should be first\r\ntaught as exercises in geometrical drawing, until the figure has\r\nbecome thoroughly familiar; it will then be an agreeable advance to be\r\ntaught the logical connections of the various lines or circles that\r\noccur. It is desirable also that the figure illustrating a theorem\r\nshould be drawn in all possible cases and shapes, that so the abstract\r\nrelations with which geometry is concerned may of themselves \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_63\" id=\"Page_63\"\u003e[63]\u003c/a\u003e\u003c/span\u003eemerge\r\nas the residue of similarity amid such great apparent diversity. In\r\nthis way the abstract demonstrations should form but a small part of\r\nthe instruction, and should be given when, by familiarity with\r\nconcrete illustrations, they have come to be felt as the natural\r\nembodiment of visible fact. In this early stage proofs should not be\r\ngiven with pedantic fullness; definitely fallacious methods, such as\r\nthat of superposition, should be rigidly excluded from the first, but\r\nwhere, without such methods, the proof would be very difficult, the\r\nresult should be rendered acceptable by arguments and illustrations\r\nwhich are explicitly contrasted with demonstrations.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn the beginning of algebra, even the most intelligent child finds, as\r\na rule, very great difficulty. The use of letters is a mystery, which\r\nseems to have no purpose except mystification. It is almost\r\nimpossible, at first, not to think that every letter stands for some\r\nparticular number, if only the teacher would reveal \u003ci\u003ewhat\u003c/i\u003e number it\r\nstands for. The fact is, that in algebra the mind is first taught to\r\nconsider general truths, truths which are not asserted to hold only of\r\nthis or that particular thing, but of any one of a whole group of\r\nthings. It is in the power of understanding and discovering such\r\ntruths that the mastery of the intellect over the whole world of\r\nthings actual and possible resides; and ability to deal with the\r\ngeneral as such is one of the gifts that a mathematical education\r\nshould bestow. But how little, as a rule, is the teacher of algebra\r\nable to explain the chasm which divides it from arithmetic, and how\r\nlittle is the learner assisted in his groping efforts at\r\ncomprehension! Usually the method that has been adopted in arithmetic\r\nis continued: rules are set forth, with no adequate explanation of\r\ntheir grounds; the pupil learns to use the rules blindly, \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_64\" id=\"Page_64\"\u003e[64]\u003c/a\u003e\u003c/span\u003eand\r\npresently, when he is able to obtain the answer that the teacher\r\ndesires, he feels that he has mastered the difficulties of the\r\nsubject. But of inner comprehension of the processes employed he has\r\nprobably acquired almost nothing.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhen algebra has been learnt, all goes smoothly until we reach those\r\nstudies in which the notion of infinity is employed\u0026mdash;the infinitesimal\r\ncalculus and the whole of higher mathematics. The solution of the\r\ndifficulties which formerly surrounded the mathematical infinite is\r\nprobably the greatest achievement of which our own age has to boast.\r\nSince the beginnings of Greek thought these difficulties have been\r\nknown; in every age the finest intellects have vainly endeavoured to\r\nanswer the apparently unanswerable questions that had been asked by\r\nZeno the Eleatic. At last Georg Cantor has found the answer, and has\r\nconquered for the intellect a new and vast province which had been\r\ngiven over to Chaos and old Night. It was assumed as self-evident,\r\nuntil Cantor and Dedekind established the opposite, that if, from any\r\ncollection of things, some were taken away, the number of things left\r\nmust always be less than the original number of things. This\r\nassumption, as a matter of fact, holds only of finite collections; and\r\nthe rejection of it, where the infinite is concerned, has been shown\r\nto remove all the difficulties that had hitherto baffled human reason\r\nin this matter, and to render possible the creation of an exact\r\nscience of the infinite. This stupendous fact ought to produce a\r\nrevolution in the higher teaching of mathematics; it has itself added\r\nimmeasurably to the educational value of the subject, and it has at\r\nlast given the means of treating with logical precision many studies\r\nwhich, until lately, were wrapped in fallacy and obscurity. By those\r\nwho were educated on the \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_65\" id=\"Page_65\"\u003e[65]\u003c/a\u003e\u003c/span\u003eold lines, the new work is considered to be\r\nappallingly difficult, abstruse, and obscure; and it must be confessed\r\nthat the discoverer, as is so often the case, has hardly himself\r\nemerged from the mists which the light of his intellect is dispelling.\r\nBut inherently, the new doctrine of the infinite, to all candid and\r\ninquiring minds, has facilitated the mastery of higher mathematics;\r\nfor hitherto, it has been necessary to learn, by a long process of\r\nsophistication, to give assent to arguments which, on first\r\nacquaintance, were rightly judged to be confused and erroneous. So far\r\nfrom producing a fearless belief in reason, a bold rejection of\r\nwhatever failed to fulfil the strictest requirements of logic, a\r\nmathematical training, during the past two centuries, encouraged the\r\nbelief that many things, which a rigid inquiry would reject as\r\nfallacious, must yet be accepted because they work in what the\r\nmathematician calls \"practice.\" By this means, a timid, compromising\r\nspirit, or else a sacerdotal belief in mysteries not intelligible to\r\nthe profane, has been bred where reason alone should have ruled. All\r\nthis it is now time to sweep away; let those who wish to penetrate\r\ninto the arcana of mathematics be taught at once the true theory in\r\nall its logical purity, and in the concatenation established by the\r\nvery essence of the entities concerned.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf we are considering mathematics as an end in itself, and not as a\r\ntechnical training for engineers, it is very desirable to preserve the\r\npurity and strictness of its reasoning. Accordingly those who have\r\nattained a sufficient familiarity with its easier portions should be\r\nled backward from propositions to which they have assented as\r\nself-evident to more and more fundamental principles from which what\r\nhad previously appeared as premises can be deduced. They should be\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_66\" id=\"Page_66\"\u003e[66]\u003c/a\u003e\u003c/span\u003etaught\u0026mdash;what the theory of infinity very aptly illustrates\u0026mdash;that many\r\npropositions seem self-evident to the untrained mind which,\r\nnevertheless, a nearer scrutiny shows to be false. By this means they\r\nwill be led to a sceptical inquiry into first principles, an\r\nexamination of the foundations upon which the whole edifice of\r\nreasoning is built, or, to take perhaps a more fitting metaphor, the\r\ngreat trunk from which the spreading branches spring. At this stage,\r\nit is well to study afresh the elementary portions of mathematics,\r\nasking no longer merely whether a given proposition is true, but also\r\nhow it grows out of the central principles of logic. Questions of this\r\nnature can now be answered with a precision and certainty which were\r\nformerly quite impossible; and in the chains of reasoning that the\r\nanswer requires the unity of all mathematical studies at last unfolds\r\nitself.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn the great majority of mathematical text-books there is a total lack\r\nof unity in method and of systematic development of a central theme.\r\nPropositions of very diverse kinds are proved by whatever means are\r\nthought most easily intelligible, and much space is devoted to mere\r\ncuriosities which in no way contribute to the main argument. But in\r\nthe greatest works, unity and inevitability are felt as in the\r\nunfolding of a drama; in the premisses a subject is proposed for\r\nconsideration, and in every subsequent step some definite advance is\r\nmade towards mastery of its nature. The love of system, of\r\ninterconnection, which is perhaps the inmost essence of the\r\nintellectual impulse, can find free play in mathematics as nowhere\r\nelse. The learner who feels this impulse must not be repelled by an\r\narray of meaningless examples or distracted by amusing oddities, but\r\nmust be encouraged to dwell upon central principles, to become\r\nfamiliar with the structure of the various subjects which are put\r\nbefore \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_67\" id=\"Page_67\"\u003e[67]\u003c/a\u003e\u003c/span\u003ehim, to travel easily over the steps of the more important\r\ndeductions. In this way a good tone of mind is cultivated, and\r\nselective attention is taught to dwell by preference upon what is\r\nweighty and essential.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhen the separate studies into which mathematics is divided have each\r\nbeen viewed as a logical whole, as a natural growth from the\r\npropositions which constitute their principles, the learner will be\r\nable to understand the fundamental science which unifies and\r\nsystematises the whole of deductive reasoning. This is symbolic\r\nlogic\u0026mdash;a study which, though it owes its inception to Aristotle, is\r\nyet, in its wider developments, a product, almost wholly, of the\r\nnineteenth century, and is indeed, in the present day, still growing\r\nwith great rapidity. The true method of discovery in symbolic logic,\r\nand probably also the best method for introducing the study to a\r\nlearner acquainted with other parts of mathematics, is the analysis of\r\nactual examples of deductive reasoning, with a view to the discovery\r\nof the principles employed. These principles, for the most part, are\r\nso embedded in our ratiocinative instincts, that they are employed\r\nquite unconsciously, and can be dragged to light only by much patient\r\neffort. But when at last they have been found, they are seen to be few\r\nin number, and to be the sole source of everything in pure\r\nmathematics. The discovery that all mathematics follows inevitably\r\nfrom a small collection of fundamental laws is one which immeasurably\r\nenhances the intellectual beauty of the whole; to those who have been\r\noppressed by the fragmentary and incomplete nature of most existing\r\nchains of deduction this discovery comes with all the overwhelming\r\nforce of a revelation; like a palace emerging from the autumn mist as\r\nthe traveller ascends an Italian hill-side, the stately storeys of the\r\nmathematical edifice appear in their \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_68\" id=\"Page_68\"\u003e[68]\u003c/a\u003e\u003c/span\u003edue order and proportion, with a\r\nnew perfection in every part.\u003c/p\u003e\r\n\r\n\u003cp\u003eUntil symbolic logic had acquired its present development, the\r\nprinciples upon which mathematics depends were always supposed to be\r\nphilosophical, and discoverable only by the uncertain, unprogressive\r\nmethods hitherto employed by philosophers. So long as this was\r\nthought, mathematics seemed to be not autonomous, but dependent upon a\r\nstudy which had quite other methods than its own. Moreover, since the\r\nnature of the postulates from which arithmetic, analysis, and geometry\r\nare to be deduced was wrapped in all the traditional obscurities of\r\nmetaphysical discussion, the edifice built upon such dubious\r\nfoundations began to be viewed as no better than a castle in the air.\r\nIn this respect, the discovery that the true principles are as much a\r\npart of mathematics as any of their consequences has very greatly\r\nincreased the intellectual satisfaction to be obtained. This\r\nsatisfaction ought not to be refused to learners capable of enjoying\r\nit, for it is of a kind to increase our respect for human powers and\r\nour knowledge of the beauties belonging to the abstract world.\u003c/p\u003e\r\n\r\n\u003cp\u003ePhilosophers have commonly held that the laws of logic, which underlie\r\nmathematics, are laws of thought, laws regulating the operations of\r\nour minds. By this opinion the true dignity of reason is very greatly\r\nlowered: it ceases to be an investigation into the very heart and\r\nimmutable essence of all things actual and possible, becoming,\r\ninstead, an inquiry into something more or less human and subject to\r\nour limitations. The contemplation of what is non-human, the discovery\r\nthat our minds are capable of dealing with material not created by\r\nthem, above all, the realisation that beauty belongs to the outer\r\nworld as to the inner, are the chief means of overcoming \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_69\" id=\"Page_69\"\u003e[69]\u003c/a\u003e\u003c/span\u003ethe terrible\r\nsense of impotence, of weakness, of exile amid hostile powers, which\r\nis too apt to result from acknowledging the all-but omnipotence of\r\nalien forces. To reconcile us, by the exhibition of its awful beauty,\r\nto the reign of Fate\u0026mdash;which is merely the literary personification of\r\nthese forces\u0026mdash;is the task of tragedy. But mathematics takes us still\r\nfurther from what is human, into the region of absolute necessity, to\r\nwhich not only the actual world, but every possible world, must\r\nconform; and even here it builds a habitation, or rather finds a\r\nhabitation eternally standing, where our ideals are fully satisfied\r\nand our best hopes are not thwarted. It is only when we thoroughly\r\nunderstand the entire independence of ourselves, which belongs to this\r\nworld that reason finds, that we can adequately realise the profound\r\nimportance of its beauty.\u003c/p\u003e\r\n\r\n\u003cp\u003eNot only is mathematics independent of us and our thoughts, but in\r\nanother sense we and the whole universe of existing things are\r\nindependent of mathematics. The apprehension of this purely ideal\r\ncharacter is indispensable, if we are to understand rightly the place\r\nof mathematics as one among the arts. It was formerly supposed that\r\npure reason could decide, in some respects, as to the nature of the\r\nactual world: geometry, at least, was thought to deal with the space\r\nin which we live. But we now know that pure mathematics can never\r\npronounce upon questions of actual existence: the world of reason, in\r\na sense, controls the world of fact, but it is not at any point\r\ncreative of fact, and in the application of its results to the world\r\nin time and space, its certainty and precision are lost among\r\napproximations and working hypotheses. The objects considered by\r\nmathematicians have, in the past, been mainly of a kind suggested by\r\nphenomena; but from such restrictions the abstract imagination \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_70\" id=\"Page_70\"\u003e[70]\u003c/a\u003e\u003c/span\u003eshould\r\nbe wholly free. A reciprocal liberty must thus be accorded: reason\r\ncannot dictate to the world of facts, but the facts cannot restrict\r\nreason\u0027s privilege of dealing with whatever objects its love of beauty\r\nmay cause to seem worthy of consideration. Here, as elsewhere, we\r\nbuild up our own ideals out of the fragments to be found in the world;\r\nand in the end it is hard to say whether the result is a creation or a\r\ndiscovery.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is very desirable, in instruction, not merely to persuade the\r\nstudent of the accuracy of important theorems, but to persuade him in\r\nthe way which itself has, of all possible ways, the most beauty. The\r\ntrue interest of a demonstration is not, as traditional modes of\r\nexposition suggest, concentrated wholly in the result; where this does\r\noccur, it must be viewed as a defect, to be remedied, if possible, by\r\nso generalising the steps of the proof that each becomes important in\r\nand for itself. An argument which serves only to prove a conclusion is\r\nlike a story subordinated to some moral which it is meant to teach:\r\nfor \u0026aelig;sthetic perfection no part of the whole should be merely a means.\r\nA certain practical spirit, a desire for rapid progress, for conquest\r\nof new realms, is responsible for the undue emphasis upon results\r\nwhich prevails in mathematical instruction. The better way is to\r\npropose some theme for consideration\u0026mdash;in geometry, a figure having\r\nimportant properties; in analysis, a function of which the study is\r\nilluminating, and so on. Whenever proofs depend upon some only of the\r\nmarks by which we define the object to be studied, these marks should\r\nbe isolated and investigated on their own account. For it is a defect,\r\nin an argument, to employ more premisses than the conclusion demands:\r\nwhat mathematicians call elegance results from employing only the\r\nessential principles in virtue of which the thesis is true. It is a\r\nmerit in \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_71\" id=\"Page_71\"\u003e[71]\u003c/a\u003e\u003c/span\u003eEuclid that he advances as far as he is able to go without\r\nemploying the axiom of parallels\u0026mdash;not, as is often said, because this\r\naxiom is inherently objectionable, but because, in mathematics, every\r\nnew axiom diminishes the generality of the resulting theorems, and the\r\ngreatest possible generality is before all things to be sought.\u003c/p\u003e\r\n\r\n\u003cp\u003eOf the effects of mathematics outside its own sphere more has been\r\nwritten than on the subject of its own proper ideal. The effect upon\r\nphilosophy has, in the past, been most notable, but most varied; in\r\nthe seventeenth century, idealism and rationalism, in the eighteenth,\r\nmaterialism and sensationalism, seemed equally its offspring. Of the\r\neffect which it is likely to have in the future it would be very rash\r\nto say much; but in one respect a good result appears probable.\r\nAgainst that kind of scepticism which abandons the pursuit of ideals\r\nbecause the road is arduous and the goal not certainly attainable,\r\nmathematics, within its own sphere, is a complete answer. Too often it\r\nis said that there is no absolute truth, but only opinion and private\r\njudgment; that each of us is conditioned, in his view of the world, by\r\nhis own peculiarities, his own taste and bias; that there is no\r\nexternal kingdom of truth to which, by patience and discipline, we may\r\nat last obtain admittance, but only truth for me, for you, for every\r\nseparate person. By this habit of mind one of the chief ends of human\r\neffort is denied, and the supreme virtue of candour, of fearless\r\nacknowledgment of what is, disappears from our moral vision. Of such\r\nscepticism mathematics is a perpetual reproof; for its edifice of\r\ntruths stands unshakable and inexpungable to all the weapons of\r\ndoubting cynicism.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe effects of mathematics upon practical life, though they should not\r\nbe regarded as the motive of our studies, may be used to answer a\r\ndoubt to which the solitary \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_72\" id=\"Page_72\"\u003e[72]\u003c/a\u003e\u003c/span\u003estudent must always be liable. In a world\r\nso full of evil and suffering, retirement into the cloister of\r\ncontemplation, to the enjoyment of delights which, however noble, must\r\nalways be for the few only, cannot but appear as a somewhat selfish\r\nrefusal to share the burden imposed upon others by accidents in which\r\njustice plays no part. Have any of us the right, we ask, to withdraw\r\nfrom present evils, to leave our fellow-men unaided, while we live a\r\nlife which, though arduous and austere, is yet plainly good in its own\r\nnature? When these questions arise, the true answer is, no doubt, that\r\nsome must keep alive the sacred fire, some must preserve, in every\r\ngeneration, the haunting vision which shadows forth the goal of so\r\nmuch striving. But when, as must sometimes occur, this answer seems\r\ntoo cold, when we are almost maddened by the spectacle of sorrows to\r\nwhich we bring no help, then we may reflect that indirectly the\r\nmathematician often does more for human happiness than any of his more\r\npractically active contemporaries. The history of science abundantly\r\nproves that a body of abstract propositions\u0026mdash;even if, as in the case\r\nof conic sections, it remains two thousand years without effect upon\r\ndaily life\u0026mdash;may yet, at any moment, be used to cause a revolution in\r\nthe habitual thoughts and occupations of every citizen. The use of\r\nsteam and electricity\u0026mdash;to take striking instances\u0026mdash;is rendered\r\npossible only by mathematics. In the results of abstract thought the\r\nworld possesses a capital of which the employment in enriching the\r\ncommon round has no hitherto discoverable limits. Nor does experience\r\ngive any means of deciding what parts of mathematics will be found\r\nuseful. Utility, therefore, can be only a consolation in moments of\r\ndiscouragement, not a guide in directing our studies.\u003c/p\u003e\r\n\r\n\u003cp\u003eFor the health of the moral life, for ennobling the tone \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_73\" id=\"Page_73\"\u003e[73]\u003c/a\u003e\u003c/span\u003eof an age or\r\na nation, the austerer virtues have a strange power, exceeding the\r\npower of those not informed and purified by thought. Of these austerer\r\nvirtues the love of truth is the chief, and in mathematics, more than\r\nelsewhere, the love of truth may find encouragement for waning faith.\r\nEvery great study is not only an end in itself, but also a means of\r\ncreating and sustaining a lofty habit of mind; and this purpose should\r\nbe kept always in view throughout the teaching and learning of\r\nmathematics.\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\u003chr style=\"width: 15%;\" /\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003ch4\u003eFOOTNOTES:\u003c/h4\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_10_10\" id=\"Footnote_10_10\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_10_10\"\u003e\u003cspan class=\"label\"\u003e[10]\u003c/span\u003e\u003c/a\u003e This passage was pointed out to me by Professor Gilbert\r\nMurray.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003ca name=\"V\" id=\"V\"\u003e\u003c/a\u003e\u003chr /\u003e\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_74\" id=\"Page_74\"\u003e[74]\u003c/a\u003e\u003c/span\u003e\u003cbr /\u003e\r\n\r\n\u003ch3\u003eV\u003cspan class=\"totoc\"\u003e\u003ca href=\"#toc\"\u003eToC\u003c/a\u003e\u003c/span\u003e\u003c/h3\u003e\r\n\r\n\u003ch4\u003eMATHEMATICS AND THE METAPHYSICIANS\u003c/h4\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003cp\u003eThe nineteenth century, which prided itself upon the invention of\r\nsteam and evolution, might have derived a more legitimate title to\r\nfame from the discovery of pure mathematics. This science, like most\r\nothers, was baptised long before it was born; and thus we find writers\r\nbefore the nineteenth century alluding to what they called pure\r\nmathematics. But if they had been asked what this subject was, they\r\nwould only have been able to say that it consisted of Arithmetic,\r\nAlgebra, Geometry, and so on. As to what these studies had in common,\r\nand as to what distinguished them from applied mathematics, our\r\nancestors were completely in the dark.\u003c/p\u003e\r\n\r\n\u003cp\u003ePure mathematics was discovered by Boole, in a work which he called\r\nthe \u003ci\u003eLaws of Thought\u003c/i\u003e (1854). This work abounds in asseverations that\r\nit is not mathematical, the fact being that Boole was too modest to\r\nsuppose his book the first ever written on mathematics. He was also\r\nmistaken in supposing that he was dealing with the laws of thought:\r\nthe question how people actually think was quite irrelevant to him,\r\nand if his book had really contained the laws of thought, it was\r\ncurious that no one should ever have thought in such a way before. His\r\nbook was in fact concerned with formal logic, and this is the same\r\nthing as mathematics.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_75\" id=\"Page_75\"\u003e[75]\u003c/a\u003e\u003c/span\u003ePure mathematics consists entirely of assertions to the effect that,\r\nif such and such a proposition is true of \u003ci\u003eanything\u003c/i\u003e, then such and\r\nsuch another proposition is true of that thing. It is essential not to\r\ndiscuss whether the first proposition is really true, and not to\r\nmention what the anything is, of which it is supposed to be true. Both\r\nthese points would belong to applied mathematics. We start, in pure\r\nmathematics, from certain rules of inference, by which we can infer\r\nthat \u003ci\u003eif\u003c/i\u003e one proposition is true, then so is some other proposition.\r\nThese rules of inference constitute the major part of the principles\r\nof formal logic. We then take any hypothesis that seems amusing, and\r\ndeduce its consequences. \u003ci\u003eIf\u003c/i\u003e our hypothesis is about \u003ci\u003eanything\u003c/i\u003e, and\r\nnot about some one or more particular things, then our deductions\r\nconstitute mathematics. Thus mathematics may be defined as the subject\r\nin which we never know what we are talking about, nor whether what we\r\nare saying is true. People who have been puzzled by the beginnings of\r\nmathematics will, I hope, find comfort in this definition, and will\r\nprobably agree that it is accurate.\u003c/p\u003e\r\n\r\n\u003cp\u003eAs one of the chief triumphs of modern mathematics consists in having\r\ndiscovered what mathematics really is, a few more words on this\r\nsubject may not be amiss. It is common to start any branch of\r\nmathematics\u0026mdash;for instance, Geometry\u0026mdash;with a certain number of\r\nprimitive ideas, supposed incapable of definition, and a certain\r\nnumber of primitive propositions or axioms, supposed incapable of\r\nproof. Now the fact is that, though there are indefinables and\r\nindemonstrables in every branch of applied mathematics, there are none\r\nin pure mathematics except such as belong to general logic. Logic,\r\nbroadly speaking, is distinguished by the fact that its propositions\r\ncan be put into a form in which they apply to anything whatever. All\r\npure mathematics\u0026mdash;Arithmetic, Analysis, \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_76\" id=\"Page_76\"\u003e[76]\u003c/a\u003e\u003c/span\u003eand Geometry\u0026mdash;is built up by\r\ncombinations of the primitive ideas of logic, and its propositions are\r\ndeduced from the general axioms of logic, such as the syllogism and\r\nthe other rules of inference. And this is no longer a dream or an\r\naspiration. On the contrary, over the greater and more difficult part\r\nof the domain of mathematics, it has been already accomplished; in the\r\nfew remaining cases, there is no special difficulty, and it is now\r\nbeing rapidly achieved. Philosophers have disputed for ages whether\r\nsuch deduction was possible; mathematicians have sat down and made the\r\ndeduction. For the philosophers there is now nothing left but graceful\r\nacknowledgments.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe subject of formal logic, which has thus at last shown itself to be\r\nidentical with mathematics, was, as every one knows, invented by\r\nAristotle, and formed the chief study (other than theology) of the\r\nMiddle Ages. But Aristotle never got beyond the syllogism, which is a\r\nvery small part of the subject, and the schoolmen never got beyond\r\nAristotle. If any proof were required of our superiority to the\r\nmedi\u0026aelig;val doctors, it might be found in this. Throughout the Middle\r\nAges, almost all the best intellects devoted themselves to formal\r\nlogic, whereas in the nineteenth century only an infinitesimal\r\nproportion of the world\u0027s thought went into this subject.\r\nNevertheless, in each decade since 1850 more has been done to advance\r\nthe subject than in the whole period from Aristotle to Leibniz. People\r\nhave discovered how to make reasoning symbolic, as it is in Algebra,\r\nso that deductions are effected by mathematical rules. They have\r\ndiscovered many rules besides the syllogism, and a new branch of\r\nlogic, called the Logic of Relatives,\u003ca name=\"FNanchor_11_11\" id=\"FNanchor_11_11\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_11_11\" class=\"fnanchor\"\u003e[11]\u003c/a\u003e has been invented to deal\r\nwith topics that wholly surpassed the powers of \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_77\" id=\"Page_77\"\u003e[77]\u003c/a\u003e\u003c/span\u003ethe old logic, though\r\nthey form the chief contents of mathematics.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is not easy for the lay mind to realise the importance of symbolism\r\nin discussing the foundations of mathematics, and the explanation may\r\nperhaps seem strangely paradoxical. The fact is that symbolism is\r\nuseful because it makes things difficult. (This is not true of the\r\nadvanced parts of mathematics, but only of the beginnings.) What we\r\nwish to know is, what can be deduced from what. Now, in the\r\nbeginnings, everything is self-evident; and it is very hard to see\r\nwhether one self-evident proposition follows from another or not.\r\nObviousness is always the enemy to correctness. Hence we invent some\r\nnew and difficult symbolism, in which nothing seems obvious. Then we\r\nset up certain rules for operating on the symbols, and the whole thing\r\nbecomes mechanical. In this way we find out what must be taken as\r\npremiss and what can be demonstrated or defined. For instance, the\r\nwhole of Arithmetic and Algebra has been shown to require three\r\nindefinable notions and five indemonstrable propositions. But without\r\na symbolism it would have been very hard to find this out. It is so\r\nobvious that two and two are four, that we can hardly make ourselves\r\nsufficiently sceptical to doubt whether it can be proved. And the same\r\nholds in other cases where self-evident things are to be proved.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut the proof of self-evident propositions may seem, to the\r\nuninitiated, a somewhat frivolous occupation. To this we might reply\r\nthat it is often by no means self-evident that one obvious proposition\r\nfollows from another obvious proposition; so that we are really\r\ndiscovering new truths when we prove what is evident by a method which\r\nis not evident. But a more interesting retort is, that since people\r\nhave tried to prove obvious propositions, they have found that many of\r\nthem are false. \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_78\" id=\"Page_78\"\u003e[78]\u003c/a\u003e\u003c/span\u003eSelf-evidence is often a mere will-o\u0027-the-wisp, which\r\nis sure to lead us astray if we take it as our guide. For instance,\r\nnothing is plainer than that a whole always has more terms than a\r\npart, or that a number is increased by adding one to it. But these\r\npropositions are now known to be usually false. Most numbers are\r\ninfinite, and if a number is infinite you may add ones to it as long\r\nas you like without disturbing it in the least. One of the merits of a\r\nproof is that it instils a certain doubt as to the result proved; and\r\nwhen what is obvious can be proved in some cases, but not in others,\r\nit becomes possible to suppose that in these other cases it is false.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe great master of the art of formal reasoning, among the men of our\r\nown day, is an Italian, Professor Peano, of the University of\r\nTurin.\u003ca name=\"FNanchor_12_12\" id=\"FNanchor_12_12\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_12_12\" class=\"fnanchor\"\u003e[12]\u003c/a\u003e He has reduced the greater part of mathematics (and he or\r\nhis followers will, in time, have reduced the whole) to strict\r\nsymbolic form, in which there are no words at all. In the ordinary\r\nmathematical books, there are no doubt fewer words than most readers\r\nwould wish. Still, little phrases occur, such as \u003ci\u003etherefore, let us\r\nassume, consider\u003c/i\u003e, or \u003ci\u003ehence it follows\u003c/i\u003e. All these, however, are a\r\nconcession, and are swept away by Professor Peano. For instance, if we\r\nwish to learn the whole of Arithmetic, Algebra, the Calculus, and\r\nindeed all that is usually called pure mathematics (except Geometry),\r\nwe must start with a dictionary of three words. One symbol stands for\r\n\u003ci\u003ezero\u003c/i\u003e, another for \u003ci\u003enumber\u003c/i\u003e, and a third for \u003ci\u003enext after\u003c/i\u003e. What these\r\nideas mean, it is necessary to know if you wish to become an\r\narithmetician. But after symbols have been invented for these three\r\nideas, not another word is required in the whole development. All\r\nfuture symbols are symbolically explained by means of these \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_79\" id=\"Page_79\"\u003e[79]\u003c/a\u003e\u003c/span\u003ethree.\r\nEven these three can be explained by means of the notions of\r\n\u003ci\u003erelation\u003c/i\u003e and \u003ci\u003eclass\u003c/i\u003e; but this requires the Logic of Relations,\r\nwhich Professor Peano has never taken up. It must be admitted that\r\nwhat a mathematician has to know to begin with is not much. There are\r\nat most a dozen notions out of which all the notions in all pure\r\nmathematics (including Geometry) are compounded. Professor Peano, who\r\nis assisted by a very able school of young Italian disciples, has\r\nshown how this may be done; and although the method which he has\r\ninvented is capable of being carried a good deal further than he has\r\ncarried it, the honour of the pioneer must belong to him.\u003c/p\u003e\r\n\r\n\u003cp\u003eTwo hundred years ago, Leibniz foresaw the science which Peano has\r\nperfected, and endeavoured to create it. He was prevented from\r\nsucceeding by respect for the authority of Aristotle, whom he could\r\nnot believe guilty of definite, formal fallacies; but the subject\r\nwhich he desired to create now exists, in spite of the patronising\r\ncontempt with which his schemes have been treated by all superior\r\npersons. From this \"Universal Characteristic,\" as he called it, he\r\nhoped for a solution of all problems, and an end to all disputes. \"If\r\ncontroversies were to arise,\" he says, \"there would be no more need of\r\ndisputation between two philosophers than between two accountants. For\r\nit would suffice to take their pens in their hands, to sit down to\r\ntheir desks, and to say to each other (with a friend as witness, if\r\nthey liked), \u0027Let us calculate.\u0027\" This optimism has now appeared to be\r\nsomewhat excessive; there still are problems whose solution is\r\ndoubtful, and disputes which calculation cannot decide. But over an\r\nenormous field of what was formerly controversial, Leibniz\u0027s dream has\r\nbecome sober fact. In the whole philosophy of mathematics, which \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_80\" id=\"Page_80\"\u003e[80]\u003c/a\u003e\u003c/span\u003eused\r\nto be at least as full of doubt as any other part of philosophy, order\r\nand certainty have replaced the confusion and hesitation which\r\nformerly reigned. Philosophers, of course, have not yet discovered\r\nthis fact, and continue to write on such subjects in the old way. But\r\nmathematicians, at least in Italy, have now the power of treating the\r\nprinciples of mathematics in an exact and masterly manner, by means of\r\nwhich the certainty of mathematics extends also to mathematical\r\nphilosophy. Hence many of the topics which used to be placed among the\r\ngreat mysteries\u0026mdash;for example, the natures of infinity, of continuity,\r\nof space, time and motion\u0026mdash;are now no longer in any degree open to\r\ndoubt or discussion. Those who wish to know the nature of these things\r\nneed only read the works of such men as Peano or Georg Cantor; they\r\nwill there find exact and indubitable expositions of all these quondam\r\nmysteries.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn this capricious world, nothing is more capricious than posthumous\r\nfame. One of the most notable examples of posterity\u0027s lack of judgment\r\nis the Eleatic Zeno. This man, who may be regarded as the founder of\r\nthe philosophy of infinity, appears in Plato\u0027s Parmenides in the\r\nprivileged position of instructor to Socrates. He invented four\r\narguments, all immeasurably subtle and profound, to prove that motion\r\nis impossible, that Achilles can never overtake the tortoise, and that\r\nan arrow in flight is really at rest. After being refuted by\r\nAristotle, and by every subsequent philosopher from that day to our\r\nown, these arguments were reinstated, and made the basis of a\r\nmathematical renaissance, by a German professor, who probably never\r\ndreamed of any connection between himself and Zeno. Weierstrass,\u003ca name=\"FNanchor_13_13\" id=\"FNanchor_13_13\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_13_13\" class=\"fnanchor\"\u003e[13]\u003c/a\u003e\r\nby strictly \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_81\" id=\"Page_81\"\u003e[81]\u003c/a\u003e\u003c/span\u003ebanishing from mathematics the use of infinitesimals, has\r\nat last shown that we live in an unchanging world, and that the arrow\r\nin its flight is truly at rest. Zeno\u0027s only error lay in inferring (if\r\nhe did infer) that, because there is no such thing as a state of\r\nchange, therefore the world is in the same state at any one time as at\r\nany other. This is a consequence which by no means follows; and in\r\nthis respect, the German mathematician is more constructive than the\r\ningenious Greek. Weierstrass has been able, by embodying his views in\r\nmathematics, where familiarity with truth eliminates the vulgar\r\nprejudices of common sense, to invest Zeno\u0027s paradoxes with the\r\nrespectable air of platitudes; and if the result is less delightful to\r\nthe lover of reason than Zeno\u0027s bold defiance, it is at any rate more\r\ncalculated to appease the mass of academic mankind.\u003c/p\u003e\r\n\r\n\u003cp\u003eZeno was concerned, as a matter of fact, with three problems, each\r\npresented by motion, but each more abstract than motion, and capable\r\nof a purely arithmetical treatment. These are the problems of the\r\ninfinitesimal, the infinite, and continuity. To state clearly the\r\ndifficulties involved, was to accomplish perhaps the hardest part of\r\nthe philosopher\u0027s task. This was done by Zeno. From him to our own\r\nday, the finest intellects of each generation in turn attacked the\r\nproblems, but achieved, broadly speaking, nothing. In our own time,\r\nhowever, three men\u0026mdash;Weierstrass, Dedekind, and Cantor\u0026mdash;have not merely\r\nadvanced the three problems, but have completely solved them. The\r\nsolutions, for those acquainted with mathematics, are so clear as to\r\nleave no longer the slightest doubt or difficulty. This achievement is\r\nprobably the greatest of which our age has to boast; and I know of no\r\nage (except perhaps the golden \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_82\" id=\"Page_82\"\u003e[82]\u003c/a\u003e\u003c/span\u003eage of Greece) which has a more\r\nconvincing proof to offer of the transcendent genius of its great men.\r\nOf the three problems, that of the infinitesimal was solved by\r\nWeierstrass; the solution of the other two was begun by Dedekind, and\r\ndefinitively accomplished by Cantor.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe infinitesimal played formerly a great part in mathematics. It was\r\nintroduced by the Greeks, who regarded a circle as differing\r\ninfinitesimally from a polygon with a very large number of very small\r\nequal sides. It gradually grew in importance, until, when Leibniz\r\ninvented the Infinitesimal Calculus, it seemed to become the\r\nfundamental notion of all higher mathematics. Carlyle tells, in his\r\n\u003ci\u003eFrederick the Great\u003c/i\u003e, how Leibniz used to discourse to Queen Sophia\r\nCharlotte of Prussia concerning the infinitely little, and how she\r\nwould reply that on that subject she needed no instruction\u0026mdash;the\r\nbehaviour of courtiers had made her thoroughly familiar with it. But\r\nphilosophers and mathematicians\u0026mdash;who for the most part had less\r\nacquaintance with courts\u0026mdash;continued to discuss this topic, though\r\nwithout making any advance. The Calculus required continuity, and\r\ncontinuity was supposed to require the infinitely little; but nobody\r\ncould discover what the infinitely little might be. It was plainly not\r\nquite zero, because a sufficiently large number of infinitesimals,\r\nadded together, were seen to make up a finite whole. But nobody could\r\npoint out any fraction which was not zero, and yet not finite. Thus\r\nthere was a deadlock. But at last Weierstrass discovered that the\r\ninfinitesimal was not needed at all, and that everything could be\r\naccomplished without it. Thus there was no longer any need to suppose\r\nthat there was such a thing. Nowadays, therefore, mathematicians are\r\nmore dignified than Leibniz: instead of talking about the infinitely\r\nsmall, they talk about the infinitely great\u0026mdash;a subject \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_83\" id=\"Page_83\"\u003e[83]\u003c/a\u003e\u003c/span\u003ewhich, however\r\nappropriate to monarchs, seems, unfortunately, to interest them even\r\nless than the infinitely little interested the monarchs to whom\r\nLeibniz discoursed.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe banishment of the infinitesimal has all sorts of odd consequences,\r\nto which one has to become gradually accustomed. For example, there is\r\nno such thing as the next moment. The interval between one moment and\r\nthe next would have to be infinitesimal, since, if we take two moments\r\nwith a finite interval between them, there are always other moments in\r\nthe interval. Thus if there are to be no infinitesimals, no two\r\nmoments are quite consecutive, but there are always other moments\r\nbetween any two. Hence there must be an infinite number of moments\r\nbetween any two; because if there were a finite number one would be\r\nnearest the first of the two moments, and therefore next to it. This\r\nmight be thought to be a difficulty; but, as a matter of fact, it is\r\nhere that the philosophy of the infinite comes in, and makes all\r\nstraight.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe same sort of thing happens in space. If any piece of matter be cut\r\nin two, and then each part be halved, and so on, the bits will become\r\nsmaller and smaller, and can theoretically be made as small as we\r\nplease. However small they may be, they can still be cut up and made\r\nsmaller still. But they will always have \u003ci\u003esome\u003c/i\u003e finite size, however\r\nsmall they may be. We never reach the infinitesimal in this way, and\r\nno finite number of divisions will bring us to points. Nevertheless\r\nthere \u003ci\u003eare\u003c/i\u003e points, only these are not to be reached by successive\r\ndivisions. Here again, the philosophy of the infinite shows us how\r\nthis is possible, and why points are not infinitesimal lengths.\u003c/p\u003e\r\n\r\n\u003cp\u003eAs regards motion and change, we get similarly curious results. People\r\nused to think that when a thing changes, it must be in a state of\r\nchange, and that when a thing \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_84\" id=\"Page_84\"\u003e[84]\u003c/a\u003e\u003c/span\u003emoves, it is in a state of motion. This\r\nis now known to be a mistake. When a body moves, all that can be said\r\nis that it is in one place at one time and in another at another. We\r\nmust not say that it will be in a neighbouring place at the next\r\ninstant, since there is no next instant. Philosophers often tell us\r\nthat when a body is in motion, it changes its position within the\r\ninstant. To this view Zeno long ago made the fatal retort that every\r\nbody always is where it is; but a retort so simple and brief was not\r\nof the kind to which philosophers are accustomed to give weight, and\r\nthey have continued down to our own day to repeat the same phrases\r\nwhich roused the Eleatic\u0027s destructive ardour. It was only recently\r\nthat it became possible to explain motion in detail in accordance with\r\nZeno\u0027s platitude, and in opposition to the philosopher\u0027s paradox. We\r\nmay now at last indulge the comfortable belief that a body in motion\r\nis just as truly where it is as a body at rest. Motion consists merely\r\nin the fact that bodies are sometimes in one place and sometimes in\r\nanother, and that they are at intermediate places at intermediate\r\ntimes. Only those who have waded through the quagmire of philosophic\r\nspeculation on this subject can realise what a liberation from antique\r\nprejudices is involved in this simple and straightforward commonplace.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe philosophy of the infinitesimal, as we have just seen, is mainly\r\nnegative. People used to believe in it, and now they have found out\r\ntheir mistake. The philosophy of the infinite, on the other hand, is\r\nwholly positive. It was formerly supposed that infinite numbers, and\r\nthe mathematical infinite generally, were self-contradictory. But as\r\nit was obvious that there were infinities\u0026mdash;for example, the number of\r\nnumbers\u0026mdash;the contradictions of infinity seemed unavoidable, and\r\nphilosophy seemed to \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_85\" id=\"Page_85\"\u003e[85]\u003c/a\u003e\u003c/span\u003ehave wandered into a \"cul-de-sac.\" This\r\ndifficulty led to Kant\u0027s antinomies, and hence, more or less\r\nindirectly, to much of Hegel\u0027s dialectic method. Almost all current\r\nphilosophy is upset by the fact (of which very few philosophers are as\r\nyet aware) that all the ancient and respectable contradictions in the\r\nnotion of the infinite have been once for all disposed of. The method\r\nby which this has been done is most interesting and instructive. In\r\nthe first place, though people had talked glibly about infinity ever\r\nsince the beginnings of Greek thought, nobody had ever thought of\r\nasking, What is infinity? If any philosopher had been asked for a\r\ndefinition of infinity, he might have produced some unintelligible\r\nrigmarole, but he would certainly not have been able to give a\r\ndefinition that had any meaning at all. Twenty years ago, roughly\r\nspeaking, Dedekind and Cantor asked this question, and, what is more\r\nremarkable, they answered it. They found, that is to say, a perfectly\r\nprecise definition of an infinite number or an infinite collection of\r\nthings. This was the first and perhaps the greatest step. It then\r\nremained to examine the supposed contradictions in this notion. Here\r\nCantor proceeded in the only proper way. He took pairs of\r\ncontradictory propositions, in which both sides of the contradiction\r\nwould be usually regarded as demonstrable, and he strictly examined\r\nthe supposed proofs. He found that all proofs adverse to infinity\r\ninvolved a certain principle, at first sight obviously true, but\r\ndestructive, in its consequences, of almost all mathematics. The\r\nproofs favourable to infinity, on the other hand, involved no\r\nprinciple that had evil consequences. It thus appeared that common\r\nsense had allowed itself to be taken in by a specious maxim, and that,\r\nwhen once this maxim was rejected, all went well.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe maxim in question is, that if one collection is part \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_86\" id=\"Page_86\"\u003e[86]\u003c/a\u003e\u003c/span\u003eof another,\r\nthe one which is a part has fewer terms than the one of which it is a\r\npart. This maxim is true of finite numbers. For example, Englishmen\r\nare only some among Europeans, and there are fewer Englishmen than\r\nEuropeans. But when we come to infinite numbers, this is no longer\r\ntrue. This breakdown of the maxim gives us the precise definition of\r\ninfinity. A collection of terms is infinite when it contains as parts\r\nother collections which have just as many terms as it has. If you can\r\ntake away some of the terms of a collection, without diminishing the\r\nnumber of terms, then there are an infinite number of terms in the\r\ncollection. For example, there are just as many even numbers as there\r\nare numbers altogether, since every number can be doubled. This may be\r\nseen by putting odd and even numbers together in one row, and even\r\nnumbers alone in a row below:\u0026mdash;\u003c/p\u003e\r\n\r\n\u003cdiv class=\"block\"\u003e\r\n\u003cp class=\"noin\"\u003e1, 2, 3, 4, 5, \u003ci\u003ead infinitum\u003c/i\u003e.\u003cbr /\u003e\r\n2, 4, 6, 8, 10, \u003ci\u003ead infinitum\u003c/i\u003e.\u003c/p\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp class=\"noin\"\u003eThere are obviously just as many numbers in the row below as in the\r\nrow above, because there is one below for each one above. This\r\nproperty, which was formerly thought to be a contradiction, is now\r\ntransformed into a harmless definition of infinity, and shows, in the\r\nabove case, that the number of finite numbers is infinite.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut the uninitiated may wonder how it is possible to deal with a\r\nnumber which cannot be counted. It is impossible to count up \u003ci\u003eall\u003c/i\u003e the\r\nnumbers, one by one, because, however many we may count, there are\r\nalways more to follow. The fact is that counting is a very vulgar and\r\nelementary way of finding out how many terms there are in a\r\ncollection. And in any case, counting gives us what mathematicians\r\ncall the \u003ci\u003eordinal\u003c/i\u003e number of our terms; that is to say, it arranges\r\nour terms in an order or \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_87\" id=\"Page_87\"\u003e[87]\u003c/a\u003e\u003c/span\u003eseries, and its result tells us what type of\r\nseries results from this arrangement. In other words, it is impossible\r\nto count things without counting some first and others afterwards, so\r\nthat counting always has to do with order. Now when there are only a\r\nfinite number of terms, we can count them in any order we like; but\r\nwhen there are an infinite number, what corresponds to counting will\r\ngive us quite different results according to the way in which we carry\r\nout the operation. Thus the ordinal number, which results from what,\r\nin a general sense may be called counting, depends not only upon how\r\nmany terms we have, but also (where the number of terms is infinite)\r\nupon the way in which the terms are arranged.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe fundamental infinite numbers are not ordinal, but are what is\r\ncalled \u003ci\u003ecardinal\u003c/i\u003e. They are not obtained by putting our terms in order\r\nand counting them, but by a different method, which tells us, to begin\r\nwith, whether two collections have the same number of terms, or, if\r\nnot, which is the greater.\u003ca name=\"FNanchor_14_14\" id=\"FNanchor_14_14\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_14_14\" class=\"fnanchor\"\u003e[14]\u003c/a\u003e It does not tell us, in the way in\r\nwhich counting does, \u003ci\u003ewhat\u003c/i\u003e number of terms a collection has; but if\r\nwe define a number as the number of terms in such and such a\r\ncollection, then this method enables us to discover whether some other\r\ncollection that may be mentioned has more or fewer terms. An\r\nillustration will show how this is done. If there existed some country\r\nin which, for one reason or another, it was impossible to take a\r\ncensus, but in which it was known that every man had a wife and every\r\nwoman a husband, then (provided polygamy was not a national\r\ninstitution) we should know, without counting, that there were exactly\r\nas many men as there were women in that country, neither more nor\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_88\" id=\"Page_88\"\u003e[88]\u003c/a\u003e\u003c/span\u003eless. This method can be applied generally. If there is some relation\r\nwhich, like marriage, connects the things in one collection each with\r\none of the things in another collection, and vice versa, then the two\r\ncollections have the same number of terms. This was the way in which\r\nwe found that there are as many even numbers as there are numbers.\r\nEvery number can be doubled, and every even number can be halved, and\r\neach process gives just one number corresponding to the one that is\r\ndoubled or halved. And in this way we can find any number of\r\ncollections each of which has just as many terms as there are finite\r\nnumbers. If every term of a collection can be hooked on to a number,\r\nand all the finite numbers are used once, and only once, in the\r\nprocess, then our collection must have just as many terms as there are\r\nfinite numbers. This is the general method by which the numbers of\r\ninfinite collections are defined.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut it must not be supposed that all infinite numbers are equal. On\r\nthe contrary, there are infinitely more infinite numbers than finite\r\nones. There are more ways of arranging the finite numbers in different\r\ntypes of series than there are finite numbers. There are probably more\r\npoints in space and more moments in time than there are finite\r\nnumbers. There are exactly as many fractions as whole numbers,\r\nalthough there are an infinite number of fractions between any two\r\nwhole numbers. But there are more irrational numbers than there are\r\nwhole numbers or fractions. There are probably exactly as many points\r\nin space as there are irrational numbers, and exactly as many points\r\non a line a millionth of an inch long as in the whole of infinite\r\nspace. There is a greatest of all infinite numbers, which is the\r\nnumber of things altogether, of every sort and kind. It is obvious\r\nthat there cannot be a greater number than this, because, \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_89\" id=\"Page_89\"\u003e[89]\u003c/a\u003e\u003c/span\u003eif\r\neverything has been taken, there is nothing left to add. Cantor has a\r\nproof that there is no greatest number, and if this proof were valid,\r\nthe contradictions of infinity would reappear in a sublimated form.\r\nBut in this one point, the master has been guilty of a very subtle\r\nfallacy, which I hope to explain in some future work.\u003ca name=\"FNanchor_15_15\" id=\"FNanchor_15_15\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_15_15\" class=\"fnanchor\"\u003e[15]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eWe can now understand why Zeno believed that Achilles cannot overtake\r\nthe tortoise and why as a matter of fact he can overtake it. We shall\r\nsee that all the people who disagreed with Zeno had no right to do so,\r\nbecause they all accepted premises from which his conclusion followed.\r\nThe argument is this: Let Achilles and the tortoise start along a road\r\nat the same time, the tortoise (as is only fair) being allowed a\r\nhandicap. Let Achilles go twice as fast as the tortoise, or ten times\r\nor a hundred times as fast. Then he will never reach the tortoise. For\r\nat every moment the tortoise is somewhere and Achilles is somewhere;\r\nand neither is ever twice in the same place while the race is going\r\non. Thus the tortoise goes to just as many places as Achilles does,\r\nbecause each is in one place at one moment, and in another at any\r\nother moment. But if Achilles were to catch up with the tortoise, the\r\nplaces where the tortoise would have been would be only part of the\r\nplaces where Achilles would have been. Here, we must suppose, Zeno\r\nappealed to the maxim that the whole has more terms than the part.\u003ca name=\"FNanchor_16_16\" id=\"FNanchor_16_16\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_16_16\" class=\"fnanchor\"\u003e[16]\u003c/a\u003e\r\nThus if Achilles were \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_90\" id=\"Page_90\"\u003e[90]\u003c/a\u003e\u003c/span\u003eto overtake the tortoise, he would have been in\r\nmore places than the tortoise; but we saw that he must, in any period,\r\nbe in exactly as many places as the tortoise. Hence we infer that he\r\ncan never catch the tortoise. This argument is strictly correct, if we\r\nallow the axiom that the whole has more terms than the part. As the\r\nconclusion is absurd, the axiom must be rejected, and then all goes\r\nwell. But there is no good word to be said for the philosophers of the\r\npast two thousand years and more, who have all allowed the axiom and\r\ndenied the conclusion.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe retention of this axiom leads to absolute contradictions, while\r\nits rejection leads only to oddities. Some of these oddities, it must\r\nbe confessed, are very odd. One of them, which I call the paradox of\r\nTristram Shandy, is the converse of the Achilles, and shows that the\r\ntortoise, if you give him time, will go just as far as Achilles.\r\nTristram Shandy, as we know, employed two years in chronicling the\r\nfirst two days of his life, and lamented that, at this rate, material\r\nwould accumulate faster than he could deal with it, so that, as years\r\nwent by, he would be farther and farther from the end of his history.\r\nNow I maintain that, if he had lived for ever, and had not wearied of\r\nhis task, then, even if his life had continued as event fully as it\r\nbegan, no part of his biography would have remained unwritten. For\r\nconsider: the hundredth day will be described in the hundredth year,\r\nthe thousandth in the thousandth year, and so on. Whatever day we may\r\nchoose as so far on that he cannot hope to reach it, that day will be\r\ndescribed in the corresponding year. Thus any day that may be\r\nmentioned will be written up sooner or later, and therefore no part of\r\nthe biography will remain permanently unwritten. This paradoxical but\r\nperfectly true proposition depends upon the fact \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_91\" id=\"Page_91\"\u003e[91]\u003c/a\u003e\u003c/span\u003ethat the number of\r\ndays in all time is no greater than the number of years.\u003c/p\u003e\r\n\r\n\u003cp\u003eThus on the subject of infinity it is impossible to avoid conclusions\r\nwhich at first sight appear paradoxical, and this is the reason why so\r\nmany philosophers have supposed that there were inherent\r\ncontradictions in the infinite. But a little practice enables one to\r\ngrasp the true principles of Cantor\u0027s doctrine, and to acquire new and\r\nbetter instincts as to the true and the false. The oddities then\r\nbecome no odder than the people at the antipodes, who used to be\r\nthought impossible because they would find it so inconvenient to stand\r\non their heads.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe solution of the problems concerning infinity has enabled Cantor to\r\nsolve also the problems of continuity. Of this, as of infinity, he has\r\ngiven a perfectly precise definition, and has shown that there are no\r\ncontradictions in the notion so defined. But this subject is so\r\ntechnical that it is impossible to give any account of it here.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe notion of continuity depends upon that of \u003ci\u003eorder\u003c/i\u003e, since\r\ncontinuity is merely a particular type of order. Mathematics has, in\r\nmodern times, brought order into greater and greater prominence. In\r\nformer days, it was supposed (and philosophers are still apt to\r\nsuppose) that quantity was the fundamental notion of mathematics. But\r\nnowadays, quantity is banished altogether, except from one little\r\ncorner of Geometry, while order more and more reigns supreme. The\r\ninvestigation of different kinds of series and their relations is now\r\na very large part of mathematics, and it has been found that this\r\ninvestigation can be conducted without any reference to quantity, and,\r\nfor the most part, without any reference to number. All types of\r\nseries are capable of formal definition, and their properties can be\r\ndeduced from the principles of symbolic logic by means of the Algebra\r\nof Relatives. \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_92\" id=\"Page_92\"\u003e[92]\u003c/a\u003e\u003c/span\u003eThe notion of a limit, which is fundamental in the\r\ngreater part of higher mathematics, used to be defined by means of\r\nquantity, as a term to which the terms of some series approximate as\r\nnearly as we please. But nowadays the limit is defined quite\r\ndifferently, and the series which it limits may not approximate to it\r\nat all. This improvement also is due to Cantor, and it is one which\r\nhas revolutionised mathematics. Only order is now relevant to limits.\r\nThus, for instance, the smallest of the infinite integers is the limit\r\nof the finite integers, though all finite integers are at an infinite\r\ndistance from it. The study of different types of series is a general\r\nsubject of which the study of ordinal numbers (mentioned above) is a\r\nspecial and very interesting branch. But the unavoidable\r\ntechnicalities of this subject render it impossible to explain to any\r\nbut professed mathematicians.\u003c/p\u003e\r\n\r\n\u003cp\u003eGeometry, like Arithmetic, has been subsumed, in recent times, under\r\nthe general study of order. It was formerly supposed that Geometry was\r\nthe study of the nature of the space in which we live, and accordingly\r\nit was urged, by those who held that what exists can only be known\r\nempirically, that Geometry should really be regarded as belonging to\r\napplied mathematics. But it has gradually appeared, by the increase of\r\nnon-Euclidean systems, that Geometry throws no more light upon the\r\nnature of space than Arithmetic throws upon the population of the\r\nUnited States. Geometry is a whole collection of deductive sciences\r\nbased on a corresponding collection of sets of axioms. One set of\r\naxioms is Euclid\u0027s; other equally good sets of axioms lead to other\r\nresults. Whether Euclid\u0027s axioms are true, is a question as to which\r\nthe pure mathematician is indifferent; and, what is more, it is a\r\nquestion which it is theoretically impossible to answer with certainty\r\nin the affirmative. It might \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_93\" id=\"Page_93\"\u003e[93]\u003c/a\u003e\u003c/span\u003epossibly be shown, by very careful\r\nmeasurements, that Euclid\u0027s axioms are false; but no measurements\r\ncould ever assure us (owing to the errors of observation) that they\r\nare exactly true. Thus the geometer leaves to the man of science to\r\ndecide, as best he may, what axioms are most nearly true in the actual\r\nworld. The geometer takes any set of axioms that seem interesting, and\r\ndeduces their consequences. What defines Geometry, in this sense, is\r\nthat the axioms must give rise to a series of more than one dimension.\r\nAnd it is thus that Geometry becomes a department in the study of\r\norder.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn Geometry, as in other parts of mathematics, Peano and his disciples\r\nhave done work of the very greatest merit as regards principles.\r\nFormerly, it was held by philosophers and mathematicians alike that\r\nthe proofs in Geometry depended on the figure; nowadays, this is known\r\nto be false. In the best books there are no figures at all. The\r\nreasoning proceeds by the strict rules of formal logic from a set of\r\naxioms laid down to begin with. If a figure is used, all sorts of\r\nthings seem obviously to follow, which no formal reasoning can prove\r\nfrom the explicit axioms, and which, as a matter of fact, are only\r\naccepted because they are obvious. By banishing the figure, it becomes\r\npossible to discover \u003ci\u003eall\u003c/i\u003e the axioms that are needed; and in this way\r\nall sorts of possibilities, which would have otherwise remained\r\nundetected, are brought to light.\u003c/p\u003e\r\n\r\n\u003cp\u003eOne great advance, from the point of view of correctness, has been\r\nmade by introducing points as they are required, and not starting, as\r\nwas formerly done, by assuming the whole of space. This method is due\r\npartly to Peano, partly to another Italian named Fano. To those\r\nunaccustomed to it, it has an air of somewhat wilful pedantry. In this\r\nway, we begin with the following \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_94\" id=\"Page_94\"\u003e[94]\u003c/a\u003e\u003c/span\u003eaxioms: (1) There is a class of\r\nentities called \u003ci\u003epoints\u003c/i\u003e. (2) There is at least one point. (3) If \u003ci\u003ea\u003c/i\u003e\r\nbe a point, there is at least one other point besides \u003ci\u003ea\u003c/i\u003e. Then we\r\nbring in the straight line joining two points, and begin again with\r\n(4), namely, on the straight line joining \u003ci\u003ea\u003c/i\u003e and \u003ci\u003eb\u003c/i\u003e, there is at\r\nleast one other point besides \u003ci\u003ea\u003c/i\u003e and \u003ci\u003eb\u003c/i\u003e. (5) There is at least one\r\npoint not on the line \u003ci\u003eab\u003c/i\u003e. And so we go on, till we have the means of\r\nobtaining as many points as we require. But the word \u003ci\u003espace\u003c/i\u003e, as Peano\r\nhumorously remarks, is one for which Geometry has no use at all.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe rigid methods employed by modern geometers have deposed Euclid\r\nfrom his pinnacle of correctness. It was thought, until recent times,\r\nthat, as Sir Henry Savile remarked in 1621, there were only two\r\nblemishes in Euclid, the theory of parallels and the theory of\r\nproportion. It is now known that these are almost the only points in\r\nwhich Euclid is free from blemish. Countless errors are involved in\r\nhis first eight propositions. That is to say, not only is it doubtful\r\nwhether his axioms are true, which is a comparatively trivial matter,\r\nbut it is certain that his propositions do not follow from the axioms\r\nwhich he enunciates. A vastly greater number of axioms, which Euclid\r\nunconsciously employs, are required for the proof of his propositions.\r\nEven in the first proposition of all, where he constructs an\r\nequilateral triangle on a given base, he uses two circles which are\r\nassumed to intersect. But no explicit axiom assures us that they do\r\nso, and in some kinds of spaces they do not always intersect. It is\r\nquite doubtful whether our space belongs to one of these kinds or not.\r\nThus Euclid fails entirely to prove his point in the very first\r\nproposition. As he is certainly not an easy author, and is terribly\r\nlong-winded, he has no longer any but an historical interest. Under\r\nthese circumstances, it is nothing less than a \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_95\" id=\"Page_95\"\u003e[95]\u003c/a\u003e\u003c/span\u003escandal that he should\r\nstill be taught to boys in England.\u003ca name=\"FNanchor_17_17\" id=\"FNanchor_17_17\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_17_17\" class=\"fnanchor\"\u003e[17]\u003c/a\u003e A book should have either\r\nintelligibility or correctness; to combine the two is impossible, but\r\nto lack both is to be unworthy of such a place as Euclid has occupied\r\nin education.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe most remarkable result of modern methods in mathematics is the\r\nimportance of symbolic logic and of rigid formalism. Mathematicians,\r\nunder the influence of Weierstrass, have shown in modern times a care\r\nfor accuracy, and an aversion to slipshod reasoning, such as had not\r\nbeen known among them previously since the time of the Greeks. The\r\ngreat inventions of the seventeenth century\u0026mdash;Analytical Geometry and\r\nthe Infinitesimal Calculus\u0026mdash;were so fruitful in new results that\r\nmathematicians had neither time nor inclination to examine their\r\nfoundations. Philosophers, who should have taken up the task, had too\r\nlittle mathematical ability to invent the new branches of mathematics\r\nwhich have now been found necessary for any adequate discussion. Thus\r\nmathematicians were only awakened from their \"dogmatic slumbers\" when\r\nWeierstrass and his followers showed that many of their most cherished\r\npropositions are in general false. Macaulay, contrasting the certainty\r\nof mathematics with the uncertainty of philosophy, asks who ever heard\r\nof a reaction against Taylor\u0027s theorem? If he had lived now, he\r\nhimself might have heard of such a reaction, for this is precisely one\r\nof the theorems which modern investigations have overthrown. Such rude\r\nshocks to mathematical faith have produced that love of formalism\r\nwhich appears, to those who are ignorant of its motive, to be mere\r\noutrageous pedantry.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_96\" id=\"Page_96\"\u003e[96]\u003c/a\u003e\u003c/span\u003eThe proof that all pure mathematics, including Geometry, is nothing\r\nbut formal logic, is a fatal blow to the Kantian philosophy. Kant,\r\nrightly perceiving that Euclid\u0027s propositions could not be deduced\r\nfrom Euclid\u0027s axioms without the help of the figures, invented a\r\ntheory of knowledge to account for this fact; and it accounted so\r\nsuccessfully that, when the fact is shown to be a mere defect in\r\nEuclid, and not a result of the nature of geometrical reasoning,\r\nKant\u0027s theory also has to be abandoned. The whole doctrine of \u003ci\u003ea\r\npriori\u003c/i\u003e intuitions, by which Kant explained the possibility of pure\r\nmathematics, is wholly inapplicable to mathematics in its present\r\nform. The Aristotelian doctrines of the schoolmen come nearer in\r\nspirit to the doctrines which modern mathematics inspire; but the\r\nschoolmen were hampered by the fact that their formal logic was very\r\ndefective, and that the philosophical logic based upon the syllogism\r\nshowed a corresponding narrowness. What is now required is to give the\r\ngreatest possible development to mathematical logic, to allow to the\r\nfull the importance of relations, and then to found upon this secure\r\nbasis a new philosophical logic, which may hope to borrow some of the\r\nexactitude and certainty of its mathematical foundation. If this can\r\nbe successfully accomplished, there is every reason to hope that the\r\nnear future will be as great an epoch in pure philosophy as the\r\nimmediate past has been in the principles of mathematics. Great\r\ntriumphs inspire great hopes; and pure thought may achieve, within our\r\ngeneration, such results as will place our time, in this respect, on a\r\nlevel with the greatest age of Greece.\u003ca name=\"FNanchor_18_18\" id=\"FNanchor_18_18\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_18_18\" class=\"fnanchor\"\u003e[18]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\u003chr style=\"width: 15%;\" /\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003ch4\u003eFOOTNOTES:\u003c/h4\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_11_11\" id=\"Footnote_11_11\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_11_11\"\u003e\u003cspan class=\"label\"\u003e[11]\u003c/span\u003e\u003c/a\u003e This subject is due in the main to Mr. C.S. Peirce.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_12_12\" id=\"Footnote_12_12\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_12_12\"\u003e\u003cspan class=\"label\"\u003e[12]\u003c/span\u003e\u003c/a\u003e I ought to have added Frege, but his writings were\r\nunknown to me when this article was written. [Note added in 1917.]\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_13_13\" id=\"Footnote_13_13\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_13_13\"\u003e\u003cspan class=\"label\"\u003e[13]\u003c/span\u003e\u003c/a\u003e Professor of Mathematics in the University of Berlin. He\r\ndied in 1897.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_14_14\" id=\"Footnote_14_14\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_14_14\"\u003e\u003cspan class=\"label\"\u003e[14]\u003c/span\u003e\u003c/a\u003e [Note added in 1917.] Although some infinite numbers are\r\ngreater than some others, it cannot be proved that of any two infinite\r\nnumbers one must be the greater.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_15_15\" id=\"Footnote_15_15\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_15_15\"\u003e\u003cspan class=\"label\"\u003e[15]\u003c/span\u003e\u003c/a\u003e Cantor was not guilty of a fallacy on this point. His\r\nproof that there is no greatest number is valid. The solution of the\r\npuzzle is complicated and depends upon the theory of types, which is\r\nexplained in \u003ci\u003ePrincipia Mathematica\u003c/i\u003e, Vol. I (Camb. Univ. Press,\r\n1910). [Note added in 1917.]\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_16_16\" id=\"Footnote_16_16\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_16_16\"\u003e\u003cspan class=\"label\"\u003e[16]\u003c/span\u003e\u003c/a\u003e This must not be regarded as a historically correct\r\naccount of what Zeno actually had in mind. It is a new argument for\r\nhis conclusion, not the argument which influenced him. On this point,\r\nsee e.g. C.D. Broad, \"Note on Achilles and the Tortoise,\" \u003ci\u003eMind\u003c/i\u003e,\r\nN.S., Vol. XXII, pp. 318-19. Much valuable work on the interpretation\r\nof Zeno has been done since this article was written. [Note added in\r\n1917.]\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_17_17\" id=\"Footnote_17_17\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_17_17\"\u003e\u003cspan class=\"label\"\u003e[17]\u003c/span\u003e\u003c/a\u003e Since the above was written, he has ceased to be used as\r\na textbook. But I fear many of the books now used are so bad that the\r\nchange is no great improvement. [Note added in 1917.]\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_18_18\" id=\"Footnote_18_18\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_18_18\"\u003e\u003cspan class=\"label\"\u003e[18]\u003c/span\u003e\u003c/a\u003e The greatest age of Greece was brought to an end by the\r\nPeloponnesian War. [Note added in 1917.]\u003c/p\u003e\u003c/div\u003e\r\n\r\n\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003ca name=\"VI\" id=\"VI\"\u003e\u003c/a\u003e\u003chr /\u003e\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_97\" id=\"Page_97\"\u003e[97]\u003c/a\u003e\u003c/span\u003e\u003cbr /\u003e\r\n\r\n\u003ch3\u003eVI\u003cspan class=\"totoc\"\u003e\u003ca href=\"#toc\"\u003eToC\u003c/a\u003e\u003c/span\u003e\u003c/h3\u003e\r\n\r\n\u003ch4\u003eON SCIENTIFIC METHOD IN PHILOSOPHY\u003c/h4\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003cp\u003eWhen we try to ascertain the motives which have led men to the\r\ninvestigation of philosophical questions, we find that, broadly\r\nspeaking, they can be divided into two groups, often antagonistic, and\r\nleading to very divergent systems. These two groups of motives are, on\r\nthe one hand, those derived from religion and ethics, and, on the\r\nother hand, those derived from science. Plato, Spinoza, and Hegel may\r\nbe taken as typical of the philosophers whose interests are mainly\r\nreligious and ethical, while Leibniz, Locke, and Hume may be taken as\r\nrepresentatives of the scientific wing. In Aristotle, Descartes,\r\nBerkeley, and Kant we find both groups of motives strongly present.\u003c/p\u003e\r\n\r\n\u003cp\u003eHerbert Spencer, in whose honour we are assembled to-day, would\r\nnaturally be classed among scientific philosophers: it was mainly from\r\nscience that he drew his data, his formulation of problems, and his\r\nconception of method. But his strong religious sense is obvious in\r\nmuch of his writing, and his ethical pre-occupations are what make him\r\nvalue the conception of evolution\u0026mdash;that conception in which, as a\r\nwhole generation has believed, science and morals are to be united in\r\nfruitful and indissoluble marriage.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is my belief that the ethical and religious motives \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_98\" id=\"Page_98\"\u003e[98]\u003c/a\u003e\u003c/span\u003ein spite of\r\nthe splendidly imaginative systems to which they have given rise, have\r\nbeen on the whole a hindrance to the progress of philosophy, and ought\r\nnow to be consciously thrust aside by those who wish to discover\r\nphilosophical truth. Science, originally, was entangled in similar\r\nmotives, and was thereby hindered in its advances. It is, I maintain,\r\nfrom science, rather than from ethics and religion, that philosophy\r\nshould draw its inspiration.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut there are two different ways in which a philosophy may seek to\r\nbase itself upon science. It may emphasise the most general \u003ci\u003eresults\u003c/i\u003e\r\nof science, and seek to give even greater generality and unity to\r\nthese results. Or it may study the \u003ci\u003emethods\u003c/i\u003e of science, and seek to\r\napply these methods, with the necessary adaptations, to its own\r\npeculiar province. Much philosophy inspired by science has gone astray\r\nthrough preoccupation with the \u003ci\u003eresults\u003c/i\u003e momentarily supposed to have\r\nbeen achieved. It is not results, but \u003ci\u003emethods\u003c/i\u003e that can be\r\ntransferred with profit from the sphere of the special sciences to the\r\nsphere of philosophy. What I wish to bring to your notice is the\r\npossibility and importance of applying to philosophical problems\r\ncertain broad principles of method which have been found successful in\r\nthe study of scientific questions.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe opposition between a philosophy guided by scientific method and a\r\nphilosophy dominated by religious and ethical ideas may be illustrated\r\nby two notions which are very prevalent in the works of philosophers,\r\nnamely the notion of \u003ci\u003ethe universe\u003c/i\u003e, and the notion of \u003ci\u003egood and\r\nevil\u003c/i\u003e. A philosopher is expected to tell us something about the nature\r\nof the universe as a whole, and to give grounds for either optimism or\r\npessimism. Both these expectations seem to me mistaken. I believe the\r\nconception of \"the universe\" to be, as its etymology indicates, a\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_99\" id=\"Page_99\"\u003e[99]\u003c/a\u003e\u003c/span\u003emere relic of pre-Copernican astronomy: and I believe the question of\r\noptimism and pessimism to be one which the philosopher will regard as\r\noutside his scope, except, possibly, to the extent of maintaining that\r\nit is insoluble.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn the days before Copernicus, the conception of the \"universe\" was\r\ndefensible on scientific grounds: the diurnal revolution of the\r\nheavenly bodies bound them together as all parts of one system, of\r\nwhich the earth was the centre. Round this apparent scientific fact,\r\nmany human desires rallied: the wish to believe Man important in the\r\nscheme of things, the theoretical desire for a comprehensive\r\nunderstanding of the Whole, the hope that the course of nature might\r\nbe guided by some sympathy with our wishes. In this way, an ethically\r\ninspired system of metaphysics grew up, whose anthropocentrism was\r\napparently warranted by the geocentrism of astronomy. When Copernicus\r\nswept away the astronomical basis of this system of thought, it had\r\ngrown so familiar, and had associated itself so intimately with men\u0027s\r\naspirations, that it survived with scarcely diminished force\u0026mdash;survived\r\neven Kant\u0027s \"Copernican revolution,\" and is still now the unconscious\r\npremiss of most metaphysical systems.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe oneness of the world is an almost undiscussed postulate of most\r\nmetaphysics. \"Reality is not merely one and self-consistent, but is a\r\nsystem of reciprocally determinate parts\"\u003ca name=\"FNanchor_19_19\" id=\"FNanchor_19_19\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_19_19\" class=\"fnanchor\"\u003e[19]\u003c/a\u003e\u0026mdash;such a statement would\r\npass almost unnoticed as a mere truism. Yet I believe that it embodies\r\na failure to effect thoroughly the \"Copernican revolution,\" and that\r\nthe apparent oneness of the world is merely the oneness of what is\r\nseen by a single spectator or apprehended by a single mind. The\r\nCritical Philosophy, although it intended to emphasise the subjective\r\nelement \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_100\" id=\"Page_100\"\u003e[100]\u003c/a\u003e\u003c/span\u003ein many apparent characteristics of the world, yet, by\r\nregarding the world in itself as unknowable, so concentrated attention\r\nupon the subjective representation that its subjectivity was soon\r\nforgotten. Having recognised the categories as the work of the mind,\r\nit was paralysed by its own recognition, and abandoned in despair the\r\nattempt to undo the work of subjective falsification. In part, no\r\ndoubt, its despair was well founded, but not, I think, in any absolute\r\nor ultimate sense. Still less was it a ground for rejoicing, or for\r\nsupposing that the nescience to which it ought to have given rise\r\ncould be legitimately exchanged for a metaphysical dogmatism.\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\u003ch4\u003eI\u003c/h4\u003e\r\n\r\n\u003cp\u003eAs regards our present question, namely, the question of the unity of\r\nthe world, the right method, as I think, has been indicated by William\r\nJames.\u003ca name=\"FNanchor_20_20\" id=\"FNanchor_20_20\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_20_20\" class=\"fnanchor\"\u003e[20]\u003c/a\u003e \"Let us now turn our backs upon ineffable or unintelligible\r\nways of accounting for the world\u0027s oneness, and inquire whether,\r\ninstead of being a principle, the \u0027oneness\u0027 affirmed may not merely be\r\na name like \u0027substance\u0027 descriptive of the fact that certain \u003ci\u003especific\r\nand verifiable connections\u003c/i\u003e are found among the parts of the\r\nexperiential flux…. We can easily conceive of things that shall have\r\nno connection whatever with each other. We may assume them to inhabit\r\ndifferent times and spaces, as the dreams of different persons do even\r\nnow. They may be so unlike and incommensurable, and so inert towards\r\none another, as never to jostle or interfere. Even now there may\r\nactually be whole universes so disparate from ours that we who know\r\nours have no means of perceiving that they exist. We conceive their\r\ndiversity, however; and by that \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_101\" id=\"Page_101\"\u003e[101]\u003c/a\u003e\u003c/span\u003efact the whole lot of them form what\r\nis known in logic as \u0027a universe of discourse.\u0027 To form a universe of\r\ndiscourse argues, as this example shows, no further kind of connexion.\r\nThe importance attached by certain monistic writers to the fact that\r\nany chaos may become a universe by merely being named, is to me\r\nincomprehensible.\" We are thus left with two kinds of unity in the\r\nexperienced world; the one what we may call the epistemological unity,\r\ndue merely to the fact that my experienced world is what \u003ci\u003eone\u003c/i\u003e\r\nexperience selects from the sum total of existence: the other that\r\ntentative and partial unity exhibited in the prevalence of scientific\r\nlaws in those portions of the world which science has hitherto\r\nmastered. Now a generalisation based upon either of these kinds of\r\nunity would be fallacious. That the things which we experience have\r\nthe common property of being experienced by us is a truism from which\r\nobviously nothing of importance can be deducible: it is clearly\r\nfallacious to draw from the fact that whatever we experience is\r\nexperienced the conclusion that therefore everything must be\r\nexperienced. The generalisation of the second kind of unity, namely,\r\nthat derived from scientific laws, would be equally fallacious, though\r\nthe fallacy is a trifle less elementary. In order to explain it let us\r\nconsider for a moment what is called the reign of law. People often\r\nspeak as though it were a remarkable fact that the physical world is\r\nsubject to invariable laws. In fact, however, it is not easy to see\r\nhow such a world could fail to obey general laws. Taking any arbitrary\r\nset of points in space, there is a function of the time corresponding\r\nto these points, i.e. expressing the motion of a particle which\r\ntraverses these points: this function may be regarded as a general law\r\nto which the behaviour of such a particle is subject. Taking all such\r\nfunctions for \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_102\" id=\"Page_102\"\u003e[102]\u003c/a\u003e\u003c/span\u003eall the particles in the universe, there will be\r\ntheoretically some one formula embracing them all, and this formula\r\nmay be regarded as the single and supreme law of the spatio-temporal\r\nworld. Thus what is surprising in physics is not the existence of\r\ngeneral laws, but their extreme simplicity. It is not the uniformity\r\nof nature that should surprise us, for, by sufficient analytic\r\ningenuity, any conceivable course of nature might be shown to exhibit\r\nuniformity. What should surprise us is the fact that the uniformity is\r\nsimple enough for us to be able to discover it. But it is just this\r\ncharacteristic of simplicity in the laws of nature hitherto discovered\r\nwhich it would be fallacious to generalise, for it is obvious that\r\nsimplicity has been a part cause of their discovery, and can,\r\ntherefore, give no ground for the supposition that other undiscovered\r\nlaws are equally simple.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe fallacies to which these two kinds of unity have given rise\r\nsuggest a caution as regards all use in philosophy of general\r\n\u003ci\u003eresults\u003c/i\u003e that science is supposed to have achieved. In the first\r\nplace, in generalising these results beyond past experience, it is\r\nnecessary to examine very carefully whether there is not some reason\r\nmaking it more probable that these results should hold of all that has\r\nbeen experienced than that they should hold of things universally. The\r\nsum total of what is experienced by mankind is a selection from the\r\nsum total of what exists, and any general character exhibited by this\r\nselection may be due to the manner of selecting rather than to the\r\ngeneral character of that from which experience selects. In the second\r\nplace, the most general results of science are the least certain and\r\nthe most liable to be upset by subsequent research. In utilizing these\r\nresults as the basis of a philosophy, we sacrifice the most valuable\r\nand remarkable characteristic of scientific method, \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_103\" id=\"Page_103\"\u003e[103]\u003c/a\u003e\u003c/span\u003enamely, that,\r\nalthough almost everything in science is found sooner or later to\r\nrequire some correction, yet this correction is almost always such as\r\nto leave untouched, or only slightly modified, the greater part of the\r\nresults which have been deduced from the premiss subsequently\r\ndiscovered to be faulty. The prudent man of science acquires a certain\r\ninstinct as to the kind of uses which may be made of present\r\nscientific beliefs without incurring the danger of complete and utter\r\nrefutation from the modifications likely to be introduced by\r\nsubsequent discoveries. Unfortunately the use of scientific\r\ngeneralisations of a sweeping kind as the basis of philosophy is just\r\nthat kind of use which an instinct of scientific caution would avoid,\r\nsince, as a rule, it would only lead to true results if the\r\ngeneralisation upon which it is based stood in \u003ci\u003eno\u003c/i\u003e need of\r\ncorrection.\u003c/p\u003e\r\n\r\n\u003cp\u003eWe may illustrate these general considerations by means of two\r\nexamples, namely, the conservation of energy and the principle of\r\nevolution.\u003c/p\u003e\r\n\r\n\u003cp\u003e(1) Let us begin with the conservation of energy, or, as Herbert\r\nSpencer used to call it, the persistence of force. He says:\u003ca name=\"FNanchor_21_21\" id=\"FNanchor_21_21\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_21_21\" class=\"fnanchor\"\u003e[21]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cdiv class=\"block\"\u003e\u003cp\u003e\"Before taking a first step in the rational interpretation of\r\nEvolution, it is needful to recognise, not only the facts that\r\nMatter is indestructible and Motion continuous, but also the fact\r\nthat Force persists. An attempt to assign the \u003ci\u003ecauses\u003c/i\u003e of\r\nEvolution would manifestly be absurd if that agency to which the\r\nmetamorphosis in general and in detail is due, could either come\r\ninto existence or cease to exist. The succession of phenomena\r\nwould in such case be altogether arbitrary, and deductive Science\r\nimpossible.\"\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_104\" id=\"Page_104\"\u003e[104]\u003c/a\u003e\u003c/span\u003eThis paragraph illustrates the kind of way in which the philosopher is\r\ntempted to give an air of absoluteness and necessity to empirical\r\ngeneralisations, of which only the approximate truth in the regions\r\nhitherto investigated can be guaranteed by the unaided methods of\r\nscience. It is very often said that the persistence of something or\r\nother is a necessary presupposition of all scientific investigation,\r\nand this presupposition is then thought to be exemplified in some\r\nquantity which physics declares to be constant. There are here, as it\r\nseems to me, three distinct errors. First, the detailed scientific\r\ninvestigation of nature does not \u003ci\u003epresuppose\u003c/i\u003e any such general laws as\r\nits results are found to verify. Apart from particular observations,\r\nscience need presuppose nothing except the general principles of\r\nlogic, and these principles are not laws of nature, for they are\r\nmerely hypothetical, and apply not only to the actual world but to\r\nwhatever is \u003ci\u003epossible\u003c/i\u003e. The second error consists in the\r\nidentification of a constant quantity with a persistent entity. Energy\r\nis a certain function of a physical system, but is not a thing or\r\nsubstance persisting throughout the changes of the system. The same is\r\ntrue of mass, in spite of the fact that mass has often been defined as\r\n\u003ci\u003equantity of matter\u003c/i\u003e. The whole conception of quantity, involving, as\r\nit does, numerical measurement based largely upon conventions, is far\r\nmore artificial, far more an embodiment of mathematical convenience,\r\nthan is commonly believed by those who philosophise on physics. Thus\r\neven if (which I cannot for a moment admit) the persistence of some\r\nentity were among the necessary postulates of science, it would be a\r\nsheer error to infer from this the constancy of any physical quantity,\r\nor the \u003ci\u003ea priori\u003c/i\u003e necessity of any such constancy which may be\r\nempirically discovered. In the third place, it \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_105\" id=\"Page_105\"\u003e[105]\u003c/a\u003e\u003c/span\u003ehas become more and\r\nmore evident with the progress of physics that large generalisations,\r\nsuch as the conservation of energy or mass, are far from certain and\r\nare very likely only approximate. Mass, which used to be regarded as\r\nthe most indubitable of physical quantities, is now generally believed\r\nto vary according to velocity, and to be, in fact, a vector quantity\r\nwhich at a given moment is different in different directions. The\r\ndetailed conclusions deduced from the supposed constancy of mass for\r\nsuch motions as used to be studied in physics will remain very nearly\r\nexact, and therefore over the field of the older investigations very\r\nlittle modification of the older results is required. But as soon as\r\nsuch a principle as the conservation of mass or of energy is erected\r\ninto a universal \u003ci\u003ea priori\u003c/i\u003e law, the slightest failure in absolute\r\nexactness is fatal, and the whole philosophic structure raised upon\r\nthis foundation is necessarily ruined. The prudent philosopher,\r\ntherefore, though he may with advantage study the methods of physics,\r\nwill be very chary of basing anything upon what happen at the moment\r\nto be the most general results apparently obtained by those methods.\u003c/p\u003e\r\n\r\n\u003cp\u003e(2) The philosophy of evolution, which was to be our second example,\r\nillustrates the same tendency to hasty generalisation, and also\r\nanother sort, namely, the undue preoccupation with ethical notions.\r\nThere are two kinds of evolutionist philosophy, of which both Hegel\r\nand Spencer represent the older and less radical kind, while\r\nPragmatism and Bergson represent the more modern and revolutionary\r\nvariety. But both these sorts of evolutionism have in common the\r\nemphasis on \u003ci\u003eprogress\u003c/i\u003e, that is, upon a continual change from the\r\nworse to the better, or from the simpler to the more complex. It\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_106\" id=\"Page_106\"\u003e[106]\u003c/a\u003e\u003c/span\u003ewould be unfair to attribute to Hegel any scientific motive or\r\nfoundation, but all the other evolutionists, including Hegel\u0027s modern\r\ndisciples, have derived their impetus very largely from the history of\r\nbiological development. To a philosophy which derives a law of\r\nuniversal progress from this history there are two objections. First,\r\nthat this history itself is concerned with a very small selection of\r\nfacts confined to an infinitesimal fragment of space and time, and\r\neven on scientific grounds probably not an average sample of events in\r\nthe world at large. For we know that decay as well as growth is a\r\nnormal occurrence in the world. An extra-terrestrial philosopher, who\r\nhad watched a single youth up to the age of twenty-one and had never\r\ncome across any other human being, might conclude that it is the\r\nnature of human beings to grow continually taller and wiser in an\r\nindefinite progress towards perfection; and this generalisation would\r\nbe just as well founded as the generalisation which evolutionists base\r\nupon the previous history of this planet. Apart, however, from this\r\nscientific objection to evolutionism, there is another, derived from\r\nthe undue admixture of ethical notions in the very idea of progress\r\nfrom which evolutionism derives its charm. Organic life, we are told,\r\nhas developed gradually from the protozoon to the philosopher, and\r\nthis development, we are assured, is indubitably an advance.\r\nUnfortunately it is the philosopher, not the protozoon, who gives us\r\nthis assurance, and we can have no security that the impartial\r\noutsider would agree with the philosopher\u0027s self-complacent\r\nassumption. This point has been illustrated by the philosopher Chuang\r\nTz\u0026#365; in the following instructive anecdote:\u003c/p\u003e\r\n\r\n\u003cdiv class=\"block\"\u003e\u003cp\u003e\"The Grand Augur, in his ceremonial robes, approached the shambles\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_107\" id=\"Page_107\"\u003e[107]\u003c/a\u003e\u003c/span\u003e\r\nand thus addressed the pigs: \u0027How can you object to die? I shall\r\nfatten you for three months. I shall discipline myself for ten\r\ndays and fast for three. I shall strew fine grass, and place you\r\nbodily upon a carved sacrificial dish. Does not this satisfy you?\u0027\u003c/p\u003e\r\n\r\n\u003cp\u003eThen, speaking from the pigs\u0027 point of view, he continued: \u0027It is\r\nbetter, perhaps, after all, to live on bran and escape the\r\nshambles….\u0027\u003c/p\u003e\r\n\r\n\u003cp\u003e\u0027But then,\u0027 added he, speaking from his own point of view, \u0027to\r\nenjoy honour when alive one would readily die on a war-shield or\r\nin the headsman\u0027s basket.\u0027\u003c/p\u003e\r\n\r\n\u003cp\u003eSo he rejected the pigs\u0027 point of view and adopted his own point\r\nof view. In what sense, then, was he different from the pigs?\"\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cp\u003eI much fear that the evolutionists too often resemble the Grand Augur\r\nand the pigs.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe ethical element which has been prominent in many of the most\r\nfamous systems of philosophy is, in my opinion, one of the most\r\nserious obstacles to the victory of scientific method in the\r\ninvestigation of philosophical questions. Human ethical notions, as\r\nChuang Tz\u0026#365; perceived, are essentially anthropocentric, and involve,\r\nwhen used in metaphysics, an attempt, however veiled, to legislate for\r\nthe universe on the basis of the present desires of men. In this way\r\nthey interfere with that receptivity to fact which is the essence of\r\nthe scientific attitude towards the world. To regard ethical notions\r\nas a key to the understanding of the world is essentially\r\npre-Copernican. It is to make man, with the hopes and ideals which he\r\nhappens to have at the present moment, the centre of the universe and\r\nthe interpreter of its supposed aims and purposes. Ethical metaphysics\r\nis fundamentally an attempt, however disguised, to \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_108\" id=\"Page_108\"\u003e[108]\u003c/a\u003e\u003c/span\u003egive legislative\r\nforce to our own wishes. This may, of course, be questioned, but I\r\nthink that it is confirmed by a consideration of the way in which\r\nethical notions arise. Ethics is essentially a product of the\r\ngregarious instinct, that is to say, of the instinct to co-operate\r\nwith those who are to form our own group against those who belong to\r\nother groups. Those who belong to our own group are good; those who\r\nbelong to hostile groups are wicked. The ends which are pursued by our\r\nown group are desirable ends, the ends pursued by hostile groups are\r\nnefarious. The subjectivity of this situation is not apparent to the\r\ngregarious animal, which feels that the general principles of justice\r\nare on the side of its own herd. When the animal has arrived at the\r\ndignity of the metaphysician, it invents ethics as the embodiment of\r\nits belief in the justice of its own herd. So the Grand Augur invokes\r\nethics as the justification of Augurs in their conflicts with pigs.\r\nBut, it may be said, this view of ethics takes no account of such\r\ntruly ethical notions as that of self-sacrifice. This, however, would\r\nbe a mistake. The success of gregarious animals in the struggle for\r\nexistence depends upon co-operation within the herd, and co-operation\r\nrequires sacrifice, to some extent, of what would otherwise be the\r\ninterest of the individual. Hence arises a conflict of desires and\r\ninstincts, since both self-preservation and the preservation of the\r\nherd are biological ends to the individual. Ethics is in origin the\r\nart of recommending to others the sacrifices required for co-operation\r\nwith oneself. Hence, by reflexion, it comes, through the operation of\r\nsocial justice, to recommend sacrifices by oneself, but all ethics,\r\nhowever refined, remains more or less subjective. Even vegetarians do\r\nnot hesitate, for example, to save the life of a man in a fever,\r\nalthough in doing so they destroy the lives of many millions of\r\nm\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_109\" id=\"Page_109\"\u003e[109]\u003c/a\u003e\u003c/span\u003eicrobes. The view of the world taken by the philosophy derived from\r\nethical notions is thus never impartial and therefore never fully\r\nscientific. As compared with science, it fails to achieve the\r\nimaginative liberation from self which is necessary to such\r\nunderstanding of the world as man can hope to achieve, and the\r\nphilosophy which it inspires is always more or less parochial, more or\r\nless infected with the prejudices of a time and a place.\u003c/p\u003e\r\n\r\n\u003cp\u003eI do not deny the importance or value, within its own sphere, of the\r\nkind of philosophy which is inspired by ethical notions. The ethical\r\nwork of Spinoza, for example, appears to me of the very highest\r\nsignificance, but what is valuable in such work is not any\r\nmetaphysical theory as to the nature of the world to which it may give\r\nrise, nor indeed anything which can be proved or disproved by\r\nargument. What is valuable is the indication of some new way of\r\nfeeling towards life and the world, some way of feeling by which our\r\nown existence can acquire more of the characteristics which we must\r\ndeeply desire. The value of such work, however immeasurable it is,\r\nbelongs with practice and not with theory. Such theoretic importance\r\nas it may possess is only in relation to human nature, not in relation\r\nto the world at large. The scientific philosophy, therefore, which\r\naims only at understanding the world and not directly at any other\r\nimprovement of human life, cannot take account of ethical notions\r\nwithout being turned aside from that submission to fact which is the\r\nessence of the scientific temper.\u003c/p\u003e\r\n\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_110\" id=\"Page_110\"\u003e[110]\u003c/a\u003e\u003c/span\u003e\u003cbr /\u003e\r\n\r\n\u003ch4\u003eII\u003c/h4\u003e\r\n\r\n\u003cp\u003eIf the notion of the universe and the notion of good and evil are\r\nextruded from scientific philosophy, it may be asked what specific\r\nproblems remain for the philosopher as opposed to the man of science?\r\nIt would be difficult to give a precise answer to this question, but\r\ncertain characteristics may be noted as distinguishing the province of\r\nphilosophy from that of the special sciences.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn the first place a philosophical proposition must be general. It\r\nmust not deal specially with things on the surface of the earth, or\r\nwith the solar system, or with any other portion of space and time. It\r\nis this need of generality which has led to the belief that philosophy\r\ndeals with the universe as a whole. I do not believe that this belief\r\nis justified, but I do believe that a philosophical proposition must\r\nbe applicable to everything that exists or may exist. It might be\r\nsupposed that this admission would be scarcely distinguishable from\r\nthe view which I wish to reject. This, however, would be an error, and\r\nan important one. The traditional view would make the universe itself\r\nthe subject of various predicates which could not be applied to any\r\nparticular thing in the universe, and the ascription of such peculiar\r\npredicates to the universe would be the special business of\r\nphilosophy. I maintain, on the contrary, that there are no\r\npropositions of which the \"universe\" is the subject; in other words,\r\nthat there is no such thing as the \"universe.\" What I do maintain is\r\nthat there are general propositions which may be asserted of each\r\nindividual thing, such as the propositions of logic. This does not\r\ninvolve that all the things there are form a whole which could be\r\nregarded as another thing and be made \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_111\" id=\"Page_111\"\u003e[111]\u003c/a\u003e\u003c/span\u003ethe subject of predicates. It\r\ninvolves only the assertion that there are properties which belong to\r\neach separate thing, not that there are properties belonging to the\r\nwhole of things collectively. The philosophy which I wish to advocate\r\nmay be called logical atomism or absolute pluralism, because, while\r\nmaintaining that there are many things, it denies that there is a\r\nwhole composed of those things. We shall see, therefore, that\r\nphilosophical propositions, instead of being concerned with the whole\r\nof things collectively, are concerned with all things distributively;\r\nand not only must they be concerned with all things, but they must be\r\nconcerned with such properties of all things as do not depend upon the\r\naccidental nature of the things that there happen to be, but are true\r\nof any possible world, independently of such facts as can only be\r\ndiscovered by our senses.\u003c/p\u003e\r\n\r\n\u003cp\u003eThis brings us to a second characteristic of philosophical\r\npropositions, namely, that they must be \u003ci\u003ea priori\u003c/i\u003e. A philosophical\r\nproposition must be such as can be neither proved nor disproved by\r\nempirical evidence. Too often we find in philosophical books arguments\r\nbased upon the course of history, or the convolutions of the brain, or\r\nthe eyes of shell-fish. Special and accidental facts of this kind are\r\nirrelevant to philosophy, which must make only such assertions as\r\nwould be equally true however the actual world were constituted.\u003c/p\u003e\r\n\r\n\u003cp\u003eWe may sum up these two characteristics of philosophical propositions\r\nby saying that \u003ci\u003ephilosophy is the science of the possible\u003c/i\u003e. But this\r\nstatement unexplained is liable to be misleading, since it may be\r\nthought that the possible is something other than the general, whereas\r\nin fact the two are indistinguishable.\u003c/p\u003e\r\n\r\n\u003cp\u003ePhilosophy, if what has been said is correct, becomes\r\nindistinguishable from logic as that word has now come \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_112\" id=\"Page_112\"\u003e[112]\u003c/a\u003e\u003c/span\u003eto be used.\r\nThe study of logic consists, broadly speaking, of two not very sharply\r\ndistinguished portions. On the one hand it is concerned with those\r\ngeneral statements which can be made concerning everything without\r\nmentioning any one thing or predicate or relation, such for example as\r\n\"if \u003ci\u003ex\u003c/i\u003e is a member of the class \u0026alpha; and every member of \u0026alpha;\r\nis a member of \u0026beta;, then \u003ci\u003ex\u003c/i\u003e is a member of the class\r\n\u0026beta;, whatever \u003ci\u003ex\u003c/i\u003e, \u0026alpha;, and \u0026beta; may\r\nbe.\" On the other hand, it is concerned with the analysis and\r\nenumeration of logical \u003ci\u003eforms\u003c/i\u003e, i.e. with the kinds of propositions\r\nthat may occur, with the various types of facts, and with the\r\nclassification of the constituents of facts. In this way logic\r\nprovides an inventory of possibilities, a repertory of abstractly\r\ntenable hypotheses.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt might be thought that such a study would be too vague and too\r\ngeneral to be of any very great importance, and that, if its problems\r\nbecame at any point sufficiently definite, they would be merged in the\r\nproblems of some special science. It appears, however, that this is\r\nnot the case. In some problems, for example, the analysis of space and\r\ntime, the nature of perception, or the theory of judgment, the\r\ndiscovery of the logical form of the facts involved is the hardest\r\npart of the work and the part whose performance has been most lacking\r\nhitherto. It is chiefly for want of the right logical hypothesis that\r\nsuch problems have hitherto been treated in such an unsatisfactory\r\nmanner, and have given rise to those contradictions or antinomies in\r\nwhich the enemies of reason among philosophers have at all times\r\ndelighted.\u003c/p\u003e\r\n\r\n\u003cp\u003eBy concentrating attention upon the investigation of logical forms, it\r\nbecomes possible at last for philosophy to deal with its problems\r\npiecemeal, and to obtain, as the sciences do, such partial and\r\nprobably not wholly correct results as subsequent investigation can\r\nutilise \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_113\" id=\"Page_113\"\u003e[113]\u003c/a\u003e\u003c/span\u003eeven while it supplements and improves them. Most\r\nphilosophies hitherto have been constructed all in one block, in such\r\na way that, if they were not wholly correct, they were wholly\r\nincorrect, and could not be used as a basis for further\r\ninvestigations. It is chiefly owing to this fact that philosophy,\r\nunlike science, has hitherto been unprogressive, because each original\r\nphilosopher has had to begin the work again from the beginning,\r\nwithout being able to accept anything definite from the work of his\r\npredecessors. A scientific philosophy such as I wish to recommend will\r\nbe piecemeal and tentative like other sciences; above all, it will be\r\nable to invent hypotheses which, even if they are not wholly true,\r\nwill yet remain fruitful after the necessary corrections have been\r\nmade. This possibility of successive approximations to the truth is,\r\nmore than anything else, the source of the triumphs of science, and to\r\ntransfer this possibility to philosophy is to ensure a progress in\r\nmethod whose importance it would be almost impossible to exaggerate.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe essence of philosophy as thus conceived is analysis, not\r\nsynthesis. To build up systems of the world, like Heine\u0027s German\r\nprofessor who knit together fragments of life and made an intelligible\r\nsystem out of them, is not, I believe, any more feasible than the\r\ndiscovery of the philosopher\u0027s stone. What is feasible is the\r\nunderstanding of general forms, and the division of traditional\r\nproblems into a number of separate and less baffling questions.\r\n\"Divide and conquer\" is the maxim of success here as elsewhere.\u003c/p\u003e\r\n\r\n\u003cp\u003eLet us illustrate these somewhat general maxims by examining their\r\napplication to the philosophy of space, for it is only in application\r\nthat the meaning or importance of a method can be understood. Suppose\r\nwe are confronted with the problem of space as presented in \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_114\" id=\"Page_114\"\u003e[114]\u003c/a\u003e\u003c/span\u003eKant\u0027s\r\nTranscendental \u0026AElig;sthetic, and suppose we wish to discover what are the\r\nelements of the problem and what hope there is of obtaining a solution\r\nof them. It will soon appear that three entirely distinct problems,\r\nbelonging to different studies, and requiring different methods for\r\ntheir solution, have been confusedly combined in the supposed single\r\nproblem with which Kant is concerned. There is a problem of logic, a\r\nproblem of physics, and a problem of theory of knowledge. Of these\r\nthree, the problem of logic can be solved exactly and perfectly; the\r\nproblem of physics can probably be solved with as great a degree of\r\ncertainty and as great an approach to exactness as can be hoped in an\r\nempirical region; the problem of theory of knowledge, however, remains\r\nvery obscure and very difficult to deal with. Let us see how these\r\nthree problems arise.\u003c/p\u003e\r\n\r\n\u003cp\u003e(1) The logical problem has arisen through the suggestions of\r\nnon-Euclidean geometry. Given a body of geometrical propositions, it\r\nis not difficult to find a minimum statement of the axioms from which\r\nthis body of propositions can be deduced. It is also not difficult, by\r\ndropping or altering some of these axioms, to obtain a more general or\r\na different geometry, having, from the point of view of pure\r\nmathematics, the same logical coherence and the same title to respect\r\nas the more familiar Euclidean geometry. The Euclidean geometry itself\r\nis true perhaps of actual space (though this is doubtful), but\r\ncertainly of an infinite number of purely arithmetical systems, each\r\nof which, from the point of view of abstract logic, has an equal and\r\nindefeasible right to be called a Euclidean space. Thus space as an\r\nobject of logical or mathematical study loses its uniqueness; not only\r\nare there many kinds of spaces, but there are an infinity of examples\r\nof each kind, \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_115\" id=\"Page_115\"\u003e[115]\u003c/a\u003e\u003c/span\u003ethough it is difficult to find any kind of which the\r\nspace of physics may be an example, and it is impossible to find any\r\nkind of which the space of physics is certainly an example. As an\r\nillustration of one possible logical system of geometry we may\r\nconsider all relations of three terms which are analogous in certain\r\nformal respects to the relation \"between\" as it appears to be in\r\nactual space. A space is then defined by means of one such three-term\r\nrelation. The points of the space are all the terms which have this\r\nrelation to something or other, and their order in the space in\r\nquestion is determined by this relation. The points of one space are\r\nnecessarily also points of other spaces, since there are necessarily\r\nother three-term relations having those same points for their field.\r\nThe space in fact is not determined by the class of its points, but by\r\nthe ordering three-term relation. When enough abstract logical\r\nproperties of such relations have been enumerated to determine the\r\nresulting kind of geometry, say, for example, Euclidean geometry, it\r\nbecomes unnecessary for the pure geometer in his abstract capacity to\r\ndistinguish between the various relations which have all these\r\nproperties. He considers the whole class of such relations, not any\r\nsingle one among them. Thus in studying a given kind of geometry the\r\npure mathematician is studying a certain class of relations defined by\r\nmeans of certain abstract logical properties which take the place of\r\nwhat used to be called axioms. The nature of geometrical \u003ci\u003ereasoning\u003c/i\u003e\r\ntherefore is purely deductive and purely logical; if any special\r\nepistemological peculiarities are to be found in geometry, it must not\r\nbe in the reasoning, but in our knowledge concerning the axioms in\r\nsome given space.\u003c/p\u003e\r\n\r\n\u003cp\u003e(2) The physical problem of space is both more interesting and more\r\ndifficult than the logical problem. \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_116\" id=\"Page_116\"\u003e[116]\u003c/a\u003e\u003c/span\u003eThe physical problem may be\r\nstated as follows: to find in the physical world, or to construct from\r\nphysical materials, a space of one of the kinds enumerated by the\r\nlogical treatment of geometry. This problem derives its difficulty\r\nfrom the attempt to accommodate to the roughness and vagueness of the\r\nreal world some system possessing the logical clearness and exactitude\r\nof pure mathematics. That this can be done with a certain degree of\r\napproximation is fairly evident If I see three people \u003ci\u003eA\u003c/i\u003e, \u003ci\u003eB\u003c/i\u003e, and\r\n\u003ci\u003eC\u003c/i\u003e sitting in a row, I become aware of the fact which may be\r\nexpressed by saying that \u003ci\u003eB\u003c/i\u003e is between \u003ci\u003eA\u003c/i\u003e and \u003ci\u003eC\u003c/i\u003e rather than that\r\n\u003ci\u003eA\u003c/i\u003e is between \u003ci\u003eB\u003c/i\u003e and \u003ci\u003eC\u003c/i\u003e, or \u003ci\u003eC\u003c/i\u003e is between \u003ci\u003eA\u003c/i\u003e and \u003ci\u003eB\u003c/i\u003e. This\r\nrelation of \"between\" which is thus perceived to hold has some of the\r\nabstract logical properties of those three-term relations which, we\r\nsaw, give rise to a geometry, but its properties fail to be exact, and\r\nare not, as empirically given, amenable to the kind of treatment at\r\nwhich geometry aims. In abstract geometry we deal with points,\r\nstraight lines, and planes; but the three people \u003ci\u003eA\u003c/i\u003e, \u003ci\u003eB\u003c/i\u003e, and \u003ci\u003eC\u003c/i\u003e\r\nwhom I see sitting in a row are not exactly points, nor is the row\r\nexactly a straight line. Nevertheless physics, which formally assumes\r\na space containing points, straight lines, and planes, is found\r\nempirically to give results applicable to the sensible world. It must\r\ntherefore be possible to find an interpretation of the points,\r\nstraight lines, and planes of physics in terms of physical data, or at\r\nany rate in terms of data together with such hypothetical additions as\r\nseem least open to question. Since all data suffer from a lack of\r\nmathematical precision through being of a certain size and somewhat\r\nvague in outline, it is plain that if such a notion as that of a point\r\nis to find any application to empirical material, the point must be\r\nneither a datum nor a hypothetical addition to \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_117\" id=\"Page_117\"\u003e[117]\u003c/a\u003e\u003c/span\u003edata, but a\r\n\u003ci\u003econstruction\u003c/i\u003e by means of data with their hypothetical additions. It\r\nis obvious that any hypothetical filling out of data is less dubious\r\nand unsatisfactory when the additions are closely analogous to data\r\nthan when they are of a radically different sort. To assume, for\r\nexample, that objects which we see continue, after we have turned away\r\nour eyes, to be more or less analogous to what they were while we were\r\nlooking, is a less violent assumption than to assume that such objects\r\nare composed of an infinite number of mathematical points. Hence in\r\nthe physical study of the geometry of physical space, points must not\r\nbe assumed \u003ci\u003eab initio\u003c/i\u003e as they are in the logical treatment of\r\ngeometry, but must be constructed as systems composed of data and\r\nhypothetical analogues of data. We are thus led naturally to define a\r\nphysical point as a certain class of those objects which are the\r\nultimate constituents of the physical world. It will be the class of\r\nall those objects which, as one would naturally say, \u003ci\u003econtain\u003c/i\u003e the\r\npoint. To secure a definition giving this result, without previously\r\nassuming that physical objects are composed of points, is an agreeable\r\nproblem in mathematical logic. The solution of this problem and the\r\nperception of its importance are due to my friend Dr. Whitehead. The\r\noddity of regarding a point as a class of physical entities wears off\r\nwith familiarity, and ought in any case not to be felt by those who\r\nmaintain, as practically every one does, that points are mathematical\r\nfictions. The word \"fiction\" is used glibly in such connexions by many\r\nmen who seem not to feel the necessity of explaining how it can come\r\nabout that a fiction can be so useful in the study of the actual world\r\nas the points of mathematical physics have been found to be. By our\r\ndefinition, which regards a point as a class of physical objects, it\r\nis explained both how \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_118\" id=\"Page_118\"\u003e[118]\u003c/a\u003e\u003c/span\u003ethe use of points can lead to important\r\nphysical results, and how we can nevertheless avoid the assumption\r\nthat points are themselves entities in the physical world.\u003c/p\u003e\r\n\r\n\u003cp\u003eMany of the mathematically convenient properties of abstract logical\r\nspaces cannot be either known to belong or known not to belong to the\r\nspace of physics. Such are all the properties connected with\r\ncontinuity. For to know that actual space has these properties would\r\nrequire an infinite exactness of sense-perception. If actual space is\r\ncontinuous, there are nevertheless many possible non-continuous spaces\r\nwhich will be empirically indistinguishable from it; and, conversely,\r\nactual space may be non-continuous and yet empirically\r\nindistinguishable from a possible continuous space. Continuity,\r\ntherefore, though obtainable in the \u003ci\u003ea priori\u003c/i\u003e region of arithmetic,\r\nis not with certainty obtainable in the space or time of the physical\r\nworld: whether these are continuous or not would seem to be a question\r\nnot only unanswered but for ever unanswerable. From the point of view\r\nof philosophy, however, the discovery that a question is unanswerable\r\nis as complete an answer as any that could possibly be obtained. And\r\nfrom the point of view of physics, where no empirical means of\r\ndistinction can be found, there can be no empirical objection to the\r\nmathematically simplest assumption, which is that of continuity.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe subject of the physical theory of space is a very large one,\r\nhitherto little explored. It is associated with a similar theory of\r\ntime, and both have been forced upon the attention of philosophically\r\nminded physicists by the discussions which have raged concerning the\r\ntheory of relativity.\u003c/p\u003e\r\n\r\n\u003cp\u003e(3) The problem with which Kant is concerned in the Transcendental\r\n\u0026AElig;sthetic is primarily the epistemological \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_119\" id=\"Page_119\"\u003e[119]\u003c/a\u003e\u003c/span\u003eproblem: \"How do we come to\r\nhave knowledge of geometry \u003ci\u003ea priori\u003c/i\u003e?\" By the distinction between the\r\nlogical and physical problems of geometry, the bearing and scope of\r\nthis question are greatly altered. Our knowledge of pure geometry is\r\n\u003ci\u003ea priori\u003c/i\u003e but is wholly logical. Our knowledge of physical geometry\r\nis synthetic, but is not \u003ci\u003ea priori\u003c/i\u003e. Our knowledge of pure geometry is\r\nhypothetical, and does not enable us to assert, for example, that the\r\naxiom of parallels is true in the physical world. Our knowledge of\r\nphysical geometry, while it does enable us to assert that this axiom\r\nis approximately verified, does not, owing to the inevitable\r\ninexactitude of observation, enable us to assert that it is verified\r\n\u003ci\u003eexactly\u003c/i\u003e. Thus, with the separation which we have made between pure\r\ngeometry and the geometry of physics, the Kantian problem collapses.\r\nTo the question, \"How is synthetic \u003ci\u003ea priori\u003c/i\u003e knowledge possible?\" we\r\ncan now reply, at any rate so far as geometry is concerned, \"It is not\r\npossible,\" if \"synthetic\" means \"not deducible from logic alone.\" Our\r\nknowledge of geometry, like the rest of our knowledge, is derived\r\npartly from logic, partly from sense, and the peculiar position which\r\nin Kant\u0027s day geometry appeared to occupy is seen now to be a\r\ndelusion. There are still some philosophers, it is true, who maintain\r\nthat our knowledge that the axiom of parallels, for example, is true\r\nof actual space, is not to be accounted for empirically, but is as\r\nKant maintained derived from an \u003ci\u003ea priori\u003c/i\u003e intuition. This position is\r\nnot logically refutable, but I think it loses all plausibility as soon\r\nas we realise how complicated and derivative is the notion of physical\r\nspace. As we have seen, the application of geometry to the physical\r\nworld in no way demands that there should really be points and\r\nstraight lines among physical entities. The principle of economy,\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_120\" id=\"Page_120\"\u003e[120]\u003c/a\u003e\u003c/span\u003etherefore, demands that we should abstain from assuming the existence\r\nof points and straight lines. As soon, however, as we accept the view\r\nthat points and straight lines are complicated constructions by means\r\nof classes of physical entities, the hypothesis that we have an \u003ci\u003ea\r\npriori\u003c/i\u003e intuition enabling us to know what happens to straight lines\r\nwhen they are produced indefinitely becomes extremely strained and\r\nharsh; nor do I think that such an hypothesis would ever have arisen\r\nin the mind of a philosopher who had grasped the nature of physical\r\nspace. Kant, under the influence of Newton, adopted, though with some\r\nvacillation, the hypothesis of absolute space, and this hypothesis,\r\nthough logically unobjectionable, is removed by Occam\u0027s razor, since\r\nabsolute space is an unnecessary entity in the explanation of the\r\nphysical world. Although, therefore, we cannot refute the Kantian\r\ntheory of an \u003ci\u003ea priori\u003c/i\u003e intuition, we can remove its grounds one by\r\none through an analysis of the problem. Thus, here as in many other\r\nphilosophical questions, the analytic method, while not capable of\r\narriving at a demonstrative result, is nevertheless capable of showing\r\nthat all the positive grounds in favour of a certain theory are\r\nfallacious and that a less unnatural theory is capable of accounting\r\nfor the facts.\u003c/p\u003e\r\n\r\n\u003cp\u003eAnother question by which the capacity of the analytic method can be\r\nshown is the question of realism. Both those who advocate and those\r\nwho combat realism seem to me to be far from clear as to the nature of\r\nthe problem which they are discussing. If we ask: \"Are our objects of\r\nperception \u003ci\u003ereal\u003c/i\u003e and are they \u003ci\u003eindependent\u003c/i\u003e of the percipient?\" it\r\nmust be supposed that we attach some meaning to the words \"real\" and\r\n\"independent,\" and yet, if either side in the controversy of realism\r\nis asked to define these two words, their answer is pretty \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_121\" id=\"Page_121\"\u003e[121]\u003c/a\u003e\u003c/span\u003esure to\r\nembody confusions such as logical analysis will reveal.\u003c/p\u003e\r\n\r\n\u003cp\u003eLet us begin with the word \"real.\" There certainly are objects of\r\nperception, and therefore, if the question whether these objects are\r\nreal is to be a substantial question, there must be in the world two\r\nsorts of objects, namely, the real and the unreal, and yet the unreal\r\nis supposed to be essentially what there is not. The question what\r\nproperties must belong to an object in order to make it real is one to\r\nwhich an adequate answer is seldom if ever forthcoming. There is of\r\ncourse the Hegelian answer, that the real is the self-consistent and\r\nthat nothing is self-consistent except the Whole; but this answer,\r\ntrue or false, is not relevant in our present discussion, which moves\r\non a lower plane and is concerned with the status of objects of\r\nperception among other objects of equal fragmentariness. Objects of\r\nperception are contrasted, in the discussions concerning realism,\r\nrather with psychical states on the one hand and matter on the other\r\nhand than with the all-inclusive whole of things. The question we have\r\ntherefore to consider is the question as to what can be meant by\r\nassigning \"reality\" to some but not all of the entities that make up\r\nthe world. Two elements, I think, make up what is felt rather than\r\nthought when the word \"reality\" is used in this sense. A thing is real\r\nif it persists at times when it is not perceived; or again, a thing is\r\nreal when it is correlated with other things in a way which experience\r\nhas led us to expect. It will be seen that reality in either of these\r\nsenses is by no means necessary to a thing, and that in fact there\r\nmight be a whole world in which nothing was real in either of these\r\nsenses. It might turn out that the objects of perception failed of\r\nreality in one or both of these respects, without its being in any way\r\ndeducible that they are \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_122\" id=\"Page_122\"\u003e[122]\u003c/a\u003e\u003c/span\u003enot parts of the external world with which\r\nphysics deals. Similar remarks will apply to the word \"independent.\"\r\nMost of the associations of this word are bound up with ideas as to\r\ncausation which it is not now possible to maintain. \u003ci\u003eA\u003c/i\u003e is independent\r\nof \u003ci\u003eB\u003c/i\u003e when \u003ci\u003eB\u003c/i\u003e is not an indispensable part of the \u003ci\u003ecause\u003c/i\u003e of \u003ci\u003eA\u003c/i\u003e.\r\nBut when it is recognised that causation is nothing more than\r\ncorrelation, and that there are correlations of simultaneity as well\r\nas of succession, it becomes evident that there is no uniqueness in a\r\nseries of casual antecedents of a given event, but that, at any point\r\nwhere there is a correlation of simultaneity, we can pass from one\r\nline of antecedents to another in order to obtain a new series of\r\ncausal antecedents. It will be necessary to specify the causal law\r\naccording to which the antecedents are to be considered. I received a\r\nletter the other day from a correspondent who had been puzzled by\r\nvarious philosophical questions. After enumerating them he says:\r\n\"These questions led me from Bonn to Strassburg, where I found\r\nProfessor Simmel.\" Now, it would be absurd to deny that these\r\nquestions caused his body to move from Bonn to Strassburg, and yet it\r\nmust be supposed that a set of purely mechanical antecedents could\r\nalso be found which would account for this transfer of matter from one\r\nplace to another. Owing to this plurality of causal series antecedent\r\nto a given event, the notion of \u003ci\u003ethe\u003c/i\u003e cause becomes indefinite, and\r\nthe question of independence becomes correspondingly ambiguous. Thus,\r\ninstead of asking simply whether \u003ci\u003eA\u003c/i\u003e is independent of \u003ci\u003eB\u003c/i\u003e, we ought\r\nto ask whether there is a series determined by such and such causal\r\nlaws leading from \u003ci\u003eB\u003c/i\u003e to \u003ci\u003eA\u003c/i\u003e. This point is important in connexion\r\nwith the particular question of objects of perception. It may be that\r\nno objects quite like those which we perceive ever exist unperceived;\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_123\" id=\"Page_123\"\u003e[123]\u003c/a\u003e\u003c/span\u003ein this case there will be a causal law according to which objects of\r\nperception are not independent of being perceived. But even if this be\r\nthe case, it may nevertheless also happen that there are purely\r\nphysical causal laws determining the occurrence of objects which are\r\nperceived by means of other objects which perhaps are not perceived.\r\nIn that case, in regard to such causal laws objects of perception will\r\nbe independent of being perceived. Thus the question whether objects\r\nof perception are independent of being perceived is, as it stands,\r\nindeterminate, and the answer will be yes or no according to the\r\nmethod adopted of making it determinate. I believe that this confusion\r\nhas borne a very large part in prolonging the controversies on this\r\nsubject, which might well have seemed capable of remaining for ever\r\nundecided. The view which I should wish to advocate is that objects of\r\nperception do not persist unchanged at times when they are not\r\nperceived, although probably objects more or less resembling them do\r\nexist at such times; that objects of perception are part, and the only\r\nempirically knowable part, of the actual subject-matter of physics,\r\nand are themselves properly to be called physical; that purely\r\nphysical laws exist determining the character and duration of objects\r\nof perception without any reference to the fact that they are\r\nperceived; and that in the establishment of such laws the propositions\r\nof physics do not presuppose any propositions of psychology or even\r\nthe existence of mind. I do not know whether realists would recognise\r\nsuch a view as realism. All that I should claim for it is, that it\r\navoids difficulties which seem to me to beset both realism and\r\nidealism as hitherto advocated, and that it avoids the appeal which\r\nthey have made to ideas which logical analysis shows to be ambiguous.\r\nA further defence and elaboration of \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_124\" id=\"Page_124\"\u003e[124]\u003c/a\u003e\u003c/span\u003ethe positions which I advocate,\r\nbut for which time is lacking now, will be found indicated in my book\r\non \u003ci\u003eOur Knowledge of the External World\u003c/i\u003e.\u003ca name=\"FNanchor_22_22\" id=\"FNanchor_22_22\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_22_22\" class=\"fnanchor\"\u003e[22]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eThe adoption of scientific method in philosophy, if I am not mistaken,\r\ncompels us to abandon the hope of solving many of the more ambitious\r\nand humanly interesting problems of traditional philosophy. Some of\r\nthese it relegates, though with little expectation of a successful\r\nsolution, to special sciences, others it shows to be such as our\r\ncapacities are essentially incapable of solving. But there remain a\r\nlarge number of the recognised problems of philosophy in regard to\r\nwhich the method advocated gives all those advantages of division into\r\ndistinct questions, of tentative, partial, and progressive advance,\r\nand of appeal to principles with which, independently of temperament,\r\nall competent students must agree. The failure of philosophy hitherto\r\nhas been due in the main to haste and ambition: patience and modesty,\r\nhere as in other sciences, will open the road to solid and durable\r\nprogress.\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\u003chr style=\"width: 15%;\" /\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003ch4\u003eFOOTNOTES:\u003c/h4\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_19_19\" id=\"Footnote_19_19\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_19_19\"\u003e\u003cspan class=\"label\"\u003e[19]\u003c/span\u003e\u003c/a\u003e Bosanquet, \u003ci\u003eLogic\u003c/i\u003e, ii, p. 211.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_20_20\" id=\"Footnote_20_20\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_20_20\"\u003e\u003cspan class=\"label\"\u003e[20]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eSome Problems of Philosophy\u003c/i\u003e, p 124.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_21_21\" id=\"Footnote_21_21\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_21_21\"\u003e\u003cspan class=\"label\"\u003e[21]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eFirst Principles\u003c/i\u003e (1862), Part II, beginning of chap.\r\nviii.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_22_22\" id=\"Footnote_22_22\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_22_22\"\u003e\u003cspan class=\"label\"\u003e[22]\u003c/span\u003e\u003c/a\u003e Open Court Company, 1914.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003ca name=\"VII\" id=\"VII\"\u003e\u003c/a\u003e\u003chr /\u003e\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_125\" id=\"Page_125\"\u003e[125]\u003c/a\u003e\u003c/span\u003e\u003cbr /\u003e\r\n\r\n\u003ch3\u003eVII\u003cspan class=\"totoc\"\u003e\u003ca href=\"#toc\"\u003eToC\u003c/a\u003e\u003c/span\u003e\u003c/h3\u003e\r\n\r\n\u003ch4\u003eTHE ULTIMATE CONSTITUENTS OF MATTER\u003ca name=\"FNanchor_23_23\" id=\"FNanchor_23_23\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_23_23\" class=\"fnanchor\"\u003e[23]\u003c/a\u003e\u003c/h4\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003cp\u003eI wish to discuss in this article no less a question than the ancient\r\nmetaphysical query, \"What is matter?\" The question, \"What is matter?\"\r\nin so far as it concerns philosophy, is, I think, already capable of\r\nan answer which in principle will be as complete as an answer can hope\r\nto be; that is to say, we can separate the problem into an essentially\r\nsoluble and an essentially insoluble portion, and we can now see how\r\nto solve the essentially soluble portion, at least as regards its main\r\noutlines. It is these outlines which I wish to suggest in the present\r\narticle. My main position, which is realistic, is, I hope and believe,\r\nnot remote from that of Professor Alexander, by whose writings on this\r\nsubject I have profited greatly.\u003ca name=\"FNanchor_24_24\" id=\"FNanchor_24_24\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_24_24\" class=\"fnanchor\"\u003e[24]\u003c/a\u003e It is also in close accord with\r\nthat of Dr. Nunn.\u003ca name=\"FNanchor_25_25\" id=\"FNanchor_25_25\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_25_25\" class=\"fnanchor\"\u003e[25]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eCommon sense is accustomed to the division of the world into mind and\r\nmatter. It is supposed by all who have never studied philosophy that\r\nthe distinction between mind and matter is perfectly clear and easy,\r\nthat the two do not at any point overlap, and that only a fool or a\r\nphilosopher could be in doubt as to whether any given entity is mental\r\nor material. This simple faith \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_126\" id=\"Page_126\"\u003e[126]\u003c/a\u003e\u003c/span\u003esurvives in Descartes and in a\r\nsomewhat modified form in Spinoza, but with Leibniz it begins to\r\ndisappear, and from his day to our own almost every philosopher of\r\nnote has criticised and rejected the dualism of common sense. It is my\r\nintention in this article to defend this dualism; but before defending\r\nit we must spend a few moments on the reasons which have prompted its\r\nrejection.\u003c/p\u003e\r\n\r\n\u003cp\u003eOur knowledge of the material world is obtained by means of the\r\nsenses, of sight and touch and so on. At first it is supposed that\r\nthings are just as they seem, but two opposite sophistications soon\r\ndestroy this na\u0026iuml;ve belief. On the one hand the physicists cut up\r\nmatter into molecules, atoms, corpuscles, and as many more such\r\nsubdivisions as their future needs may make them postulate, and the\r\nunits at which they arrive are uncommonly different from the visible,\r\ntangible objects of daily life. A unit of matter tends more and more\r\nto be something like an electromagnetic field filling all space,\r\nthough having its greatest intensity in a small region. Matter\r\nconsisting of such elements is as remote from daily life as any\r\nmetaphysical theory. It differs from the theories of metaphysicians\r\nonly in the fact that its practical efficacy proves that it contains\r\nsome measure of truth and induces business men to invest money on the\r\nstrength of it; but, in spite of its connection with the money market,\r\nit remains a metaphysical theory none the less.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe second kind of sophistication to which the world of common sense\r\nhas been subjected is derived from the psychologists and\r\nphysiologists. The physiologists point out that what we see depends\r\nupon the eye, that what we hear depends upon the ear, and that all our\r\nsenses are liable to be affected by anything which affects the brain,\r\nlike alcohol or hasheesh. Psychologists point out how much of what we\r\nthink we see is supplied by association \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_127\" id=\"Page_127\"\u003e[127]\u003c/a\u003e\u003c/span\u003eor unconscious inference, how\r\nmuch is mental interpretation, and how doubtful is the residuum which\r\ncan be regarded as crude datum. From these facts it is argued by the\r\npsychologists that the notion of a datum passively received by the\r\nmind is a delusion, and it is argued by the physiologists that even if\r\na pure datum of sense could be obtained by the analysis of experience,\r\nstill this datum could not belong, as common sense supposes, to the\r\nouter world, since its whole nature is conditioned by our nerves and\r\nsense organs, changing as they change in ways which it is thought\r\nimpossible to connect with any change in the matter supposed to be\r\nperceived. This physiologist\u0027s argument is exposed to the rejoinder,\r\nmore specious than solid, that our knowledge of the existence of the\r\nsense organs and nerves is obtained by that very process which the\r\nphysiologist has been engaged in discrediting, since the existence of\r\nthe nerves and sense organs is only known through the evidence of the\r\nsenses themselves. This argument may prove that some reinterpretation\r\nof the results of physiology is necessary before they can acquire\r\nmetaphysical validity. But it does not upset the physiological\r\nargument in so far as this constitutes merely a \u003ci\u003ereductio ad absurdum\u003c/i\u003e\r\nof na\u0026iuml;ve realism.\u003c/p\u003e\r\n\r\n\u003cp\u003eThese various lines of argument prove, I think, that some part of the\r\nbeliefs of common sense must be abandoned. They prove that, if we take\r\nthese beliefs as a whole, we are forced into conclusions which are in\r\npart self-contradictory; but such arguments cannot of themselves\r\ndecide what portion of our common-sense beliefs is in need of\r\ncorrection. Common sense believes that what we see is physical,\r\noutside the mind, and continuing to exist if we shut our eyes or turn\r\nthem in another direction. I believe that common sense is right in\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_128\" id=\"Page_128\"\u003e[128]\u003c/a\u003e\u003c/span\u003eregarding what we see as physical and (in one of several possible\r\nsenses) outside the mind, but is probably wrong in supposing that it\r\ncontinues to exist when we are no longer looking at it. It seems to me\r\nthat the whole discussion of matter has been obscured by two errors\r\nwhich support each other. The first of these is the error that what we\r\nsee, or perceive through any of our other senses, is subjective: the\r\nsecond is the belief that what is physical must be persistent.\r\nWhatever physics may regard as the ultimate constituents of matter, it\r\nalways supposes these constituents to be indestructible. Since the\r\nimmediate data of sense are not indestructible but in a state of\r\nperpetual flux, it is argued that these data themselves cannot be\r\namong the ultimate constituents of matter. I believe this to be a\r\nsheer mistake. The persistent particles of mathematical physics I\r\nregard as logical constructions, symbolic fictions enabling us to\r\nexpress compendiously very complicated assemblages of facts; and, on\r\nthe other hand, I believe that the actual data in sensation, the\r\nimmediate objects of sight or touch or hearing, are extra-mental,\r\npurely physical, and among the ultimate constituents of matter.\u003c/p\u003e\r\n\r\n\u003cp\u003eMy meaning in regard to the impermanence of physical entities may\r\nperhaps be made clearer by the use of Bergson\u0027s favourite illustration\r\nof the cinematograph. When I first read Bergson\u0027s statement that the\r\nmathematician conceives the world after the analogy of a\r\ncinematograph, I had never seen a cinematograph, and my first visit to\r\none was determined by the desire to verify Bergson\u0027s statement, which\r\nI found to be completely true, at least so far as I am concerned.\r\nWhen, in a picture palace, we see a man rolling down hill, or running\r\naway from the police, or falling into a river, or doing any of those\r\nother things to which men in such places are addicted, we know \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_129\" id=\"Page_129\"\u003e[129]\u003c/a\u003e\u003c/span\u003ethat\r\nthere is not really only one man moving, but a succession of films,\r\neach with a different momentary man. The illusion of persistence\r\narises only through the approach to continuity in the series of\r\nmomentary men. Now what I wish to suggest is that in this respect the\r\ncinema is a better metaphysician than common sense, physics, or\r\nphilosophy. The real man too, I believe, however the police may swear\r\nto his identity, is really a series of momentary men, each different\r\none from the other, and bound together, not by a numerical identity,\r\nbut by continuity and certain intrinsic causal laws. And what applies\r\nto men applies equally to tables and chairs, the sun, moon and stars.\r\nEach of these is to be regarded, not as one single persistent entity,\r\nbut as a series of entities succeeding each other in time, each\r\nlasting for a very brief period, though probably not for a mere\r\nmathematical instant. In saying this I am only urging the same kind of\r\ndivision in time as we are accustomed to acknowledge in the case of\r\nspace. A body which fills a cubic foot will be admitted to consist of\r\nmany smaller bodies, each occupying only a very tiny volume; similarly\r\na thing which persists for an hour is to be regarded as composed of\r\nmany things of less duration. A true theory of matter requires a\r\ndivision of things into time-corpuscles as well as into\r\nspace-corpuscles.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe world may be conceived as consisting of a multitude of entities\r\narranged in a certain pattern. The entities which are arranged I shall\r\ncall \"particulars.\" The arrangement or pattern results from relations\r\namong particulars. Classes or series of particulars, collected\r\ntogether on account of some property which makes it convenient to be\r\nable to speak of them as wholes, are what I call logical constructions\r\nor symbolic fictions. The particulars are to be conceived, not on the\r\nanalogy of bricks \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_130\" id=\"Page_130\"\u003e[130]\u003c/a\u003e\u003c/span\u003ein a building, but rather on the analogy of notes\r\nin a symphony. The ultimate constituents of a symphony (apart from\r\nrelations) are the notes, each of which lasts only for a very short\r\ntime. We may collect together all the notes played by one instrument:\r\nthese may be regarded as the analogues of the successive particulars\r\nwhich common sense would regard as successive states of one \"thing.\"\r\nBut the \"thing\" ought to be regarded as no more \"real\" or\r\n\"substantial\" than, for example, the r\u0026ocirc;le of the trombone. As soon as\r\n\"things\" are conceived in this manner it will be found that the\r\ndifficulties in the way of regarding immediate objects of sense as\r\nphysical have largely disappeared.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhen people ask, \"Is the object of sense mental or physical?\" they\r\nseldom have any clear idea either what is meant by \"mental\" or\r\n\"physical,\" or what criteria are to be applied for deciding whether a\r\ngiven entity belongs to one class or the other. I do not know how to\r\ngive a sharp definition of the word \"mental,\" but something may be\r\ndone by enumerating occurrences which are indubitably mental:\r\nbelieving, doubting, wishing, willing, being pleased or pained, are\r\ncertainly mental occurrences; so are what we may call experiences,\r\nseeing, hearing, smelling, perceiving generally. But it does not\r\nfollow from this that what is seen, what is heard, what is smelt, what\r\nis perceived, must be mental. When I see a flash of lightning, my\r\nseeing of it is mental, but what I see, although it is not quite the\r\nsame as what anybody else sees at the same moment, and although it\r\nseems very unlike what the physicist would describe as a flash of\r\nlightning, is not mental. I maintain, in fact, that if the physicist\r\ncould describe truly and fully all that occurs in the physical world\r\nwhen there is a flash of lightning, it would contain as a constituent\r\nwhat I see, and also what \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_131\" id=\"Page_131\"\u003e[131]\u003c/a\u003e\u003c/span\u003eis seen by anybody else who would commonly\r\nbe said to see the same flash. What I mean may perhaps be made plainer\r\nby saying that if my body could remain in exactly the same state in\r\nwhich it is, although my mind had ceased to exist, precisely that\r\nobject which I now see when I see the flash would exist, although of\r\ncourse I should not see it, since my seeing is mental. The principal\r\nreasons which have led people to reject this view have, I think, been\r\ntwo: first, that they did not adequately distinguish between my seeing\r\nand what I see; secondly, that the causal dependence of what I see\r\nupon my body has made people suppose that what I see cannot be\r\n\"outside\" me. The first of these reasons need not detain us, since the\r\nconfusion only needs to be pointed out in order to be obviated; but\r\nthe second requires some discussion, since it can only be answered by\r\nremoving current misconceptions, on the one hand as to the nature of\r\nspace, and on the other, as to the meaning of causal dependence.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhen people ask whether colours, for example, or other secondary\r\nqualities are inside or outside the mind, they seem to suppose that\r\ntheir meaning must be clear, and that it ought to be possible to say\r\nyes or no without any further discussion of the terms involved. In\r\nfact, however, such terms as \"inside\" or \"outside\" are very ambiguous.\r\nWhat is meant by asking whether this or that is \"in\" the mind? The\r\nmind is not like a bag or a pie; it does not occupy a certain region\r\nin space, or, if (in a sense) it does, what is in that region is\r\npresumably part of the brain, which would not be said to be in the\r\nmind. When people say that sensible qualities are in the mind, they do\r\nnot mean \"spatially contained in\" in the sense in which the blackbirds\r\nwere in the pie. We might regard the mind as an assemblage of\r\nparticulars, namely, what \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_132\" id=\"Page_132\"\u003e[132]\u003c/a\u003e\u003c/span\u003ewould be called \"states of mind,\" which\r\nwould belong together in virtue of some specific common quality. The\r\ncommon quality of all states of mind would be the quality designated\r\nby the word \"mental\"; and besides this we should have to suppose that\r\neach separate person\u0027s states of mind have some common characteristic\r\ndistinguishing them from the states of mind of other people. Ignoring\r\nthis latter point, let us ask ourselves whether the quality designated\r\nby the word \"mental\" does, as a matter of observation, actually belong\r\nto objects of sense, such as colours or noises. I think any candid\r\nperson must reply that, however difficult it may be to know what we\r\nmean by \"mental,\" it is not difficult to see that colours and noises\r\nare not mental in the sense of having that intrinsic peculiarity which\r\nbelongs to beliefs and wishes and volitions, but not to the physical\r\nworld. Berkeley advances on this subject a plausible argument\u003ca name=\"FNanchor_26_26\" id=\"FNanchor_26_26\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_26_26\" class=\"fnanchor\"\u003e[26]\u003c/a\u003e\r\nwhich seems to me to rest upon an ambiguity in the word \"pain.\" He\r\nargues that the realist supposes the heat which he feels in\r\napproaching a fire to be something outside his mind, but that as he\r\napproaches nearer and nearer to the fire the sensation of heat passes\r\nimperceptibly into pain, and that no one could regard pain as\r\nsomething outside the mind. In reply to this argument, it should be\r\nobserved in the first place that the heat of which we are immediately\r\naware is not in the fire but in our own body. It is only by inference\r\nthat the fire is judged to be the cause of the heat which we feel in\r\nour body. In the second place (and this is the more important point),\r\nwhen we speak of pain we may mean one of two things: we may mean the\r\nobject of the sensation or other experience which has the quality of\r\nbeing painful, \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_133\" id=\"Page_133\"\u003e[133]\u003c/a\u003e\u003c/span\u003eor we may mean the quality of painfulness itself. When\r\na man says he has a pain in his great toe, what he means is that he\r\nhas a sensation associated with his great toe and having the quality\r\nof painfulness. The sensation itself, like every sensation, consists\r\nin experiencing a sensible object, and the experiencing has that\r\nquality of painfulness which only mental occurrences can have, but\r\nwhich may belong to thoughts or desires, as well as to sensations. But\r\nin common language we speak of the sensible object experienced in a\r\npainful sensation as a pain, and it is this way of speaking which\r\ncauses the confusion upon which the plausibility of Berkeley\u0027s\r\nargument depends. It would be absurd to attribute the quality of\r\npainfulness to anything non-mental, and hence it comes to be thought\r\nthat what we call a pain in the toe must be mental. In fact, however,\r\nit is not the sensible object in such a case which is painful, but the\r\nsensation, that is to say, the experience of the sensible object. As\r\nthe heat which we experience from the fire grows greater, the\r\nexperience passes gradually from being pleasant to being painful, but\r\nneither the pleasure nor the pain is a quality of the object\r\nexperienced as opposed to the experience, and it is therefore a\r\nfallacy to argue that this object must be mental on the ground that\r\npainfulness can only be attributed to what is mental.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf, then, when we say that something is in the mind we mean that it\r\nhas a certain recognisable intrinsic characteristic such as belongs to\r\nthoughts and desires, it must be maintained on grounds of immediate\r\ninspection that objects of sense are not in any mind.\u003c/p\u003e\r\n\r\n\u003cp\u003eA different meaning of \"in the mind\" is, however, to be inferred from\r\nthe arguments advanced by those who regard sensible objects as being\r\nin the mind. The arguments used are, in the main, such as would prove\r\nthe \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_134\" id=\"Page_134\"\u003e[134]\u003c/a\u003e\u003c/span\u003ecausal dependence of objects of sense upon the percipient. Now\r\nthe notion of causal dependence is very obscure and difficult, much\r\nmore so in fact than is generally realised by philosophers. I shall\r\nreturn to this point in a moment. For the present, however, accepting\r\nthe notion of causal dependence without criticism, I wish to urge that\r\nthe dependence in question is rather upon our bodies than upon our\r\nminds. The visual appearance of an object is altered if we shut one\r\neye, or squint, or look previously at something dazzling; but all\r\nthese are bodily acts, and the alterations which they effect are to be\r\nexplained by physiology and optics, not by psychology.\u003ca name=\"FNanchor_27_27\" id=\"FNanchor_27_27\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_27_27\" class=\"fnanchor\"\u003e[27]\u003c/a\u003e They are in\r\nfact of exactly the same kind as the alterations effected by\r\nspectacles or a microscope. They belong therefore to the theory of the\r\nphysical world, and can have no bearing upon the question whether what\r\nwe see is causally dependent upon the mind. What they do tend to\r\nprove, and what I for my part have no wish to deny, is that what we\r\nsee is causally dependent upon our body and is not, as crude common\r\nsense would suppose, something which would exist equally if our eyes\r\nand nerves and brain were absent, any more than the visual appearance\r\npresented by an object seen through a microscope would remain if the\r\nmicroscope were removed. So long as it is supposed that the physical\r\nworld is composed of stable and more or less permanent constituents,\r\nthe fact that what we see is changed by changes in our body appears to\r\nafford reason for regarding what we see as not an ultimate constituent\r\nof matter. But if it is recognised that the ultimate constituents of\r\nmatter are as circumscribed in duration as in spatial extent, the\r\nwhole of this difficulty vanishes.\u003c/p\u003e\r\n\r\n\u003cp\u003eThere remains, however, another difficulty, connected with space. When\r\nwe look at the sun we wish to know \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_135\" id=\"Page_135\"\u003e[135]\u003c/a\u003e\u003c/span\u003esomething about the sun itself,\r\nwhich is ninety-three million miles away; but what we see is dependent\r\nupon our eyes, and it is difficult to suppose that our eyes can affect\r\nwhat happens at a distance of ninety-three million miles. Physics\r\ntells us that certain electromagnetic waves start from the sun, and\r\nreach our eyes after about eight minutes. They there produce\r\ndisturbances in the rods and cones, thence in the optic nerve, thence\r\nin the brain. At the end of this purely physical series, by some odd\r\nmiracle, comes the experience which we call \"seeing the sun,\" and it\r\nis such experiences which form the whole and sole reason for our\r\nbelief in the optic nerve, the rods and cones, the ninety-three\r\nmillion miles, the electromagnetic waves, and the sun itself. It is\r\nthis curious oppositeness of direction between the order of causation\r\nas affirmed by physics, and the order of evidence as revealed by\r\ntheory of knowledge, that causes the most serious perplexities in\r\nregard to the nature of physical reality. Anything that invalidates\r\nour seeing, as a source of knowledge concerning physical reality,\r\ninvalidates also the whole of physics and physiology. And yet,\r\nstarting from a common-sense acceptance of our seeing, physics has\r\nbeen led step by step to the construction of the causal chain in which\r\nour seeing is the last link, and the immediate object which we see\r\ncannot be regarded as that initial cause which we believe to be\r\nninety-three million miles away, and which we are inclined to regard\r\nas the \"real\" sun.\u003c/p\u003e\r\n\r\n\u003cp\u003eI have stated this difficulty as forcibly as I can, because I believe\r\nthat it can only be answered by a radical analysis and reconstruction\r\nof all the conceptions upon whose employment it depends.\u003c/p\u003e\r\n\r\n\u003cp\u003eSpace, time, matter and cause, are the chief of these conceptions. Let\r\nus begin with the conception of cause.\u003c/p\u003e\r\n\r\n\u003cp\u003eCausal dependence, as I observed a moment ago, is a \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_136\" id=\"Page_136\"\u003e[136]\u003c/a\u003e\u003c/span\u003econception which\r\nit is very dangerous to accept at its face value. There exists a\r\nnotion that in regard to any event there is something which may be\r\ncalled \u003ci\u003ethe\u003c/i\u003e cause of that event\u0026mdash;some one definite occurrence,\r\nwithout which the event would have been impossible and with which it\r\nbecomes necessary. An event is supposed to be dependent upon its cause\r\nin some way which in it is not dependent upon other things. Thus men\r\nwill urge that the mind is dependent upon the brain, or, with equal\r\nplausibility, that the brain is dependent upon the mind. It seems not\r\nimprobable that if we had sufficient knowledge we could infer the\r\nstate of a man\u0027s mind from the state of his brain, or the state of his\r\nbrain from the state of his mind. So long as the usual conception of\r\ncausal dependence is retained, this state of affairs can be used by\r\nthe materialist to urge that the state of our brain causes our\r\nthoughts, and by the idealist to urge that our thoughts cause the\r\nstate of our brain. Either contention is equally valid or equally\r\ninvalid. The fact seems to be that there are many correlations of the\r\nsort which may be called causal, and that, for example, either a\r\nphysical or a mental event can be predicted, theoretically, either\r\nfrom a sufficient number of physical antecedents or from a sufficient\r\nnumber of mental antecedents. To speak of \u003ci\u003ethe\u003c/i\u003e cause of an event is\r\ntherefore misleading. Any set of antecedents from which the event can\r\ntheoretically be inferred by means of correlations might be called a\r\ncause of the event. But to speak of \u003ci\u003ethe\u003c/i\u003e cause is to imply a\r\nuniqueness which does not exist.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe relevance of this to the experience which we call \"seeing the sun\"\r\nis obvious. The fact that there exists a chain of antecedents which\r\nmakes our seeing dependent upon the eyes and nerves and brain does not\r\neven tend to show that there is not another chain of antecedents in\r\nwhich the eyes and nerves and brain as physical things are ignored. If\r\nwe are to escape from the dilemma which \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_137\" id=\"Page_137\"\u003e[137]\u003c/a\u003e\u003c/span\u003eseemed to arise out of the\r\nphysiological causation of what we see when we say we see the sun, we\r\nmust find, at least in theory, a way of stating causal laws for the\r\nphysical world, in which the units are not material things, such as\r\nthe eyes and nerves and brain, but momentary particulars of the same\r\nsort as our momentary visual object when we look at the sun. The sun\r\nitself and the eyes and nerves and brain must be regarded as\r\nassemblages of momentary particulars. Instead of supposing, as we\r\nnaturally do when we start from an uncritical acceptance of the\r\napparent dicta of physics, that \u003ci\u003ematter\u003c/i\u003e is what is \"really real\" in\r\nthe physical world, and that the immediate objects of sense are mere\r\nphantasms, we must regard matter as a logical construction, of which\r\nthe constituents will be just such evanescent particulars as may, when\r\nan observer happens to be present, become data of sense to that\r\nobserver. What physics regards as the sun of eight minutes ago will be\r\na whole assemblage of particulars, existing at different times,\r\nspreading out from a centre with the velocity of light, and containing\r\namong their number all those visual data which are seen by people who\r\nare now looking at the sun. Thus the sun of eight minutes ago is a\r\nclass of particulars, and what I see when I now look at the sun is one\r\nmember of this class. The various particulars constituting this class\r\nwill be correlated with each other by a certain continuity and certain\r\nintrinsic laws of variation as we pass outwards from the centre,\r\ntogether with certain modifications correlated extrinsically with\r\nother particulars which are not members of this class. It is these\r\nextrinsic modifications which represent the sort of facts that, in our\r\nformer account, appeared as the influence of the eyes and nerves in\r\nmodifying the appearance of the sun.\u003ca name=\"FNanchor_28_28\" id=\"FNanchor_28_28\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_28_28\" class=\"fnanchor\"\u003e[28]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_138\" id=\"Page_138\"\u003e[138]\u003c/a\u003e\u003c/span\u003eThe \u003ci\u003eprima facie\u003c/i\u003e difficulties in the way of this view are chiefly\r\nderived from an unduly conventional theory of space. It might seem at\r\nfirst sight as if we had packed the world much fuller than it could\r\npossibly hold. At every place between us and the sun, we said, there\r\nis to be a particular which is to be a member of the sun as it was a\r\nfew minutes ago. There will also, of course, have to be a particular\r\nwhich is a member of any planet or fixed star that may happen to be\r\nvisible from that place. At the place where I am, there will be\r\nparticulars which will be members severally of all the \"things\" I am\r\nnow said to be perceiving. Thus throughout the world, everywhere,\r\nthere will be an enormous number of particulars coexisting in the same\r\nplace. But these troubles result from contenting ourselves too readily\r\nwith the merely three-dimensional space to which schoolmasters have\r\naccustomed us. The space of the real world is a space of six\r\ndimensions, and as soon as we realise this we see that there is plenty\r\nof room for all the particulars for which we want to find positions.\r\nIn order to realise this we have only to return for a moment from the\r\npolished space of physics to the rough and untidy space of our\r\nimmediate sensible experience. The space of one man\u0027s sensible objects\r\nis a three-dimensional space. It does not appear probable that two men\r\never both perceive at the same time any one sensible object; when they\r\nare said to see the same thing or hear the same noise, there will\r\nalways be some difference, however slight, between the actual shapes\r\nseen or the actual sounds heard. If this is so, and if, as is\r\ngenerally assumed, position in space is purely relative, it follows\r\nthat the space of one man\u0027s objects and the space of another man\u0027s\r\nobjects have no place in common, that they are in fact different\r\nspaces, and not merely different parts of one space. I mean by this\r\nthat such immediate spatial relations as are perceived to hold\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_139\" id=\"Page_139\"\u003e[139]\u003c/a\u003e\u003c/span\u003ebetween the different parts of the sensible space perceived by one\r\nman, do not hold between parts of sensible spaces perceived by\r\ndifferent men. There are therefore a multitude of three-dimensional\r\nspaces in the world: there are all those perceived by observers, and\r\npresumably also those which are not perceived, merely because no\r\nobserver is suitably situated for perceiving them.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut although these spaces do not have to one another the same kind of\r\nspatial relations as obtain between the parts of one of them, it is\r\nnevertheless possible to arrange these spaces themselves in a\r\nthree-dimensional order. This is done by means of the correlated\r\nparticulars which we regard as members (or aspects) of one physical\r\nthing. When a number of people are said to see the same object, those\r\nwho would be said to be near to the object see a particular occupying\r\na larger part of their field of vision than is occupied by the\r\ncorresponding particular seen by people who would be said to be\r\nfarther from the thing. By means of such considerations it is\r\npossible, in ways which need not now be further specified, to arrange\r\nall the different spaces in a three-dimensional series. Since each of\r\nthe spaces is itself three-dimensional, the whole world of particulars\r\nis thus arranged in a six-dimensional space, that is to say, six\r\nco-ordinates will be required to assign completely the position of any\r\ngiven particular, namely, three to assign its position in its own\r\nspace and three more to assign the position of its space among the\r\nother spaces.\u003c/p\u003e\r\n\r\n\u003cp\u003eThere are two ways of classifying particulars: we may take together\r\nall those that belong to a given \"perspective,\" or all those that are,\r\nas common sense would say, different \"aspects\" of the same \"thing.\"\r\nFor example, if I am (as is said) seeing the sun, what I see belongs\r\nto two assemblages: (1) the assemblage of all my present objects of\r\nsense, which is what I call a \"perspective\"; \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_140\" id=\"Page_140\"\u003e[140]\u003c/a\u003e\u003c/span\u003e(2) the assemblage of\r\nall the different particulars which would be called aspects of the sun\r\nof eight minutes ago\u0026mdash;this assemblage is what I define as \u003ci\u003ebeing\u003c/i\u003e the\r\nsun of eight minutes ago. Thus \"perspectives\" and \"things\" are merely\r\ntwo different ways of classifying particulars. It is to be observed\r\nthat there is no \u003ci\u003ea priori\u003c/i\u003e necessity for particulars to be\r\nsusceptible of this double classification. There may be what might be\r\ncalled \"wild\" particulars, not having the usual relations by which the\r\nclassification is effected; perhaps dreams and hallucinations are\r\ncomposed of particulars which are \"wild\" in this sense.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe exact definition of what is meant by a perspective is not quite\r\neasy. So long as we confine ourselves to visible objects or to objects\r\nof touch we might define the perspective of a given particular as \"all\r\nparticulars which have a simple (direct) spatial relation to the given\r\nparticular.\" Between two patches of colour which I see now, there is a\r\ndirect spatial relation which I equally see. But between patches of\r\ncolour seen by different men there is only an indirect constructed\r\nspatial relation by means of the placing of \"things\" in physical space\r\n(which is the same as the space composed of perspectives). Those\r\nparticulars which have direct spatial relations to a given particular\r\nwill belong to the same perspective. But if, for example, the sounds\r\nwhich I hear are to belong to the same perspective with the patches of\r\ncolour which I see, there must be particulars which have no direct\r\nspatial relation and yet belong to the same perspective. We cannot\r\ndefine a perspective as all the data of one percipient at one time,\r\nbecause we wish to allow the possibility of perspectives which are not\r\nperceived by any one. There will be need, therefore, in defining a\r\nperspective, of some principle derived neither from psychology nor\r\nfrom space.\u003c/p\u003e\r\n\r\n\u003cp\u003eSuch a principle may be obtained from the \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_141\" id=\"Page_141\"\u003e[141]\u003c/a\u003e\u003c/span\u003econsideration of \u003ci\u003etime\u003c/i\u003e.\r\nThe one all-embracing time, like the one all-embracing space, is a\r\nconstruction; there is no \u003ci\u003edirect\u003c/i\u003e time-relation between particulars\r\nbelonging to my perspective and particulars belonging to another\r\nman\u0027s. On the other hand, any two particulars of which I am aware are\r\neither simultaneous or successive, and their simultaneity or\r\nsuccessiveness is sometimes itself a datum to me. We may therefore\r\ndefine the perspective to which a given particular belongs as \"all\r\nparticulars simultaneous with the given particular,\" where\r\n\"simultaneous\" is to be understood as a direct simple relation, not\r\nthe derivative constructed relation of physics. It may be observed\r\nthat the introduction of \"local time\" suggested by the principle of\r\nrelativity has effected, for purely scientific reasons, much the same\r\nmultiplication of times as we have just been advocating.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe sum-total of all the particulars that are (directly) either\r\nsimultaneous with or before or after a given particular may be defined\r\nas the \"biography\" to which that particular belongs. It will be\r\nobserved that, just as a perspective need not be actually perceived by\r\nany one, so a biography need not be actually lived by any one. Those\r\nbiographies that are lived by no one are called \"official.\"\u003c/p\u003e\r\n\r\n\u003cp\u003eThe definition of a \"thing\" is effected by means of continuity and of\r\ncorrelations which have a certain differential independence of other\r\n\"things.\" That is to say, given a particular in one perspective, there\r\nwill usually in a neighbouring perspective be a very similar\r\nparticular, differing from the given particular, to the first order of\r\nsmall quantities, according to a law involving only the difference of\r\nposition of the two perspectives in perspective space, and not any of\r\nthe other \"things\" in the universe. It is this continuity and\r\ndifferential independence in the law of change as we pass from one\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_142\" id=\"Page_142\"\u003e[142]\u003c/a\u003e\u003c/span\u003eperspective to another that defines the class of particulars which is\r\nto be called \"one thing.\"\u003c/p\u003e\r\n\r\n\u003cp\u003eBroadly speaking, we may say that the physicist finds it convenient to\r\nclassify particulars into \"things,\" while the psychologist finds it\r\nconvenient to classify them into \"perspectives\" and \"biographies,\"\r\nsince one perspective \u003ci\u003emay\u003c/i\u003e constitute the momentary data of one\r\npercipient, and one biography \u003ci\u003emay\u003c/i\u003e constitute the whole of the data\r\nof one percipient throughout his life.\u003c/p\u003e\r\n\r\n\u003cp\u003eWe may now sum up our discussion. Our object has been to discover as\r\nfar as possible the nature of the ultimate constituents of the\r\nphysical world. When I speak of the \"physical world,\" I mean, to begin\r\nwith, the world dealt with by physics. It is obvious that physics is\r\nan empirical science, giving us a certain amount of knowledge and\r\nbased upon evidence obtained through the senses. But partly through\r\nthe development of physics itself, partly through arguments derived\r\nfrom physiology, psychology or metaphysics, it has come to be thought\r\nthat the immediate data of sense could not themselves form part of the\r\nultimate constituents of the physical world, but were in some sense\r\n\"mental,\" \"in the mind,\" or \"subjective.\" The grounds for this view,\r\nin so far as they depend upon physics, can only be adequately dealt\r\nwith by rather elaborate constructions depending upon symbolic logic,\r\nshowing that out of such materials as are provided by the senses it is\r\npossible to construct classes and series having the properties which\r\nphysics assigns to matter. Since this argument is difficult and\r\ntechnical, I have not embarked upon it in this article. But in so far\r\nas the view that sense-data are \"mental\" rests upon physiology,\r\npsychology, or metaphysics, I have tried to show that it rests upon\r\nconfusions and prejudices\u0026mdash;prejudices in favour of permanence in the\r\nultimate constituents of matter, and \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_143\" id=\"Page_143\"\u003e[143]\u003c/a\u003e\u003c/span\u003econfusions derived from unduly\r\nsimple notions as to space, from the causal correlation of sense-data\r\nwith sense-organs, and from failure to distinguish between sense-data\r\nand sensations. If what we have said on these subjects is valid, the\r\nexistence of sense-data is logically independent of the existence of\r\nmind, and is causally dependent upon the \u003ci\u003ebody\u003c/i\u003e of the percipient\r\nrather than upon his mind. The causal dependence upon the body of the\r\npercipient, we found, is a more complicated matter than it appears to\r\nbe, and, like all causal dependence, is apt to give rise to erroneous\r\nbeliefs through misconceptions as to the nature of causal correlation.\r\nIf we have been right in our contentions, sense-data are merely those\r\namong the ultimate constituents of the physical world, of which we\r\nhappen to be immediately aware; they themselves are purely physical,\r\nand all that is mental in connection with them is our awareness of\r\nthem, which is irrelevant to their nature and to their place in\r\nphysics.\u003c/p\u003e\r\n\r\n\u003cp\u003eUnduly simple notions as to space have been a great stumbling-block to\r\nrealists. When two men look at the same table, it is supposed that\r\nwhat the one sees and what the other sees are in the same place. Since\r\nthe shape and colour are not quite the same for the two men, this\r\nraises a difficulty, hastily solved, or rather covered up, by\r\ndeclaring what each sees to be purely \"subjective\"\u0026mdash;though it would\r\npuzzle those who use this glib word to say what they mean by it. The\r\ntruth seems to be that space\u0026mdash;and time also\u0026mdash;is much more complicated\r\nthan it would appear to be from the finished structure of physics, and\r\nthat the one all-embracing three-dimensional space is a logical\r\nconstruction, obtained by means of correlations from a crude space of\r\nsix dimensions. The particulars occupying this six-dimensional space,\r\nclassified in one way, form \"things,\" from which with certain further\r\nmanipulations we can obtain what physics can \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_144\" id=\"Page_144\"\u003e[144]\u003c/a\u003e\u003c/span\u003eregard as matter;\r\nclassified in another way, they form \"perspectives\" and \"biographies,\"\r\nwhich may, if a suitable percipient happens to exist, form\r\nrespectively the sense-data of a momentary or of a total experience.\r\nIt is only when physical \"things\" have been dissected into series of\r\nclasses of particulars, as we have done, that the conflict between the\r\npoint of view of physics and the point of view of psychology can be\r\novercome. This conflict, if what has been said is not mistaken, flows\r\nfrom different methods of classification, and vanishes as soon as its\r\nsource is discovered.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn favour of the theory which I have briefly outlined, I do not claim\r\nthat it is \u003ci\u003ecertainly\u003c/i\u003e true. Apart from the likelihood of mistakes,\r\nmuch of it is avowedly hypothetical. What I do claim for the theory is\r\nthat it \u003ci\u003emay\u003c/i\u003e be true, and that this is more than can be said for any\r\nother theory except the closely analogous theory of Leibniz. The\r\ndifficulties besetting realism, the confusions obstructing any\r\nphilosophical account of physics, the dilemma resulting from\r\ndiscrediting sense-data, which yet remain the sole source of our\r\nknowledge of the outer world\u0026mdash;all these are avoided by the theory\r\nwhich I advocate. This does not prove the theory to be true, since\r\nprobably many other theories might be invented which would have the\r\nsame merits. But it does prove that the theory has a better chance of\r\nbeing true than any of its present competitors, and it suggests that\r\nwhat can be known with certainty is likely to be discoverable by\r\ntaking our theory as a starting-point, and gradually freeing it from\r\nall such assumptions as seem irrelevant, unnecessary, or unfounded. On\r\nthese grounds, I recommend it to attention as a hypothesis and a basis\r\nfor further work, though not as itself a finished or adequate solution\r\nof the problem with which it deals.\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\u003chr style=\"width: 15%;\" /\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003ch4\u003eFOOTNOTES:\u003c/h4\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_23_23\" id=\"Footnote_23_23\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_23_23\"\u003e\u003cspan class=\"label\"\u003e[23]\u003c/span\u003e\u003c/a\u003e An address delivered to the Philosophical Society of\r\nManchester in February, 1915. Reprinted from \u003ci\u003eThe Monist\u003c/i\u003e, July,\r\n1915.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_24_24\" id=\"Footnote_24_24\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_24_24\"\u003e\u003cspan class=\"label\"\u003e[24]\u003c/span\u003e\u003c/a\u003e Cf. especially Samuel Alexander, \"The Basis of Realism,\"\r\n\u003ci\u003eBritish Academy\u003c/i\u003e, Vol. VI.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_25_25\" id=\"Footnote_25_25\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_25_25\"\u003e\u003cspan class=\"label\"\u003e[25]\u003c/span\u003e\u003c/a\u003e \"Are Secondary Qualities Independent of Perception?\"\r\n\u003ci\u003eProc. Arist. Soc.\u003c/i\u003e, 1909-10, pp. 191-218.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_26_26\" id=\"Footnote_26_26\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_26_26\"\u003e\u003cspan class=\"label\"\u003e[26]\u003c/span\u003e\u003c/a\u003e First dialogue between Hylas and Philonous, \u003ci\u003eWorks\u003c/i\u003e\r\n(Fraser\u0027s edition 1901). I. p. 384.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_27_27\" id=\"Footnote_27_27\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_27_27\"\u003e\u003cspan class=\"label\"\u003e[27]\u003c/span\u003e\u003c/a\u003e This point has been well urged by the American\r\nrealists.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_28_28\" id=\"Footnote_28_28\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_28_28\"\u003e\u003cspan class=\"label\"\u003e[28]\u003c/span\u003e\u003c/a\u003e Cf. T.P. Nunn, \"Are Secondary Qualities Independent of\r\nPerception?\" \u003ci\u003eProc. Arist. Soc.\u003c/i\u003e, 1909-1910.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003ca name=\"VIII\" id=\"VIII\"\u003e\u003c/a\u003e\u003chr /\u003e\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_145\" id=\"Page_145\"\u003e[145]\u003c/a\u003e\u003c/span\u003e\u003cbr /\u003e\r\n\r\n\u003ch3\u003eVIII\u003cspan class=\"totoc\"\u003e\u003ca href=\"#toc\"\u003eToC\u003c/a\u003e\u003c/span\u003e\u003c/h3\u003e\r\n\r\n\u003ch4\u003eTHE RELATION OF SENSE-DATA TO PHYSICS\u003c/h4\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003ch4\u003eI. THE PROBLEM STATED\u003c/h4\u003e\r\n\r\n\u003cp\u003ePhysics is said to be an empirical science, based upon observation and\r\nexperiment.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is supposed to be verifiable, i.e. capable of calculating\r\nbeforehand results subsequently confirmed by observation and\r\nexperiment.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhat can we learn by observation and experiment?\u003c/p\u003e\r\n\r\n\u003cp\u003eNothing, so far as physics is concerned, except immediate data of\r\nsense: certain patches of colour, sounds, tastes, smells, etc., with\r\ncertain spatio-temporal relations.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe supposed contents of the physical world are \u003ci\u003eprima facie\u003c/i\u003e very\r\ndifferent from these: molecules have no colour, atoms make no noise,\r\nelectrons have no taste, and corpuscles do not even smell.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf such objects are to be verified, it must be solely through their\r\nrelation to sense-data: they must have some kind of correlation with\r\nsense-data, and must be verifiable through their correlation \u003ci\u003ealone\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut how is the correlation itself ascertained? A correlation can only\r\nbe ascertained empirically by the correlated objects being constantly\r\n\u003ci\u003efound\u003c/i\u003e together. But in our case, only one term of the correlation,\r\nnamely, the sensible term, is ever \u003ci\u003efound\u003c/i\u003e: the other term seems\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_146\" id=\"Page_146\"\u003e[146]\u003c/a\u003e\u003c/span\u003eessentially incapable of being found. Therefore, it would seem, the\r\ncorrelation with objects of sense, by which physics was to be\r\nverified, is itself utterly and for ever unverifiable.\u003c/p\u003e\r\n\r\n\u003cp\u003eThere are two ways of avoiding this result.\u003c/p\u003e\r\n\r\n\u003cp\u003e(1) We may say that we know some principle \u003ci\u003ea priori\u003c/i\u003e, without the\r\nneed of empirical verification, e.g. that our sense-data have \u003ci\u003ecauses\u003c/i\u003e\r\nother than themselves, and that something can be known about these\r\ncauses by inference from their effects. This way has been often\r\nadopted by philosophers. It may be necessary to adopt this way to some\r\nextent, but in so far as it is adopted physics ceases to be empirical\r\nor based upon experiment and observation alone. Therefore this way is\r\nto be avoided as much as possible.\u003c/p\u003e\r\n\r\n\u003cp\u003e(2) We may succeed in actually defining the objects of physics as\r\nfunctions of sense-data. Just in so far as physics leads to\r\nexpectations, this \u003ci\u003emust\u003c/i\u003e be possible, since we can only \u003ci\u003eexpect\u003c/i\u003e what\r\ncan be experienced. And in so far as the physical state of affairs is\r\ninferred from sense-data, it must be capable of expression as a\r\nfunction of sense-data. The problem of accomplishing this expression\r\nleads to much interesting logico-mathematical work.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn physics as commonly set forth, sense-data appear as functions of\r\nphysical objects: when such-and-such waves impinge upon the eye, we\r\nsee such-and-such colours, and so on. But the waves are in fact\r\ninferred from the colours, not vice versa. Physics cannot be regarded\r\nas validly based upon empirical data until the waves have been\r\nexpressed as functions of the colours and other sense-data.\u003c/p\u003e\r\n\r\n\u003cp\u003eThus if physics is to be verifiable we are faced with the following\r\nproblem: Physics exhibits sense-data as functions of physical objects,\r\nbut verification is only possible if physical objects can be exhibited\r\nas functions of \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_147\" id=\"Page_147\"\u003e[147]\u003c/a\u003e\u003c/span\u003esense-data. We have therefore to solve the equations\r\ngiving sense-data in terms of physical objects, so as to make them\r\ninstead give physical objects in terms of sense-data.\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\r\n\u003ch4\u003eII. CHARACTERISTICS OF SENSE-DATA\u003c/h4\u003e\r\n\r\n\u003cp\u003eWhen I speak of a \"sense-datum,\" I do not mean the whole of what is\r\ngiven in sense at one time. I mean rather such a part of the whole as\r\nmight be singled out by attention: particular patches of colour,\r\nparticular noises, and so on. There is some difficulty in deciding\r\nwhat is to be considered \u003ci\u003eone\u003c/i\u003e sense-datum: often attention causes\r\ndivisions to appear where, so far as can be discovered, there were no\r\ndivisions before. An observed complex fact, such as that this patch of\r\nred is to the left of that patch of blue, is also to be regarded as a\r\ndatum from our present point of view: epistemologically, it does not\r\ndiffer greatly from a simple sense-datum as regards its function in\r\ngiving knowledge. Its \u003ci\u003elogical\u003c/i\u003e structure is very different, however,\r\nfrom that of sense: \u003ci\u003esense\u003c/i\u003e gives acquaintance with particulars, and\r\nis thus a two-term relation in which the object can be \u003ci\u003enamed\u003c/i\u003e but not\r\n\u003ci\u003easserted\u003c/i\u003e, and is inherently incapable of truth or falsehood, whereas\r\nthe observation of a complex fact, which may be suitably called\r\nperception, is not a two-term relation, but involves the propositional\r\nform on the object-side, and gives knowledge of a truth, not mere\r\nacquaintance with a particular. This logical difference, important as\r\nit is, is not very relevant to our present problem; and it will be\r\nconvenient to regard data of perception as included among sense-data\r\nfor the purposes of this paper. It is to be observed that the\r\nparticulars which are constituents of a datum of perception are always\r\nsense-data in the strict sense.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_148\" id=\"Page_148\"\u003e[148]\u003c/a\u003e\u003c/span\u003eConcerning sense-data, we know that they are there while they are\r\ndata, and this is the epistemological basis of all our knowledge of\r\nexternal particulars. (The meaning of the word \"external\" of course\r\nraises problems which will concern us later.) We do not know, except\r\nby means of more or less precarious inferences, whether the objects\r\nwhich are at one time sense-data continue to exist at times when they\r\nare not data. Sense-data at the times when they are data are all that\r\nwe directly and primitively know of the external world; hence in\r\nepistemology the fact that they are \u003ci\u003edata\u003c/i\u003e is all-important. But the\r\nfact that they are all that we directly know gives, of course, no\r\npresumption that they are all that there is. If we could construct an\r\nimpersonal metaphysic, independent of the accidents of our knowledge\r\nand ignorance, the privileged position of the actual data would\r\nprobably disappear, and they would probably appear as a rather\r\nhaphazard selection from a mass of objects more or less like them. In\r\nsaying this, I assume only that it is probable that there are\r\nparticulars with which we are not acquainted. Thus the special\r\nimportance of sense-data is in relation to epistemology, not to\r\nmetaphysics. In this respect, physics is to be reckoned as\r\nmetaphysics: it is impersonal, and nominally pays no special attention\r\nto sense-data. It is only when we ask how physics can be \u003ci\u003eknown\u003c/i\u003e that\r\nthe importance of sense-data re-emerges.\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\r\n\u003ch4\u003eIII. SENSIBILIA\u003c/h4\u003e\r\n\r\n\u003cp\u003eI shall give the name \u003ci\u003esensibilia\u003c/i\u003e to those objects which have the\r\nsame metaphysical and physical status as sense-data, without\r\nnecessarily being data to any mind. Thus the relation of a \u003ci\u003esensibile\u003c/i\u003e\r\nto a sense-datum is like that of a man to a husband: a man becomes a\r\nhusband by \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_149\" id=\"Page_149\"\u003e[149]\u003c/a\u003e\u003c/span\u003eentering into the relation of marriage, and similarly a\r\n\u003ci\u003esensibile\u003c/i\u003e becomes a sense-datum by entering into the relation of\r\nacquaintance. It is important to have both terms; for we wish to\r\ndiscuss whether an object which is at one time a sense-datum can still\r\nexist at a time when it is not a sense-datum. We cannot ask \"Can\r\nsense-data exist without being given?\" for that is like asking \"Can\r\nhusbands exist without being married?\" We must ask \"Can \u003ci\u003esensibilia\u003c/i\u003e\r\nexist without being given?\" and also \"Can a particular \u003ci\u003esensibile\u003c/i\u003e be\r\nat one time a sense-datum, and at another not?\" Unless we have the\r\nword \u003ci\u003esensibile\u003c/i\u003e as well as the word \"sense-datum,\" such questions are\r\napt to entangle us in trivial logical puzzles.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt will be seen that all sense-data are \u003ci\u003esensibilia\u003c/i\u003e. It is a\r\nmetaphysical question whether all \u003ci\u003esensibilia\u003c/i\u003e are sense-data, and an\r\nepistemological question whether there exist means of inferring\r\n\u003ci\u003esensibilia\u003c/i\u003e which are not data from those that are.\u003c/p\u003e\r\n\r\n\u003cp\u003eA few preliminary remarks, to be amplified as we proceed, will serve\r\nto elucidate the use which I propose to make of \u003ci\u003esensibilia\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003eI regard sense-data as not mental, and as being, in fact, part of the\r\nactual subject-matter of physics. There are arguments, shortly to be\r\nexamined, for their subjectivity, but these arguments seem to me only\r\nto prove \u003ci\u003ephysiological\u003c/i\u003e subjectivity, i.e. causal dependence on the\r\nsense-organs, nerves, and brain. The appearance which a thing presents\r\nto us is causally dependent upon these, in exactly the same way as it\r\nis dependent upon intervening fog or smoke or coloured glass. Both\r\ndependences are contained in the statement that the appearance which a\r\npiece of matter presents when viewed from a given place is a function\r\nnot only of the piece of matter, but also of the intervening medium.\r\n(The terms used in \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_150\" id=\"Page_150\"\u003e[150]\u003c/a\u003e\u003c/span\u003ethis statement\u0026mdash;\"matter,\" \"view from a given\r\nplace,\" \"appearance,\" \"intervening medium\"\u0026mdash;will all be defined in the\r\ncourse of the present paper.) We have not the means of ascertaining\r\nhow things appear from places not surrounded by brain and nerves and\r\nsense-organs, because we cannot leave the body; but continuity makes\r\nit not unreasonable to suppose that they present \u003ci\u003esome\u003c/i\u003e appearance at\r\nsuch places. Any such appearance would be included among \u003ci\u003esensibilia\u003c/i\u003e.\r\nIf\u0026mdash;\u003ci\u003eper impossibile\u003c/i\u003e\u0026mdash;there were a complete human body with no mind\r\ninside it, all those \u003ci\u003esensibilia\u003c/i\u003e would exist, in relation to that\r\nbody, which would be sense-data if there were a mind in the body. What\r\nthe mind adds to \u003ci\u003esensibilia\u003c/i\u003e, in fact, is \u003ci\u003emerely\u003c/i\u003e awareness:\r\neverything else is physical or physiological.\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\r\n\u003ch4\u003eIV. SENSE-DATA ARE PHYSICAL\u003c/h4\u003e\r\n\r\n\u003cp\u003eBefore discussing this question it will be well to define the sense in\r\nwhich the terms \"mental\" and \"physical\" are to be used. The word\r\n\"physical,\" in all preliminary discussions, is to be understood as\r\nmeaning \"what is dealt with by physics.\" Physics, it is plain, tells\r\nus something about some of the constituents of the actual world; what\r\nthese constituents are may be doubtful, but it is they that are to be\r\ncalled physical, whatever their nature may prove to be.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe definition of the term \"mental\" is more difficult, and can only be\r\nsatisfactorily given after many difficult controversies have been\r\ndiscussed and decided. For present purposes therefore I must content\r\nmyself with assuming a dogmatic answer to these controversies. I shall\r\ncall a particular \"mental\" when it is aware of something, and I shall\r\ncall a fact \"mental\" when it contains a mental particular as a\r\nconstituent.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_151\" id=\"Page_151\"\u003e[151]\u003c/a\u003e\u003c/span\u003eIt will be seen that the mental and the physical are not necessarily\r\nmutually exclusive, although I know of no reason to suppose that they\r\noverlap.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe doubt as to the correctness of our definition of the \"mental\" is\r\nof little importance in our present discussion. For what I am\r\nconcerned to maintain is that sense-data are physical, and this being\r\ngranted it is a matter of indifference in our present inquiry whether\r\nor not they are also mental. Although I do not hold, with Mach and\r\nJames and the \"new realists,\" that the difference between the mental\r\nand the physical is \u003ci\u003emerely\u003c/i\u003e one of arrangement, yet what I have to\r\nsay in the present paper is compatible with their doctrine and might\r\nhave been reached from their standpoint.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn discussions on sense-data, two questions are commonly confused,\r\nnamely:\u003c/p\u003e\r\n\r\n\u003cp\u003e(1) Do sensible objects persist when we are not sensible of them? in\r\nother words, do \u003ci\u003esensibilia\u003c/i\u003e which are data at a certain time\r\nsometimes continue to exist at times when they are not data? And (2)\r\nare sense-data mental or physical?\u003c/p\u003e\r\n\r\n\u003cp\u003eI propose to assert that sense-data are physical, while yet\r\nmaintaining that they probably never persist unchanged after ceasing\r\nto be data. The view that they do not persist is often thought, quite\r\nerroneously in my opinion, to imply that they are mental; and this\r\nhas, I believe, been a potent source of confusion in regard to our\r\npresent problem. If there were, as some have held, a \u003ci\u003elogical\r\nimpossibility\u003c/i\u003e in sense-data persisting after ceasing to be data, that\r\ncertainly would tend to show that they were mental; but if, as I\r\ncontend, their non-persistence is merely a probable inference from\r\nempirically ascertained causal laws, then it carries no such\r\nimplication with it, and we are quite free to treat them as part of\r\nthe subject-matter of physics.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_152\" id=\"Page_152\"\u003e[152]\u003c/a\u003e\u003c/span\u003eLogically a sense-datum is an object, a particular of which the\r\nsubject is aware. It does not contain the subject as a part, as for\r\nexample beliefs and volitions do. The existence of the sense-datum is\r\ntherefore not logically dependent upon that of the subject; for the\r\nonly way, so far as I know, in which the existence of \u003ci\u003eA\u003c/i\u003e can be\r\n\u003ci\u003elogically\u003c/i\u003e dependent upon the existence of \u003ci\u003eB\u003c/i\u003e is when \u003ci\u003eB\u003c/i\u003e is part of\r\n\u003ci\u003eA\u003c/i\u003e. There is therefore no \u003ci\u003ea priori\u003c/i\u003e reason why a particular which is\r\na sense-datum should not persist after it has ceased to be a datum,\r\nnor why other similar particulars should not exist without ever being\r\ndata. The view that sense-data are mental is derived, no doubt, in\r\npart from their physiological subjectivity, but in part also from a\r\nfailure to distinguish between sense-data and \"sensations.\" By a\r\nsensation I mean the fact consisting in the subject\u0027s awareness of the\r\nsense-datum. Thus a sensation is a complex of which the subject is a\r\nconstituent and which therefore is mental. The sense-datum, on the\r\nother hand, stands over against the subject as that external object of\r\nwhich in sensation the subject is aware. It is true that the\r\nsense-datum is in many cases in the subject\u0027s body, but the subject\u0027s\r\nbody is as distinct from the subject as tables and chairs are, and is\r\nin fact merely a part of the material world. So soon, therefore, as\r\nsense-data are clearly distinguished from sensations, and as their\r\nsubjectivity is recognised to be physiological not psychical, the\r\nchief obstacles in the way of regarding them as physical are removed.\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\r\n\u003ch4\u003eV. \"SENSIBILIA\" AND \"THINGS\"\u003c/h4\u003e\r\n\r\n\u003cp\u003eBut if \"sensibilia\" are to be recognised as the ultimate constituents\r\nof the physical world, a long and difficult journey is to be performed\r\nbefore we can arrive either at \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_153\" id=\"Page_153\"\u003e[153]\u003c/a\u003e\u003c/span\u003ethe \"thing\" of common sense or at the\r\n\"matter\" of physics. The supposed impossibility of combining the\r\ndifferent sense-data which are regarded as appearances of the same\r\n\"thing\" to different people has made it seem as though these\r\n\"sensibilia\" must be regarded as mere subjective phantasms. A given\r\ntable will present to one man a rectangular appearance, while to\r\nanother it appears to have two acute angles and two obtuse angles; to\r\none man it appears brown, while to another, towards whom it reflects\r\nthe light, it appears white and shiny. It is said, not wholly without\r\nplausibility, that these different shapes and different colours cannot\r\nco-exist simultaneously in the same place, and cannot therefore both\r\nbe constituents of the physical world. This argument I must confess\r\nappeared to me until recently to be irrefutable. The contrary opinion\r\nhas, however, been ably maintained by Dr. T.P. Nunn in an article\r\nentitled: \"Are Secondary Qualities Independent of Perception?\"\u003ca name=\"FNanchor_29_29\" id=\"FNanchor_29_29\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_29_29\" class=\"fnanchor\"\u003e[29]\u003c/a\u003e The\r\nsupposed impossibility derives its apparent force from the phrase:\r\n\"\u003ci\u003ein the same place\u003c/i\u003e,\" and it is precisely in this phrase that its\r\nweakness lies. The conception of space is too often treated in\r\nphilosophy\u0026mdash;even by those who on reflection would not defend such\r\ntreatment\u0026mdash;as though it were as given, simple, and unambiguous as\r\nKant, in his psychological innocence, supposed. It is the unperceived\r\nambiguity of the word \"place\" which, as we shall shortly see, has\r\ncaused the difficulties to realists and given an undeserved advantage\r\nto their opponents. Two \"places\" of different kinds are involved in\r\nevery sense-datum, namely the place \u003ci\u003eat\u003c/i\u003e which it appears and the\r\nplace \u003ci\u003efrom\u003c/i\u003e which it appears. These belong to different spaces,\r\nalthough, as we shall see, it is possible, with certain limitations,\r\nto establish a correlation between them. \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_154\" id=\"Page_154\"\u003e[154]\u003c/a\u003e\u003c/span\u003eWhat we call the different\r\nappearances of the same thing to different observers are each in a\r\nspace private to the observer concerned. No place in the private world\r\nof one observer is identical with a place in the private world of\r\nanother observer. There is therefore no question of combining the\r\ndifferent appearances in the one place; and the fact that they cannot\r\nall exist in one place affords accordingly no ground whatever for\r\nquestioning their physical reality. The \"thing\" of common sense may in\r\nfact be identified with the whole class of its appearances\u0026mdash;where,\r\nhowever, we must include among appearances not only those which are\r\nactual sense-data, but also those \"sensibilia,\" if any, which, on\r\ngrounds of continuity and resemblance, are to be regarded as belonging\r\nto the same system of appearances, although there happen to be no\r\nobservers to whom they are data.\u003c/p\u003e\r\n\r\n\u003cp\u003eAn example may make this clearer. Suppose there are a number of people\r\nin a room, all seeing, as they say, the same tables and chairs, walls\r\nand pictures. No two of these people have exactly the same sense-data,\r\nyet there is sufficient similarity among their data to enable them to\r\ngroup together certain of these data as appearances of one \"thing\" to\r\nthe several spectators, and others as appearances of another \"thing.\"\r\nBesides the appearances which a given thing in the room presents to\r\nthe actual spectators, there are, we may suppose, other appearances\r\nwhich it would present to other possible spectators. If a man were to\r\nsit down between two others, the appearance which the room would\r\npresent to him would be intermediate between the appearances which it\r\npresents to the two others: and although this appearance would not\r\nexist as it is without the sense organs, nerves and brain, of the\r\nnewly arrived spectator, still it is not unnatural to suppose that,\r\nfrom the position \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_155\" id=\"Page_155\"\u003e[155]\u003c/a\u003e\u003c/span\u003ewhich he now occupies, \u003ci\u003esome\u003c/i\u003e appearance of the\r\nroom existed before his arrival. This supposition, however, need\r\nmerely be noticed and not insisted upon.\u003c/p\u003e\r\n\r\n\u003cp\u003eSince the \"thing\" cannot, without indefensible partiality, be\r\nidentified with any single one of its appearances, it came to be\r\nthought of as something distinct from all of them and underlying them.\r\nBut by the principle of Occam\u0027s razor, if the class of appearances\r\nwill fulfil the purposes for the sake of which the thing was invented\r\nby the prehistoric metaphysicians to whom common sense is due, economy\r\ndemands that we should identify the thing with the class of its\r\nappearances. It is not necessary to \u003ci\u003edeny\u003c/i\u003e a substance or substratum\r\nunderlying these appearances; it is merely expedient to abstain from\r\nasserting this unnecessary entity. Our procedure here is precisely\r\nanalogous to that which has swept away from the philosophy of\r\nmathematics the useless menagerie of metaphysical monsters with which\r\nit used to be infested.\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\r\n\u003ch4\u003eVI. CONSTRUCTIONS VERSUS INFERENCES\u003c/h4\u003e\r\n\r\n\u003cp\u003eBefore proceeding to analyse and explain the ambiguities of the word\r\n\"place,\" a few general remarks on method are desirable. The supreme\r\nmaxim in scientific philosophising is this:\u003c/p\u003e\r\n\r\n\u003cdiv class=\"block\"\u003e\u003cp\u003e\u003ci\u003eWherever possible, logical constructions are to be substituted\r\nfor inferred entities.\u003c/i\u003e\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cp\u003eSome examples of the substitution of construction for inference in the\r\nrealm of mathematical philosophy may serve to elucidate the uses of\r\nthis maxim. Take first the case of irrationals. In old days,\r\nirrationals were inferred as the supposed limits of series of\r\nrationals which had no rational limit; but the objection to this\r\nprocedure was \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_156\" id=\"Page_156\"\u003e[156]\u003c/a\u003e\u003c/span\u003ethat it left the existence of irrationals merely\r\noptative, and for this reason the stricter methods of the present day\r\nno longer tolerate such a definition. We now define an irrational\r\nnumber as a certain class of ratios, thus constructing it logically by\r\nmeans of ratios, instead of arriving at it by a doubtful inference\r\nfrom them. Take again the case of cardinal numbers. Two equally\r\nnumerous collections appear to have something in common: this\r\nsomething is supposed to be their cardinal number. But so long as the\r\ncardinal number is inferred from the collections, not constructed in\r\nterms of them, its existence must remain in doubt, unless in virtue of\r\na metaphysical postulate \u003ci\u003ead hoc\u003c/i\u003e. By defining the cardinal number of\r\na given collection as the class of all equally numerous collections,\r\nwe avoid the necessity of this metaphysical postulate, and thereby\r\nremove a needless element of doubt from the philosophy of arithmetic.\r\nA similar method, as I have shown elsewhere, can be applied to classes\r\nthemselves, which need not be supposed to have any metaphysical\r\nreality, but can be regarded as symbolically constructed fictions.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe method by which the construction proceeds is closely analogous in\r\nthese and all similar cases. Given a set of propositions nominally\r\ndealing with the supposed inferred entities, we observe the properties\r\nwhich are required of the supposed entities in order to make these\r\npropositions true. By dint of a little logical ingenuity, we then\r\nconstruct some logical function of less hypothetical entities which\r\nhas the requisite properties. This constructed function we substitute\r\nfor the supposed inferred entities, and thereby obtain a new and less\r\ndoubtful interpretation of the body of propositions in question. This\r\nmethod, so fruitful in the philosophy of mathematics, will be found\r\nequally applicable in the philosophy of \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_157\" id=\"Page_157\"\u003e[157]\u003c/a\u003e\u003c/span\u003ephysics, where, I do not\r\ndoubt, it would have been applied long ago but for the fact that all\r\nwho have studied this subject hitherto have been completely ignorant\r\nof mathematical logic. I myself cannot claim originality in the\r\napplication of this method to physics, since I owe the suggestion and\r\nthe stimulus for its application entirely to my friend and\r\ncollaborator Dr. Whitehead, who is engaged in applying it to the more\r\nmathematical portions of the region intermediate between sense-data\r\nand the points, instants and particles of physics.\u003c/p\u003e\r\n\r\n\u003cp\u003eA complete application of the method which substitutes constructions\r\nfor inferences would exhibit matter wholly in terms of sense-data, and\r\neven, we may add, of the sense-data of a single person, since the\r\nsense-data of others cannot be known without some element of\r\ninference. This, however, must remain for the present an ideal, to be\r\napproached as nearly as possible, but to be reached, if at all, only\r\nafter a long preliminary labour of which as yet we can only see the\r\nvery beginning. The inferences which are unavoidable can, however, be\r\nsubjected to certain guiding principles. In the first place they\r\nshould always be made perfectly explicit, and should be formulated in\r\nthe most general manner possible. In the second place the inferred\r\nentities should, whenever this can be done, be similar to those whose\r\nexistence is given, rather than, like the Kantian \u003ci\u003eDing an sich\u003c/i\u003e,\r\nsomething wholly remote from the data which nominally support the\r\ninference. The inferred entities which I shall allow myself are of two\r\nkinds: (\u003ci\u003ea\u003c/i\u003e) the sense-data of other people, in favour of which there\r\nis the evidence of testimony, resting ultimately upon the analogical\r\nargument in favour of minds other than my own; (\u003ci\u003eb\u003c/i\u003e) the \"sensibilia\"\r\nwhich would appear from places where there happen to be no minds, and\r\nwhich I suppose to be real although they are no one\u0027s \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_158\" id=\"Page_158\"\u003e[158]\u003c/a\u003e\u003c/span\u003edata. Of these\r\ntwo classes of inferred entities, the first will probably be allowed\r\nto pass unchallenged. It would give me the greatest satisfaction to be\r\nable to dispense with it, and thus establish physics upon a\r\nsolipsistic basis; but those\u0026mdash;and I fear they are the majority\u0026mdash;in\r\nwhom the human affections are stronger than the desire for logical\r\neconomy, will, no doubt, not share my desire to render solipsism\r\nscientifically satisfactory. The second class of inferred entities\r\nraises much more serious questions. It may be thought monstrous to\r\nmaintain that a thing can present any appearance at all in a place\r\nwhere no sense organs and nervous structure exist through which it\r\ncould appear. I do not myself feel the monstrosity; nevertheless I\r\nshould regard these supposed appearances only in the light of a\r\nhypothetical scaffolding, to be used while the edifice of physics is\r\nbeing raised, though possibly capable of being removed as soon as the\r\nedifice is completed. These \"sensibilia\" which are not data to anyone\r\nare therefore to be taken rather as an illustrative hypothesis and as\r\nan aid in preliminary statement than as a dogmatic part of the\r\nphilosophy of physics in its final form.\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\r\n\u003ch4\u003eVII. PRIVATE SPACE AND THE SPACE OF PERSPECTIVES\u003c/h4\u003e\r\n\r\n\u003cp\u003eWe have now to explain the ambiguity in the word \"place,\" and how it\r\ncomes that two places of different sorts are associated with every\r\nsense-datum, namely the place \u003ci\u003eat\u003c/i\u003e which it is and the place \u003ci\u003efrom\u003c/i\u003e\r\nwhich it is perceived. The theory to be advocated is closely analogous\r\nto Leibniz\u0027s monadology, from which it differs chiefly in being less\r\nsmooth and tidy.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe first fact to notice is that, so far as can be discovered, no\r\nsensibile is ever a datum to two people at \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_159\" id=\"Page_159\"\u003e[159]\u003c/a\u003e\u003c/span\u003eonce. The things seen by\r\ntwo different people are often closely similar, so similar that the\r\nsame \u003ci\u003ewords\u003c/i\u003e can be used to denote them, without which communication\r\nwith others concerning sensible objects would be impossible. But, in\r\nspite of this similarity, it would seem that some difference always\r\narises from difference in the point of view. Thus each person, so far\r\nas his sense-data are concerned, lives in a private world. This\r\nprivate world contains its own space, or rather spaces, for it would\r\nseem that only experience teaches us to correlate the space of sight\r\nwith the space of touch and with the various other spaces of other\r\nsenses. This multiplicity of private spaces, however, though\r\ninteresting to the psychologist, is of no great importance in regard\r\nto our present problem, since a merely solipsistic experience enables\r\nus to correlate them into the one private space which embraces all our\r\nown sense-data. The place \u003ci\u003eat\u003c/i\u003e which a sense-datum is, is a place in\r\nprivate space. This place therefore is different from any place in the\r\nprivate space of another percipient. For if we assume, as logical\r\neconomy demands, that all position is relative, a place is only\r\ndefinable by the things in or around it, and therefore the same place\r\ncannot occur in two private worlds which have no common constituent.\r\nThe question, therefore, of combining what we call different\r\nappearances of the same thing in the same place does not arise, and\r\nthe fact that a given object appears to different spectators to have\r\ndifferent shapes and colours affords no argument against the physical\r\nreality of all these shapes and colours.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn addition to the private spaces belonging to the private worlds of\r\ndifferent percipients, there is, however, another space, in which one\r\nwhole private world counts as a point, or at least as a spatial unit.\r\nThis might be \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_160\" id=\"Page_160\"\u003e[160]\u003c/a\u003e\u003c/span\u003edescribed as the space of points of view, since each\r\nprivate world may be regarded as the appearance which the universe\r\npresents from a certain point of view. I prefer, however, to speak of\r\nit as the space of \u003ci\u003eperspectives\u003c/i\u003e, in order to obviate the suggestion\r\nthat a private world is only real when someone views it. And for the\r\nsame reason, when I wish to speak of a private world without assuming\r\na percipient, I shall call it a \"perspective.\"\u003c/p\u003e\r\n\r\n\u003cp\u003eWe have now to explain how the different perspectives are ordered in\r\none space. This is effected by means of the correlated \"sensibilia\"\r\nwhich are regarded as the appearances, in different perspectives, of\r\none and the same thing. By moving, and by testimony, we discover that\r\ntwo different perspectives, though they cannot both contain the same\r\n\"sensibilia,\" may nevertheless contain very similar ones; and the\r\nspatial order of a certain group of \"sensibilia\" in a private space of\r\none perspective is found to be identical with, or very similar to, the\r\nspatial order of the correlated \"sensibilia\" in the private space of\r\nanother perspective. In this way one \"sensibile\" in one perspective is\r\ncorrelated with one \"sensibile\" in another. Such correlated\r\n\"sensibilia\" will be called \"appearances of one thing.\" In Leibniz\u0027s\r\nmonadology, since each monad mirrored the whole universe, there was in\r\neach perspective a \"sensibile\" which was an appearance of each thing.\r\nIn our system of perspectives, we make no such assumption of\r\ncompleteness. A given thing will have appearances in some\r\nperspectives, but presumably not in certain others. The \"thing\" being\r\ndefined as the class of its appearances, if \u0026kappa; is the\r\nclass of perspectives in which a certain thing \u0026theta; appears,\r\nthen \u0026theta; is a member of the multiplicative class of \u0026kappa;, \u0026kappa;\r\nbeing a class of mutually exclusive classes of\r\n\"sensibilia.\" And \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_161\" id=\"Page_161\"\u003e[161]\u003c/a\u003e\u003c/span\u003esimilarly a perspective is a member of the\r\nmultiplicative class of the things which appear in it.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe arrangement of perspectives in a space is effected by means of the\r\ndifferences between the appearances of a given thing in the various\r\nperspectives. Suppose, say, that a certain penny appears in a number\r\nof different perspectives; in some it looks larger and in some\r\nsmaller, in some it looks circular, in others it presents the\r\nappearance of an ellipse of varying eccentricity. We may collect\r\ntogether all those perspectives in which the appearance of the penny\r\nis circular. These we will place on one straight line, ordering them\r\nin a series by the variations in the apparent size of the penny. Those\r\nperspectives in which the penny appears as a straight line of a\r\ncertain thickness will similarly be placed upon a plane (though in\r\nthis case there will be many different perspectives in which the penny\r\nis of the same size; when one arrangement is completed these will form\r\na circle concentric with the penny), and ordered as before by the\r\napparent size of the penny. By such means, all those perspectives in\r\nwhich the penny presents a visual appearance can be arranged in a\r\nthree-dimensional spatial order. Experience shows that the same\r\nspatial order of perspectives would have resulted if, instead of the\r\npenny, we had chosen any other thing which appeared in all the\r\nperspectives in question, or any other method of utilising the\r\ndifferences between the appearances of the same things in different\r\nperspectives. It is this empirical fact which has made it possible to\r\nconstruct the one all-embracing space of physics.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe space whose construction has just been explained, and whose\r\nelements are whole perspectives, will be called \"perspective-space.\"\u003c/p\u003e\r\n\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_162\" id=\"Page_162\"\u003e[162]\u003c/a\u003e\u003c/span\u003e\u003cbr /\u003e\r\n\r\n\u003ch4\u003eVIII. THE PLACING OF \"THINGS\" AND \"SENSIBILIA\" IN PERSPECTIVE SPACE\u003c/h4\u003e\r\n\r\n\u003cp\u003eThe world which we have so far constructed is a world of six\r\ndimensions, since it is a three-dimensional series of perspectives,\r\neach of which is itself three-dimensional. We have now to explain the\r\ncorrelation between the perspective space and the various private\r\nspaces contained within the various perspectives severally. It is by\r\nmeans of this correlation that the one three-dimensional space of\r\nphysics is constructed; and it is because of the unconscious\r\nperformance of this correlation that the distinction between\r\nperspective space and the percipient\u0027s private space has been blurred,\r\nwith disastrous results for the philosophy of physics. Let us revert\r\nto our penny: the perspectives in which the penny appears larger are\r\nregarded as being nearer to the penny than those in which it appears\r\nsmaller, but as far as experience goes the apparent size of the penny\r\nwill not grow beyond a certain limit, namely, that where (as we say)\r\nthe penny is so near the eye that if it were any nearer it could not\r\nbe seen. By touch we may prolong the series until the penny touches\r\nthe eye, but no further. If we have been travelling along a line of\r\nperspectives in the previously defined sense, we may, however, by\r\nimagining the penny removed, prolong the line of perspectives by\r\nmeans, say, of another penny; and the same may be done with any other\r\nline of perspectives defined by means of the penny. All these lines\r\nmeet in a certain place, that is, in a certain perspective. This\r\nperspective will be defined as \"the place where the penny is.\"\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is now evident in what sense two places in constructed physical\r\nspace are associated with a given \"sensibile.\" There is first the\r\nplace which is the \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_163\" id=\"Page_163\"\u003e[163]\u003c/a\u003e\u003c/span\u003eperspective of which the \"sensibile\" is a member.\r\nThis is the place \u003ci\u003efrom\u003c/i\u003e which the \"sensibile\" appears. Secondly there\r\nis the place where the thing is of which the \"sensibile\" is a member,\r\nin other words an appearance; this is the place \u003ci\u003eat\u003c/i\u003e which the\r\n\"sensibile\" appears. The \"sensibile\" which is a member of one\r\nperspective is correlated with another perspective, namely, that which\r\nis the place where the thing is of which the \"sensibile\" is an\r\nappearance. To the psychologist the \"place from which\" is the more\r\ninteresting, and the \"sensibile\" accordingly appears to him subjective\r\nand where the percipient is. To the physicist the \"place at which\" is\r\nthe more interesting, and the \"sensibile\" accordingly appears to him\r\nphysical and external. The causes, limits and partial justification of\r\neach of these two apparently incompatible views are evident from the\r\nabove duplicity of places associated with a given \"sensibile.\"\u003c/p\u003e\r\n\r\n\u003cp\u003eWe have seen that we can assign to a physical thing a place in the\r\nperspective space. In this way different parts of our body acquire\r\npositions in perspective space, and therefore there is a meaning\r\n(whether true or false need not much concern us) in saying that the\r\nperspective to which our sense-data belong is inside our head. Since\r\nour mind is correlated with the perspective to which our sense-data\r\nbelong, we may regard this perspective as being the position of our\r\nmind in perspective space. If, therefore, this perspective is, in the\r\nabove defined sense, inside our head, there is a good meaning for the\r\nstatement that the mind is in the head. We can now say of the various\r\nappearances of a given thing that some of them are nearer to the thing\r\nthan others; those are nearer which belong to perspectives that are\r\nnearer to \"the place where the thing is.\" We can thus find a meaning,\r\ntrue or false, for the statement that more is to \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_164\" id=\"Page_164\"\u003e[164]\u003c/a\u003e\u003c/span\u003ebe learnt about a\r\nthing by examining it close to than by viewing it from a distance. We\r\ncan also find a meaning for the phrase \"the things which intervene\r\nbetween the subject and a thing of which an appearance is a datum to\r\nhim.\" One reason often alleged for the subjectivity of sense-data is\r\nthat the appearance of a thing may change when we find it hard to\r\nsuppose that the thing itself has changed\u0026mdash;for example, when the\r\nchange is due to our shutting our eyes, or to our screwing them up so\r\nas to make the thing look double. If the thing is defined as the class\r\nof its appearances (which is the definition adopted above), there is\r\nof course necessarily \u003ci\u003esome\u003c/i\u003e change in the thing whenever any one of\r\nits appearances changes. Nevertheless there is a very important\r\ndistinction between two different ways in which the appearances may\r\nchange. If after looking at a thing I shut my eyes, the appearance of\r\nmy eyes changes in every perspective in which there is such an\r\nappearance, whereas most of the appearances of the thing will remain\r\nunchanged. We may say, as a matter of definition, that a thing changes\r\nwhen, however near to the thing an appearance of it may be, there are\r\nchanges in appearances as near as, or still nearer to, the thing. On\r\nthe other hand we shall say that the change is in some other thing if\r\nall appearances of the thing which are at not more than a certain\r\ndistance from the thing remain unchanged, while only comparatively\r\ndistant appearances of the thing are altered. From this consideration\r\nwe are naturally led to the consideration of \u003ci\u003ematter\u003c/i\u003e, which must be\r\nour next topic.\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\r\n\u003ch4\u003eIX. THE DEFINITION OF MATTER\u003c/h4\u003e\r\n\r\n\u003cp\u003eWe defined the \"physical thing\" as the class of its appearances, but\r\nthis can hardly be taken as a definition of matter. We want to be able\r\nto express the fact that \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_165\" id=\"Page_165\"\u003e[165]\u003c/a\u003e\u003c/span\u003ethe appearance of a thing in a given\r\nperspective is causally affected by the matter between the thing and\r\nthe perspective. We have found a meaning for \"between a thing and a\r\nperspective.\" But we want matter to be something other than the whole\r\nclass of appearances of a thing, in order to state the influence of\r\nmatter on appearances.\u003c/p\u003e\r\n\r\n\u003cp\u003eWe commonly assume that the information we get about a thing is more\r\naccurate when the thing is nearer. Far off, we see it is a man; then\r\nwe see it is Jones; then we see he is smiling. Complete accuracy would\r\nonly be attainable as a limit: if the appearances of Jones as we\r\napproach him tend towards a limit, that limit may be taken to be what\r\nJones really is. It is obvious that from the point of view of physics\r\nthe appearances of a thing close to \"count\" more than the appearances\r\nfar off. We may therefore set up the following tentative definition:\u003c/p\u003e\r\n\r\n\u003cp\u003eThe \u003ci\u003ematter\u003c/i\u003e of a given thing is the limit of its appearances as their\r\ndistance from the thing diminishes.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt seems probable that there is something in this definition, but it\r\nis not quite satisfactory, because empirically there is no such limit\r\nto be obtained from sense-data. The definition will have to be eked\r\nout by constructions and definitions. But probably it suggests the\r\nright direction in which to look.\u003c/p\u003e\r\n\r\n\u003cp\u003eWe are now in a position to understand in outline the reverse journey\r\nfrom matter to sense-data which is performed by physics. The\r\nappearance of a thing in a given perspective is a function of the\r\nmatter composing the thing and of the intervening matter. The\r\nappearance of a thing is altered by intervening smoke or mist, by blue\r\nspectacles or by alterations in the sense-organs or nerves of the\r\npercipient (which also must be reckoned as part of the intervening\r\nmedium). The nearer we approach to \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_166\" id=\"Page_166\"\u003e[166]\u003c/a\u003e\u003c/span\u003ethe thing, the less its appearance\r\nis affected by the intervening matter. As we travel further and\r\nfurther from the thing, its appearances diverge more and more from\r\ntheir initial character; and the causal laws of their divergence are\r\nto be stated in terms of the matter which lies between them and the\r\nthing. Since the appearances at very small distances are less affected\r\nby causes other than the thing itself, we come to think that the limit\r\ntowards which these appearances tend as the distance diminishes is\r\nwhat the thing \"really is,\" as opposed to what it merely seems to be.\r\nThis, together with its necessity for the statement of causal laws,\r\nseems to be the source of the entirely erroneous feeling that matter\r\nis more \"real\" than sense-data.\u003c/p\u003e\r\n\r\n\u003cp\u003eConsider for example the infinite divisibility of matter. In looking\r\nat a given thing and approaching it, one sense-datum will become\r\nseveral, and each of these will again divide. Thus \u003ci\u003eone\u003c/i\u003e appearance\r\nmay represent \u003ci\u003emany\u003c/i\u003e things, and to this process there seems no end.\r\nHence in the limit, when we approach indefinitely near to the thing\r\nthere will be an indefinite number of units of matter corresponding to\r\nwhat, at a finite distance, is only one appearance. This is how\r\ninfinite divisibility arises.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe whole causal efficacy of a thing resides in its matter. This is in\r\nsome sense an empirical fact, but it would be hard to state it\r\nprecisely, because \"causal efficacy\" is difficult to define.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhat can be known empirically about the matter of a thing is only\r\napproximate, because we cannot get to know the appearances of the\r\nthing from very small distances, and cannot accurately infer the limit\r\nof these appearances. But it \u003ci\u003eis\u003c/i\u003e inferred \u003ci\u003eapproximately\u003c/i\u003e by means of\r\nthe appearances we can observe. It then turns out that these\r\nappearances can be exhibited by physics as a function of \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_167\" id=\"Page_167\"\u003e[167]\u003c/a\u003e\u003c/span\u003ethe matter\r\nin our immediate neighbourhood; e.g. the visual appearance of a\r\ndistant object is a function of the light-waves that reach the eyes.\r\nThis leads to confusions of thought, but offers no real difficulty.\u003c/p\u003e\r\n\r\n\u003cp\u003eOne appearance, of a visible object for example, is not sufficient to\r\ndetermine its other simultaneous appearances, although it goes a\r\ncertain distance towards determining them. The determination of the\r\nhidden structure of a thing, so far as it is possible at all, can only\r\nbe effected by means of elaborate dynamical inferences.\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\r\n\u003ch4\u003eX. TIME\u003ca name=\"FNanchor_30_30\" id=\"FNanchor_30_30\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_30_30\" class=\"fnanchor\"\u003e[30]\u003c/a\u003e\u003c/h4\u003e\r\n\r\n\u003cp\u003eIt seems that the one all-embracing time is a construction, like the\r\none all-embracing space. Physics itself has become conscious of this\r\nfact through the discussions connected with relativity.\u003c/p\u003e\r\n\r\n\u003cp\u003eBetween two perspectives which both belong to one person\u0027s experience,\r\nthere will be a direct time-relation of before and after. This\r\nsuggests a way of dividing history in the same sort of way as it is\r\ndivided by different experiences, but without introducing experience\r\nor anything mental: we may define a \"biography\" as everything that is\r\n(directly) earlier or later than, or simultaneous with, a given\r\n\"sensibile.\" This will give a series of perspectives, which \u003ci\u003emight\u003c/i\u003e\r\nall form parts of one person\u0027s experience, though it is not necessary\r\nthat all or any of them should actually do so. By this means, the\r\nhistory of the world is divided into a number of mutually exclusive\r\nbiographies.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_168\" id=\"Page_168\"\u003e[168]\u003c/a\u003e\u003c/span\u003eWe have now to correlate the times in the different biographies. The\r\nnatural thing would be to say that the appearances of a given\r\n(momentary) thing in two different perspectives belonging to different\r\nbiographies are to be taken as simultaneous; but this is not\r\nconvenient. Suppose \u003ci\u003eA\u003c/i\u003e shouts to \u003ci\u003eB\u003c/i\u003e, and \u003ci\u003eB\u003c/i\u003e replies as soon as he\r\nhears \u003ci\u003eA\u0027s\u003c/i\u003e shout. Then between \u003ci\u003eA\u0027s\u003c/i\u003e hearing of his own shout and his\r\nhearing of \u003ci\u003eB\u0027s\u003c/i\u003e there is an interval; thus if we made \u003ci\u003eA\u0027s\u003c/i\u003e and \u003ci\u003eB\u0027s\u003c/i\u003e\r\nhearing of the same shout exactly simultaneous with each other, we\r\nshould have events exactly simultaneous with a given event but not\r\nwith each other. To obviate this, we assume a \"velocity of sound.\"\r\nThat is, we assume that the time when \u003ci\u003eB\u003c/i\u003e hears \u003ci\u003eA\u0027s\u003c/i\u003e shout is\r\nhalf-way between the time when \u003ci\u003eA\u003c/i\u003e hears his own shout and the time\r\nwhen he hears \u003ci\u003eB\u0027s\u003c/i\u003e. In this way the correlation is effected.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhat has been said about sound applies of course equally to light. The\r\ngeneral principle is that the appearances, in different perspectives,\r\nwhich are to be grouped together as constituting what a certain thing\r\nis at a certain moment, are not to be all regarded as being at that\r\nmoment. On the contrary they spread outward from the thing with\r\nvarious velocities according to the nature of the appearances. Since\r\nno \u003ci\u003edirect\u003c/i\u003e means exist of correlating the time in one biography with\r\nthe time in another, this temporal grouping of the appearances\r\nbelonging to a given thing at a given moment is in part conventional.\r\nIts motive is partly to secure the verification of such maxims as that\r\nevents which are exactly simultaneous with the same event are exactly\r\nsimultaneous with one another, partly to secure convenience in the\r\nformulation of causal laws.\u003c/p\u003e\r\n\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_169\" id=\"Page_169\"\u003e[169]\u003c/a\u003e\u003c/span\u003e\u003cbr /\u003e\r\n\r\n\u003ch4\u003eXI. THE PERSISTENCE OF THINGS AND MATTER\u003c/h4\u003e\r\n\r\n\u003cp\u003eApart from any of the fluctuating hypotheses of physics, three main\r\nproblems arise in connecting the world of physics with the world of\r\nsense, namely:\u003c/p\u003e\r\n\r\n\u003cdiv class=\"block\"\u003e\r\n\u003cp class=\"noin\"\u003e1. the construction of a single space;\u003cbr /\u003e\r\n2. the construction of a single time;\u003cbr /\u003e\r\n3. the construction of permanent things or matter.\u003c/p\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eWe have already considered the first and second of these problems; it\r\nremains to consider the third.\u003c/p\u003e\r\n\r\n\u003cp\u003eWe have seen how correlated appearances in different perspectives are\r\ncombined to form one \"thing\" at one moment in the all-embracing time\r\nof physics. We have now to consider how appearances at different times\r\nare combined as belonging to one \"thing,\" and how we arrive at the\r\npersistent \"matter\" of physics. The assumption of permanent substance,\r\nwhich technically underlies the procedure of physics, cannot of course\r\nbe regarded as metaphysically legitimate: just as the one thing\r\nsimultaneously seen by many people is a construction, so the one thing\r\nseen at different times by the same or different people must be a\r\nconstruction, being in fact nothing but a certain grouping of certain\r\n\"sensibilia.\"\u003c/p\u003e\r\n\r\n\u003cp\u003eWe have seen that the momentary state of a \"thing\" is an assemblage of\r\n\"sensibilia,\" in different perspectives, not all simultaneous in the\r\none constructed time, but spreading out from \"the place where the\r\nthing is\" with velocities depending upon the nature of the\r\n\"sensibilia.\" The time \u003ci\u003eat\u003c/i\u003e which the \"thing\" is in this state is the\r\nlower limit of the times at which these appearances occur. We have now\r\nto consider what leads us to speak of another set of appearances as\r\nbelonging to the same \"thing\" at a different time.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_170\" id=\"Page_170\"\u003e[170]\u003c/a\u003e\u003c/span\u003eFor this purpose, we may, at least to begin with, confine ourselves\r\nwithin a single biography. If we can always say when two \"sensibilia\"\r\nin a given biography are appearances of one thing, then, since we have\r\nseen how to connect \"sensibilia\" in different biographies as\r\nappearances of the same momentary state of a thing, we shall have all\r\nthat is necessary for the complete construction of the history of a\r\nthing.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is to be observed, to begin with, that the identity of a thing for\r\ncommon sense is not always correlated with the identity of matter for\r\nphysics. A human body is one persisting thing for common sense, but\r\nfor physics its matter is constantly changing. We may say, broadly,\r\nthat the common-sense conception is based upon continuity in\r\nappearances at the ordinary distances of sense-data, while the\r\nphysical conception is based upon the continuity of appearances at\r\nvery small distances from the thing. It is probable that the\r\ncommon-sense conception is not capable of complete precision. Let us\r\ntherefore concentrate our attention upon the conception of the\r\npersistence of matter in physics.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe first characteristic of two appearances of the same piece of\r\nmatter at different times is \u003ci\u003econtinuity\u003c/i\u003e. The two appearances must be\r\nconnected by a series of intermediaries, which, if time and space form\r\ncompact series, must themselves form a compact series. The colour of\r\nthe leaves is different in autumn from what it is in summer; but we\r\nbelieve that the change occurs gradually, and that, if the colours are\r\ndifferent at two given times, there are intermediate times at which\r\nthe colours are intermediate between those at the given times.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut there are two considerations that are important as regards\r\ncontinuity.\u003c/p\u003e\r\n\r\n\u003cp\u003eFirst, it is largely hypothetical. We do not observe \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_171\" id=\"Page_171\"\u003e[171]\u003c/a\u003e\u003c/span\u003eany one thing\r\ncontinuously, and it is merely a hypothesis to assume that, while we\r\nare not observing it, it passes through conditions intermediate\r\nbetween those in which it is perceived. During uninterrupted\r\nobservation, it is true, continuity is nearly verified; but even here,\r\nwhen motions are very rapid, as in the case of explosions, the\r\ncontinuity is not actually capable of direct verification. Thus we can\r\nonly say that the sense-data are found to \u003ci\u003epermit\u003c/i\u003e a hypothetical\r\ncomplement of \"sensibilia\" such as will preserve continuity, and that\r\ntherefore there \u003ci\u003emay\u003c/i\u003e be such a complement. Since, however, we have\r\nalready made such use of hypothetical \"sensibilia,\" we will let this\r\npoint pass, and admit such \"sensibilia\" as are required to preserve\r\ncontinuity.\u003c/p\u003e\r\n\r\n\u003cp\u003eSecondly, continuity is not a sufficient criterion of material\r\nidentity. It is true that in many cases, such as rocks, mountains,\r\ntables, chairs, etc., where the appearances change slowly, continuity\r\nis sufficient, but in other cases, such as the parts of an\r\napproximately homogeneous fluid, it fails us utterly. We can travel by\r\nsensibly continuous gradations from any one drop of the sea at any one\r\ntime to any other drop at any other time. We infer the motions of\r\nsea-water from the effects of the current, but they cannot be inferred\r\nfrom direct sensible observation together with the assumption of\r\ncontinuity.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe characteristic required in addition to continuity is conformity\r\nwith the laws of dynamics. Starting from what common sense regards as\r\npersistent things, and making only such modifications as from time to\r\ntime seem reasonable, we arrive at assemblages of \"sensibilia\" which\r\nare found to obey certain simple laws, namely those of dynamics. By\r\nregarding \"sensibilia\" at different times as belonging to the same\r\npiece of matter, we are able to define \u003ci\u003emotion\u003c/i\u003e, which presupposes the\r\nassumption \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_172\" id=\"Page_172\"\u003e[172]\u003c/a\u003e\u003c/span\u003eor construction of something persisting throughout the\r\ntime of the motion. The motions which are regarded as occurring,\r\nduring a period in which all the \"sensibilia\" and the times of their\r\nappearance are given, will be different according to the manner in\r\nwhich we combine \"sensibilia\" at different times as belonging to the\r\nsame piece of matter. Thus even when the whole history of the world is\r\ngiven in every particular, the question what motions take place is\r\nstill to a certain extent arbitrary even after the assumption of\r\ncontinuity. Experience shows that it is possible to determine motions\r\nin such a way as to satisfy the laws of dynamics, and that this\r\ndetermination, roughly and on the whole, is fairly in agreement with\r\nthe common-sense opinions about persistent things. This determination,\r\ntherefore, is adopted, and leads to a criterion by which we can\r\ndetermine, sometimes practically, sometimes only theoretically,\r\nwhether two appearances at different times are to be regarded as\r\nbelonging to the same piece of matter. The persistence of all matter\r\nthroughout all time can, I imagine, be secured by definition.\u003c/p\u003e\r\n\r\n\u003cp\u003eTo recommend this conclusion, we must consider what it is that is\r\nproved by the empirical success of physics. What is proved is that its\r\nhypotheses, though unverifiable where they go beyond sense-data, are\r\nat no point in contradiction with sense-data, but, on the contrary,\r\nare ideally such as to render all sense-data calculable when a\r\nsufficient collection of \"sensibilia\" is given. Now physics has found\r\nit empirically possible to collect sense-data into series, each series\r\nbeing regarded as belonging to one \"thing,\" and behaving, with regard\r\nto the laws of physics, in a way in which series not belonging to one\r\nthing would in general not behave. If it is to be unambiguous whether\r\ntwo appearances belong to the same \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_173\" id=\"Page_173\"\u003e[173]\u003c/a\u003e\u003c/span\u003ething or not, there must be only\r\none way of grouping appearances so that the resulting things obey the\r\nlaws of physics. It would be very difficult to prove that this is the\r\ncase, but for our present purposes we may let this point pass, and\r\nassume that there is only one way. Thus we may lay down the following\r\ndefinition: \u003ci\u003ePhysical things are those series of appearances whose\r\nmatter obeys the laws of physics\u003c/i\u003e. That such series exist is an\r\nempirical fact, which constitutes the verifiability of physics.\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\r\n\u003ch4\u003eXII. ILLUSIONS, HALLUCINATIONS, AND DREAMS\u003c/h4\u003e\r\n\r\n\u003cp\u003eIt remains to ask how, in our system, we are to find a place for\r\nsense-data which apparently fail to have the usual connection with the\r\nworld of physics. Such sense-data are of various kinds, requiring\r\nsomewhat different treatment. But all are of the sort that would be\r\ncalled \"unreal,\" and therefore, before embarking upon the discussion,\r\ncertain logical remarks must be made upon the conceptions of reality\r\nand unreality.\u003c/p\u003e\r\n\r\n\u003cp\u003eMr. A. Wolf\u003ca name=\"FNanchor_31_31\" id=\"FNanchor_31_31\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_31_31\" class=\"fnanchor\"\u003e[31]\u003c/a\u003e says:\u003c/p\u003e\r\n\r\n\u003cdiv class=\"block\"\u003e\u003cp\u003e\"The conception of mind as a system of transparent activities is,\r\nI think, also untenable because of its failure to account for the\r\nvery possibility of dreams and hallucinations. It seems impossible\r\nto realise how a bare, transparent activity can be directed to\r\nwhat is not there, to apprehend what is not given.\"\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cp\u003eThis statement is one which, probably, most people would endorse. But\r\nit is open to two objections. First it is difficult to see how an\r\nactivity, however un-\"transparent,\" can be directed towards a nothing:\r\na term of a relation cannot be a mere nonentity. Secondly, no reason\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_174\" id=\"Page_174\"\u003e[174]\u003c/a\u003e\u003c/span\u003eis given, and I am convinced that none can be given, for the assertion\r\nthat dream-objects are not \"there\" and not \"given.\" Let us take the\r\nsecond point first.\u003c/p\u003e\r\n\r\n\u003cp\u003e(1) The belief that dream-objects are not given comes, I think, from\r\nfailure to distinguish, as regards waking life, between the\r\nsense-datum and the corresponding \"thing.\" In dreams, there is no such\r\ncorresponding \"thing\" as the dreamer supposes; if, therefore, the\r\n\"thing\" were given in waking life, as e.g. Meinong maintains,\u003ca name=\"FNanchor_32_32\" id=\"FNanchor_32_32\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_32_32\" class=\"fnanchor\"\u003e[32]\u003c/a\u003e then\r\nthere would be a difference in respect of givenness between dreams and\r\nwaking life. But if, as we have maintained, what is given is never the\r\nthing, but merely one of the \"sensibilia\" which compose the thing,\r\nthen what we apprehend in a dream is just as much given as what we\r\napprehend in waking life.\u003c/p\u003e\r\n\r\n\u003cp\u003eExactly the same argument applies as to the dream-objects being\r\n\"there.\" They have their position in the private space of the\r\nperspective of the dreamer; where they fail is in their correlation\r\nwith other private spaces and therefore with perspective space. But in\r\nthe only sense in which \"there\" can be a datum, they are \"there\" just\r\nas truly as any of the sense-data of waking life.\u003c/p\u003e\r\n\r\n\u003cp\u003e(2) The conception of \"illusion\" or \"unreality,\" and the correlative\r\nconception of \"reality,\" are generally used in a way which embodies\r\nprofound logical confusions. Words that go in pairs, such as \"real\"\r\nand \"unreal,\" \"existent\" and \"non-existent,\" \"valid\" and \"invalid,\"\r\netc., are all derived from the one fundamental pair, \"true\" and\r\n\"false.\" Now \"true\" and \"false\" are applicable only\u0026mdash;except in\r\nderivative significations\u0026mdash;to \u003ci\u003epropositions\u003c/i\u003e. Thus wherever the above\r\npairs can be significantly applied, we must be dealing either with\r\npropositions or with such incomplete phrases as \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_175\" id=\"Page_175\"\u003e[175]\u003c/a\u003e\u003c/span\u003eonly acquire meaning\r\nwhen put into a context which, with them, forms a proposition. Thus\r\nsuch pairs of words can be applied to \u003ci\u003edescriptions\u003c/i\u003e,\u003ca name=\"FNanchor_33_33\" id=\"FNanchor_33_33\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_33_33\" class=\"fnanchor\"\u003e[33]\u003c/a\u003e but not to\r\nproper names: in other words, they have no application whatever to\r\ndata, but only to entities or non-entities described in terms of data.\u003c/p\u003e\r\n\r\n\u003cp\u003eLet us illustrate by the terms \"existence\" and \"non-existence.\" Given\r\nany datum \u003ci\u003ex\u003c/i\u003e, it is meaningless either to assert or to deny that \u003ci\u003ex\u003c/i\u003e\r\n\"exists.\" We might be tempted to say: \"Of course \u003ci\u003ex\u003c/i\u003e exists, for\r\notherwise it could not be a datum.\" But such a statement is really\r\nmeaningless, although it is significant and true to say \"My present\r\nsense-datum exists,\" and it may also be true that \"\u003ci\u003ex\u003c/i\u003e is my present\r\nsense-datum.\" The inference from these two propositions to \"\u003ci\u003ex\u003c/i\u003e\r\nexists\" is one which seems irresistible to people unaccustomed to\r\nlogic; yet the apparent proposition inferred is not merely false, but\r\nstrictly meaningless. To say \"My present sense-datum exists\" is to say\r\n(roughly): \"There is an object of which \u0027my present sense-datum\u0027 is a\r\ndescription.\" But we cannot say: \"There is an object of which \u0027\u003ci\u003ex\u003c/i\u003e\u0027 is\r\na description,\" because \u0027\u003ci\u003ex\u003c/i\u003e\u0027 is (in the case we are supposing) a\r\nname, not a description. Dr. Whitehead and I have explained this point\r\nfully elsewhere (\u003ci\u003eloc. cit.\u003c/i\u003e) with the help of symbols, without which\r\nit is hard to understand; I shall not therefore here repeat the\r\ndemonstration of the above propositions, but shall proceed with their\r\napplication to our present problem.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe fact that \"existence\" is only applicable to descriptions is\r\nconcealed by the use of what are grammatically proper names in a way\r\nwhich really transforms them into descriptions. It is, for example, a\r\nlegitimate \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_176\" id=\"Page_176\"\u003e[176]\u003c/a\u003e\u003c/span\u003equestion whether Homer existed; but here \"Homer\" means\r\n\"the author of the Homeric poems,\" and is a description. Similarly we\r\nmay ask whether God exists; but then \"God\" means \"the Supreme Being\"\r\nor \"the \u003ci\u003eens realissimum\u003c/i\u003e\" or whatever other description we may\r\nprefer. If \"God\" were a proper name, God would have to be a datum; and\r\nthen no question could arise as to His existence. The distinction\r\nbetween existence and other predicates, which Kant obscurely felt, is\r\nbrought to light by the theory of descriptions, and is seen to remove\r\n\"existence\" altogether from the fundamental notions of metaphysics.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhat has been said about \"existence\" applies equally to \"reality,\"\r\nwhich may, in fact, be taken as synonymous with \"existence.\"\r\nConcerning the immediate objects in illusions, hallucinations, and\r\ndreams, it is meaningless to ask whether they \"exist\" or are \"real.\"\r\nThere they are, and that ends the matter. But we may legitimately\r\ninquire as to the existence or reality of \"things\" or other\r\n\"sensibilia\" inferred from such objects. It is the unreality of these\r\n\"things\" and other \"sensibilia,\" together with a failure to notice\r\nthat they are not data, which has led to the view that the objects of\r\ndreams are unreal.\u003c/p\u003e\r\n\r\n\u003cp\u003eWe may now apply these considerations in detail to the stock arguments\r\nagainst realism, though what is to be said will be mainly a repetition\r\nof what others have said before.\u003c/p\u003e\r\n\r\n\u003cp\u003e(1) We have first the variety of normal appearances, supposed to be\r\nincompatible. This is the case of the different shapes and colours\r\nwhich a given thing presents to different spectators. Locke\u0027s water\r\nwhich seems both hot and cold belongs to this class of cases. Our\r\nsystem of different perspectives fully accounts for these cases, and\r\nshows that they afford no argument against realism.\u003c/p\u003e\r\n\r\n\u003cp\u003e(2) We have cases where the correlation between \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_177\" id=\"Page_177\"\u003e[177]\u003c/a\u003e\u003c/span\u003edifferent senses is\r\nunusual. The bent stick in water belongs here. People say it looks\r\nbent but is straight: this only means that it is straight to the\r\ntouch, though bent to sight. There is no \"illusion,\" but only a false\r\ninference, if we think that the stick would feel bent to the touch.\r\nThe stick would look just as bent in a photograph, and, as Mr.\r\nGladstone used to say, \"the photograph cannot lie.\"\u003ca name=\"FNanchor_34_34\" id=\"FNanchor_34_34\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_34_34\" class=\"fnanchor\"\u003e[34]\u003c/a\u003e The case of\r\nseeing double also belongs here, though in this case the cause of the\r\nunusual correlation is physiological, and would therefore not operate\r\nin a photograph. It is a mistake to ask whether the \"thing\" is\r\nduplicated when we see it double. The \"thing\" is a whole system of\r\n\"sensibilia,\" and it is only those visual \"sensibilia\" which are data\r\nto the percipient that are duplicated. The phenomenon has a purely\r\nphysiological explanation; indeed, in view of our having two eyes, it\r\nis in less need of explanation than the single visual sense-datum\r\nwhich we normally obtain from the things on which we focus.\u003c/p\u003e\r\n\r\n\u003cp\u003e(3) We come now to cases like dreams, which may, at the moment of\r\ndreaming, contain nothing to arouse suspicion, but are condemned on\r\nthe ground of their supposed incompatibility with earlier and later\r\ndata. Of course it often happens that dream-objects fail to behave in\r\nthe accustomed manner: heavy objects fly, solid objects melt, babies\r\nturn into pigs or undergo even greater changes. But none of these\r\nunusual occurrences \u003ci\u003eneed\u003c/i\u003e happen in a dream, and it is not on account\r\nof such occurrences that dream-objects are called \"unreal.\" It is\r\ntheir lack of continuity with the dreamer\u0027s past and future that makes\r\nhim, when he wakes, condemn them; and it is their lack \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_178\" id=\"Page_178\"\u003e[178]\u003c/a\u003e\u003c/span\u003eof correlation\r\nwith other private worlds that makes others condemn them. Omitting the\r\nlatter ground, our reason for condemning them is that the \"things\"\r\nwhich we infer from them cannot be combined according to the laws of\r\nphysics with the \"things\" inferred from waking sense-data. This might\r\nbe used to condemn the \"things\" inferred from the data of dreams.\r\nDream-data are no doubt appearances of \"things,\" but not of such\r\n\"things\" as the dreamer supposes. I have no wish to combat\r\npsychological theories of dreams, such as those of the\r\npsycho-analysts. But there certainly are cases where (whatever\r\npsychological causes may contribute) the presence of physical causes\r\nalso is very evident. For instance, a door banging may produce a dream\r\nof a naval engagement, with images of battleships and sea and smoke.\r\nThe whole dream will be an appearance of the door banging, but owing\r\nto the peculiar condition of the body (especially the brain) during\r\nsleep, this appearance is not that expected to be produced by a door\r\nbanging, and thus the dreamer is led to entertain false beliefs. But\r\nhis sense-data are still physical, and are such as a completed physics\r\nwould include and calculate.\u003c/p\u003e\r\n\r\n\u003cp\u003e(4) The last class of illusions are those which cannot be discovered\r\nwithin one person\u0027s experience, except through the discovery of\r\ndiscrepancies with the experiences of others. Dreams might conceivably\r\nbelong to this class, if they were jointed sufficiently neatly into\r\nwaking life; but the chief instances are recurrent sensory\r\nhallucinations of the kind that lead to insanity. What makes the\r\npatient, in such cases, become what others call insane is the fact\r\nthat, within his own experience, there is nothing to show that the\r\nhallucinatory sense-data do not have the usual kind of connection with\r\n\"sensibilia\" in other perspectives. Of course he may learn this\r\nthrough testimony, but he \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_179\" id=\"Page_179\"\u003e[179]\u003c/a\u003e\u003c/span\u003eprobably finds it simpler to suppose that\r\nthe testimony is untrue and that he is being wilfully deceived. There\r\nis, so far as I can see, no theoretical criterion by which the patient\r\ncan decide, in such a case, between the two equally satisfactory\r\nhypotheses of his madness and of his friends\u0027 mendacity.\u003c/p\u003e\r\n\r\n\u003cp\u003eFrom the above instances it would appear that abnormal sense-data, of\r\nthe kind which we regard as deceptive, have intrinsically just the\r\nsame status as any others, but differ as regards their correlations or\r\ncausal connections with other \"sensibilia\" and with \"things.\" Since\r\nthe usual correlations and connections become part of our unreflective\r\nexpectations, and even seem, except to the psychologist, to form part\r\nof our data, it comes to be thought, mistakenly, that in such cases\r\nthe data are unreal, whereas they are merely the causes of false\r\ninferences. The fact that correlations and connections of unusual\r\nkinds occur adds to the difficulty of inferring things from sense and\r\nof expressing physics in terms of sense-data. But the unusualness\r\nwould seem to be always physically or physiologically explicable, and\r\ntherefore raises only a complication, not a philosophical objection.\u003c/p\u003e\r\n\r\n\u003cp\u003eI conclude, therefore, that no valid objection exists to the view\r\nwhich regards sense-data as part of the actual substance of the\r\nphysical world, and that, on the other hand, this view is the only one\r\nwhich accounts for the empirical verifiability of physics. In the\r\npresent paper, I have given only a rough preliminary sketch. In\r\nparticular, the part played by \u003ci\u003etime\u003c/i\u003e in the construction of the\r\nphysical world is, I think, more fundamental than would appear from\r\nthe above account. I should hope that, with further elaboration, the\r\npart played by unperceived \"sensibilia\" could be indefinitely\r\ndiminished, probably by invoking the history of a \"thing\" to eke out\r\nthe inferences derivable from its momentary appearance.\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\u003chr style=\"width: 15%;\" /\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003ch4\u003eFOOTNOTES:\u003c/h4\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_29_29\" id=\"Footnote_29_29\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_29_29\"\u003e\u003cspan class=\"label\"\u003e[29]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eProc. Arist. Soc.\u003c/i\u003e, 1909-1910, pp. 191-218.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_30_30\" id=\"Footnote_30_30\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_30_30\"\u003e\u003cspan class=\"label\"\u003e[30]\u003c/span\u003e\u003c/a\u003e On this subject, compare \u003ci\u003eA Theory of Time and Space\u003c/i\u003e,\r\nby Mr. A.A. Robb (Camb. Univ. Press), which first suggested to me the\r\nviews advocated here, though I have, for present purposes, omitted\r\nwhat is most interesting and novel in his theory. Mr. Robb has given a\r\nsketch of his theory in a pamphlet with the same title (Heffer and\r\nSons, Cambridge, 1913).\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_31_31\" id=\"Footnote_31_31\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_31_31\"\u003e\u003cspan class=\"label\"\u003e[31]\u003c/span\u003e\u003c/a\u003e \"Natural Realism and Present Tendencies in Philosophy,\"\r\n\u003ci\u003eProc. Arist. Soc.\u003c/i\u003e, 1908-1909, p. 165.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_32_32\" id=\"Footnote_32_32\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_32_32\"\u003e\u003cspan class=\"label\"\u003e[32]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eDie Erfahrungsgrundlagen unseres Wissens\u003c/i\u003e, p. 28.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_33_33\" id=\"Footnote_33_33\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_33_33\"\u003e\u003cspan class=\"label\"\u003e[33]\u003c/span\u003e\u003c/a\u003e Cf. \u003ci\u003ePrincipia Mathematica\u003c/i\u003e, Vol. I, * 14, and\r\nIntroduction, Chap. III. For the definition of \u003ci\u003eexistence\u003c/i\u003e, cf. * 14.\r\n02.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_34_34\" id=\"Footnote_34_34\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_34_34\"\u003e\u003cspan class=\"label\"\u003e[34]\u003c/span\u003e\u003c/a\u003e Cf. Edwin B. Holt, \u003ci\u003eThe Place of Illusory Experience in\r\na Realistic World.\u003c/i\u003e \"The New Realism,\" p. 303, both on this point and\r\nas regards \u003ci\u003eseeing double\u003c/i\u003e.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003ca name=\"IX\" id=\"IX\"\u003e\u003c/a\u003e\u003chr /\u003e\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_180\" id=\"Page_180\"\u003e[180]\u003c/a\u003e\u003c/span\u003e\u003cbr /\u003e\r\n\r\n\u003ch3\u003eIX\u003cspan class=\"totoc\"\u003e\u003ca href=\"#toc\"\u003eToC\u003c/a\u003e\u003c/span\u003e\u003c/h3\u003e\r\n\r\n\u003ch4\u003eON THE NOTION OF CAUSE\u003c/h4\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003cp\u003eIn the following paper I wish, first, to maintain that the word\r\n\"cause\" is so inextricably bound up with misleading associations as to\r\nmake its complete extrusion from the philosophical vocabulary\r\ndesirable; secondly, to inquire what principle, if any, is employed in\r\nscience in place of the supposed \"law of causality\" which philosophers\r\nimagine to be employed; thirdly, to exhibit certain confusions,\r\nespecially in regard to teleology and determinism, which appear to me\r\nto be connected with erroneous notions as to causality.\u003c/p\u003e\r\n\r\n\u003cp\u003eAll philosophers, of every school, imagine that causation is one of\r\nthe fundamental axioms or postulates of science, yet, oddly enough, in\r\nadvanced sciences such as gravitational astronomy, the word \"cause\"\r\nnever occurs. Dr. James Ward, in his \u003ci\u003eNaturalism and Agnosticism\u003c/i\u003e,\r\nmakes this a ground of complaint against physics: the business of\r\nthose who wish to ascertain the ultimate truth about the world, he\r\napparently thinks, should be the discovery of causes, yet physics\r\nnever even seeks them. To me it seems that philosophy ought not to\r\nassume such legislative functions, and that the reason why physics has\r\nceased to look for causes is that, in fact, there are no such things.\r\nThe law of causality, I believe, like much that passes muster among\r\nphilosophers, is a relic of a bygone age, surviving, like the\r\nmonarchy, only because it is erroneously supposed to do no harm. \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_181\" id=\"Page_181\"\u003e[181]\u003c/a\u003e\u003c/span\u003eIn\r\norder to find out what philosophers commonly understand by \"cause,\" I\r\nconsulted Baldwin\u0027s \u003ci\u003eDictionary\u003c/i\u003e, and was rewarded beyond my\r\nexpectations, for I found the following three mutually incompatible\r\ndefinitions:\u0026mdash;\u003c/p\u003e\r\n\r\n\u003cdiv class=\"block3\"\u003e\u003cp class=\"hang\"\u003e\"\u003cspan class=\"sc\"\u003eCausality.\u003c/span\u003e (1) The necessary connection of events in\r\nthe time-series….\u003c/p\u003e\r\n\r\n\u003cp class=\"hang\"\u003e\"\u003cspan class=\"sc\"\u003eCause\u003c/span\u003e (notion of). Whatever may be included in the\r\nthought or perception of a process as taking place in\r\nconsequence of another process….\u003c/p\u003e\r\n\r\n\u003cp class=\"hang\"\u003e\"\u003cspan class=\"sc\"\u003eCause and Effect.\u003c/span\u003e (1) Cause and effect … are\r\ncorrelative terms denoting any two distinguishable things,\r\nphases, or aspects of reality, which are so related to each\r\nother that whenever the first ceases to exist the second comes\r\ninto existence immediately after, and whenever the second comes\r\ninto existence the first has ceased to exist immediately\r\nbefore.\"\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cp\u003eLet us consider these three definitions in turn. The first, obviously,\r\nis unintelligible without a definition of \"necessary.\" Under this\r\nhead, Baldwin\u0027s \u003ci\u003eDictionary\u003c/i\u003e gives the following:\u0026mdash;\u003c/p\u003e\r\n\r\n\u003cdiv class=\"block3\"\u003e\u003cp class=\"hang\"\u003e\"\u003cspan class=\"sc\"\u003eNecessary.\u003c/span\u003e That is necessary which not only is true,\r\nbut would be true under all circumstances. Something more than\r\nbrute compulsion is, therefore, involved in the conception;\r\nthere is a general law under which the thing takes place.\"\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cp\u003eThe notion of cause is so intimately connected with that of necessity\r\nthat it will be no digression to linger over the above definition,\r\nwith a view to discovering, if possible, \u003ci\u003esome\u003c/i\u003e meaning of which it is\r\ncapable; for, as it stands, it is very far from having any definite\r\nsignification.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe first point to notice is that, if any meaning is to be given to\r\nthe phrase \"would be true under all circumstances,\" the subject of it\r\nmust be a propositional \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_182\" id=\"Page_182\"\u003e[182]\u003c/a\u003e\u003c/span\u003efunction, not a proposition.\u003ca name=\"FNanchor_35_35\" id=\"FNanchor_35_35\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_35_35\" class=\"fnanchor\"\u003e[35]\u003c/a\u003e A\r\nproposition is simply true or false, and that ends the matter: there\r\ncan be no question of \"circumstances.\" \"Charles I\u0027s head was cut off\"\r\nis just as true in summer as in winter, on Sundays as on Mondays. Thus\r\nwhen it is worth saying that something \"would be true under all\r\ncircumstances,\" the something in question must be a propositional\r\nfunction, i.e. an expression containing a variable, and becoming a\r\nproposition when a value is assigned to the variable; the varying\r\n\"circumstances\" alluded to are then the different values of which the\r\nvariable is capable. Thus if \"necessary\" means \"what is true under all\r\ncircumstances,\" then \"if \u003ci\u003ex\u003c/i\u003e is a man, \u003ci\u003ex\u003c/i\u003e is mortal\" is necessary,\r\nbecause it is true for any possible value of \u003ci\u003ex\u003c/i\u003e. Thus we should be\r\nled to the following definition:\u0026mdash;\u003c/p\u003e\r\n\r\n\u003cdiv class=\"block3\"\u003e\u003cp class=\"hang\"\u003e\"\u003cspan class=\"sc\"\u003eNecessary\u003c/span\u003e is a predicate of a propositional function,\r\nmeaning that it is true for all possible values of its\r\nargument or arguments.\"\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cp\u003eUnfortunately, however, the definition in Baldwin\u0027s \u003ci\u003eDictionary\u003c/i\u003e says\r\nthat what is necessary is not only \"true under all circumstances\" but\r\nis also \"true.\" Now these two are incompatible. Only propositions can\r\nbe \"true,\" and only propositional functions can be \"true under all\r\ncircumstances.\" Hence the definition as it stands is nonsense. What is\r\nmeant seems to be this: \"A proposition is necessary when it is a value\r\nof a propositional function which is true under all circumstances,\r\ni.e. for all values of its argument or arguments.\" But if we adopt\r\nthis definition, the same proposition will be necessary or contingent\r\naccording as we choose one or other of its \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_183\" id=\"Page_183\"\u003e[183]\u003c/a\u003e\u003c/span\u003eterms as the argument to\r\nour propositional function. For example, \"if Socrates is a man,\r\nSocrates is mortal,\" is necessary if Socrates is chosen as argument,\r\nbut not if \u003ci\u003eman\u003c/i\u003e or \u003ci\u003emortal\u003c/i\u003e is chosen. Again, \"if Socrates is a man,\r\nPlato is mortal,\" will be necessary if either Socrates or \u003ci\u003eman\u003c/i\u003e is\r\nchosen as argument, but not if Plato or \u003ci\u003emortal\u003c/i\u003e is chosen. However,\r\nthis difficulty can be overcome by specifying the constituent which is\r\nto be regarded as argument, and we thus arrive at the following\r\ndefinition:\u003c/p\u003e\r\n\r\n\u003cp\u003e\"A proposition is \u003ci\u003enecessary\u003c/i\u003e with respect to a given constituent if\r\nit remains true when that constituent is altered in any way compatible\r\nwith the proposition remaining significant.\"\u003c/p\u003e\r\n\r\n\u003cp\u003eWe may now apply this definition to the definition of causality quoted\r\nabove. It is obvious that the argument must be the time at which the\r\nearlier event occurs. Thus an instance of causality will be such as:\r\n\"If the event \u003ci\u003ee\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e occurs at the time \u003ci\u003et\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e, it will be followed by\r\nthe event \u003ci\u003ee\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e.\" This proposition is intended to be necessary with\r\nrespect to \u003ci\u003et\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e, i.e. to remain true however \u003ci\u003et\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e may be varied.\r\nCausality, as a universal law, will then be the following: \"Given any\r\nevent \u003ci\u003ee\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e, there is an event \u003ci\u003ee\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e such that, whenever \u003ci\u003ee\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e occurs,\r\n\u003ci\u003ee\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e occurs later.\" But before this can be considered precise, we\r\nmust specify how much later \u003ci\u003ee\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e is to occur. Thus the principle\r\nbecomes:\u0026mdash;\u003c/p\u003e\r\n\r\n\u003cp\u003e\"Given any event \u003ci\u003ee\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e, there is an event \u003ci\u003ee\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e and a time-interval\r\n\u0026tau; such that, whenever \u003ci\u003ee\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e occurs, \u003ci\u003ee\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e follows after an\r\ninterval \u0026tau;.\"\u003c/p\u003e\r\n\r\n\u003cp\u003eI am not concerned as yet to consider whether this law is true or\r\nfalse. For the present, I am merely concerned to discover what the law\r\nof causality is supposed to be. I pass, therefore, to the other\r\ndefinitions quoted above.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_184\" id=\"Page_184\"\u003e[184]\u003c/a\u003e\u003c/span\u003eThe second definition need not detain us long, for two reasons. First,\r\nbecause it is psychological: not the \"thought or perception\" of a\r\nprocess, but the process itself, must be what concerns us in\r\nconsidering causality. Secondly, because it is circular: in speaking\r\nof a process as \"taking place in consequence of\" another process, it\r\nintroduces the very notion of cause which was to be defined.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe third definition is by far the most precise; indeed as regards\r\nclearness it leaves nothing to be desired. But a great difficulty is\r\ncaused by the temporal contiguity of cause and effect which the\r\ndefinition asserts. No two instants are contiguous, since the\r\ntime-series is compact; hence either the cause or the effect or both\r\nmust, if the definition is correct, endure for a finite time; indeed,\r\nby the wording of the definition it is plain that both are assumed to\r\nendure for a finite time. But then we are faced with a dilemma: if the\r\ncause is a process involving change within itself, we shall require\r\n(if causality is universal) causal relations between its earlier and\r\nlater parts; moreover, it would seem that only the later parts can be\r\nrelevant to the effect, since the earlier parts are not contiguous to\r\nthe effect, and therefore (by the definition) cannot influence the\r\neffect. Thus we shall be led to diminish the duration of the cause\r\nwithout limit, and however much we may diminish it, there will still\r\nremain an earlier part which might be altered without altering the\r\neffect, so that the true cause, as defined, will not have been\r\nreached, for it will be observed that the definition excludes\r\nplurality of causes. If, on the other hand, the cause is purely\r\nstatic, involving no change within itself, then, in the first place,\r\nno such cause is to be found in nature, and in the second place, it\r\nseems strange\u0026mdash;too strange to be accepted, in spite of bare \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_185\" id=\"Page_185\"\u003e[185]\u003c/a\u003e\u003c/span\u003elogical\r\npossibility\u0026mdash;that the cause, after existing placidly for some time,\r\nshould suddenly explode into the effect, when it might just as well\r\nhave done so at any earlier time, or have gone on unchanged without\r\nproducing its effect. This dilemma, therefore, is fatal to the view\r\nthat cause and effect can be contiguous in time; if there are causes\r\nand effects, they must be separated by a finite time-interval \u0026tau;,\r\nas was assumed in the above interpretation of the first\r\ndefinition.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhat is essentially the same statement of the law of causality as the\r\none elicited above from the first of Baldwin\u0027s definitions is given by\r\nother philosophers. Thus John Stuart Mill says:\u0026mdash;\u003c/p\u003e\r\n\r\n\u003cp\u003e\"The Law of Causation, the recognition of which is the main pillar of\r\ninductive science, is but the familiar truth, that invariability of\r\nsuccession is found by observation to obtain between every fact in\r\nnature and some other fact which has preceded it.\"\u003ca name=\"FNanchor_36_36\" id=\"FNanchor_36_36\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_36_36\" class=\"fnanchor\"\u003e[36]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eAnd Bergson, who has rightly perceived that the law as stated by\r\nphilosophers is worthless, nevertheless continues to suppose that it\r\nis used in science. Thus he says:\u0026mdash;\u003c/p\u003e\r\n\r\n\u003cp\u003e\"Now, it is argued, this law [the law of causality] means that every\r\nphenomenon is determined by its conditions, or, in other words, that\r\nthe same causes produce the same effects.\"\u003ca name=\"FNanchor_37_37\" id=\"FNanchor_37_37\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_37_37\" class=\"fnanchor\"\u003e[37]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eAnd again:\u0026mdash;\u003c/p\u003e\r\n\r\n\u003cp\u003e\"We perceive physical phenomena, and these phenomena obey laws. This\r\nmeans: (1) That phenomena \u003ci\u003ea\u003c/i\u003e, \u003ci\u003eb\u003c/i\u003e, \u003ci\u003ec\u003c/i\u003e, \u003ci\u003ed\u003c/i\u003e, previously perceived,\r\ncan occur again in the same shape; (2) that a certain phenomenon P,\r\nwhich \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_186\" id=\"Page_186\"\u003e[186]\u003c/a\u003e\u003c/span\u003eappeared after the conditions \u003ci\u003ea\u003c/i\u003e, \u003ci\u003eb\u003c/i\u003e, \u003ci\u003ec\u003c/i\u003e, \u003ci\u003ed\u003c/i\u003e, and after\r\nthese conditions only, will not fail to recur as soon as the same\r\nconditions are again present.\"\u003ca name=\"FNanchor_38_38\" id=\"FNanchor_38_38\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_38_38\" class=\"fnanchor\"\u003e[38]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eA great part of Bergson\u0027s attack on science rests on the assumption\r\nthat it employs this principle. In fact, it employs no such principle,\r\nbut philosophers\u0026mdash;even Bergson\u0026mdash;are too apt to take their views on\r\nscience from each other, not from science. As to what the principle\r\nis, there is a fair consensus among philosophers of different schools.\r\nThere are, however, a number of difficulties which at once arise. I\r\nomit the question of plurality of causes for the present, since other\r\ngraver questions have to be considered. Two of these, which are forced\r\non our attention by the above statement of the law, are the\r\nfollowing:\u0026mdash;\u003c/p\u003e\r\n\r\n\u003cdiv class=\"block\"\u003e\u003cp\u003e(1) What is meant by an \"event\"?\u003c/p\u003e\r\n\r\n\u003cp\u003e(2) How long may the time-interval be between cause and effect?\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cp\u003e(1) An \"event,\" in the statement of the law, is obviously intended to\r\nbe something that is likely to recur since otherwise the law becomes\r\ntrivial. It follows that an \"event\" is not a particular, but some\r\nuniversal of which there may be many instances. It follows also that\r\nan \"event\" must be something short of the whole state of the universe,\r\nsince it is highly improbable that this will recur. What is meant by\r\nan \"event\" is something like striking a match, or dropping a penny\r\ninto the slot of an automatic machine. If such an event is to recur,\r\nit must not be defined too narrowly: we must not state with what\r\ndegree of force the match is to be struck, nor what is to be the\r\ntemperature of the penny. For if such considerations were relevant,\r\nour \"event\" would occur at \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_187\" id=\"Page_187\"\u003e[187]\u003c/a\u003e\u003c/span\u003emost once, and the law would cease to give\r\ninformation. An \"event,\" then, is a universal defined sufficiently\r\nwidely to admit of many particular occurrences in time being instances\r\nof it.\u003c/p\u003e\r\n\r\n\u003cp\u003e(2) The next question concerns the time-interval. Philosophers, no\r\ndoubt, think of cause and effect as contiguous in time, but this, for\r\nreasons already given, is impossible. Hence, since there are no\r\ninfinitesimal time-intervals, there must be some finite lapse of time\r\n\u0026tau; between cause and effect. This, however, at once raises\r\ninsuperable difficulties. However short we make the interval \u0026tau;,\r\nsomething may happen during this interval which prevents the\r\nexpected result. I put my penny in the slot, but before I can draw out\r\nmy ticket there is an earthquake which upsets the machine and my\r\ncalculations. In order to be sure of the expected effect, we must know\r\nthat there is nothing in the environment to interfere with it. But\r\nthis means that the supposed cause is not, by itself, adequate to\r\ninsure the effect. And as soon as we include the environment, the\r\nprobability of repetition is diminished, until at last, when the whole\r\nenvironment is included, the probability of repetition becomes almost\r\n\u003ci\u003enil\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn spite of these difficulties, it must, of course, be admitted that\r\nmany fairly dependable regularities of sequence occur in daily life.\r\nIt is these regularities that have suggested the supposed law of\r\ncausality; where they are found to fail, it is thought that a better\r\nformulation could have been found which would have never failed. I am\r\nfar from denying that there may be such sequences which in fact never\r\ndo fail. It may be that there will never be an exception to the rule\r\nthat when a stone of more than a certain mass, moving with more than a\r\ncertain velocity, comes in contact with a pane of glass of \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_188\" id=\"Page_188\"\u003e[188]\u003c/a\u003e\u003c/span\u003eless than\r\na certain thickness, the glass breaks. I also do not deny that the\r\nobservation of such regularities, even when they are not without\r\nexceptions, is useful in the infancy of a science: the observation\r\nthat unsupported bodies in air usually fall was a stage on the way to\r\nthe law of gravitation. What I deny is that science assumes the\r\nexistence of invariable uniformities of sequence of this kind, or that\r\nit aims at discovering them. All such uniformities, as we saw, depend\r\nupon a certain vagueness in the definition of the \"events.\" That\r\nbodies fall is a vague qualitative statement; science wishes to know\r\nhow fast they fall. This depends upon the shape of the bodies and the\r\ndensity of the air. It is true that there is more nearly uniformity\r\nwhen they fall in a vacuum; so far as Galileo could observe, the\r\nuniformity is then complete. But later it appeared that even there the\r\nlatitude made a difference, and the altitude. Theoretically, the\r\nposition of the sun and moon must make a difference. In short, every\r\nadvance in a science takes us farther away from the crude uniformities\r\nwhich are first observed, into greater differentiation of antecedent\r\nand consequent, and into a continually wider circle of antecedents\r\nrecognised as relevant.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe principle \"same cause, same effect,\" which philosophers imagine to\r\nbe vital to science, is therefore utterly otiose. As soon as the\r\nantecedents have been given sufficiently fully to enable the\r\nconsequent to be calculated with some exactitude, the antecedents have\r\nbecome so complicated that it is very unlikely they will ever recur.\r\nHence, if this were the principle involved, science would remain\r\nutterly sterile.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe importance of these considerations lies partly in the fact that\r\nthey lead to a more correct account of scientific procedure, partly in\r\nthe fact that they remove \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_189\" id=\"Page_189\"\u003e[189]\u003c/a\u003e\u003c/span\u003ethe analogy with human volition which makes\r\nthe conception of cause such a fruitful source of fallacies. The\r\nlatter point will become clearer by the help of some illustrations.\r\nFor this purpose I shall consider a few maxims which have played a\r\ngreat part in the history of philosophy.\u003c/p\u003e\r\n\r\n\u003cp\u003e(1) \"Cause and effect must more or less resemble each other.\" This\r\nprinciple was prominent in the philosophy of occasionalism, and is\r\nstill by no means extinct. It is still often thought, for example,\r\nthat mind could not have grown up in a universe which previously\r\ncontained nothing mental, and one ground for this belief is that\r\nmatter is too dissimilar from mind to have been able to cause it. Or,\r\nmore particularly, what are termed the nobler parts of our nature are\r\nsupposed to be inexplicable, unless the universe always contained\r\nsomething at least equally noble which could cause them. All such\r\nviews seem to depend upon assuming some unduly simplified law of\r\ncausality; for, in any legitimate sense of \"cause\" and \"effect,\"\r\nscience seems to show that they are usually very widely dissimilar,\r\nthe \"cause\" being, in fact, two states of the whole universe, and the\r\n\"effect\" some particular event.\u003c/p\u003e\r\n\r\n\u003cp\u003e(2) \"Cause is analogous to volition, since there must be an\r\nintelligible \u003ci\u003enexus\u003c/i\u003e between cause and effect.\" This maxim is, I\r\nthink, often unconsciously in the imaginations of philosophers who\r\nwould reject it when explicitly stated. It is probably operative in\r\nthe view we have just been considering, that mind could not have\r\nresulted from a purely material world. I do not profess to know what\r\nis meant by \"intelligible\"; it seems to mean \"familiar to\r\nimagination.\" Nothing is less \"intelligible,\" in any other sense, than\r\nthe connection between \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_190\" id=\"Page_190\"\u003e[190]\u003c/a\u003e\u003c/span\u003ean act of will and its fulfilment. But\r\nobviously the sort of nexus desired between cause and effect is such\r\nas could only hold between the \"events\" which the supposed law of\r\ncausality contemplates; the laws which replace causality in such a\r\nscience as physics leave no room for any two events between which a\r\nnexus could be sought.\u003c/p\u003e\r\n\r\n\u003cp\u003e(3) \"The cause \u003ci\u003ecompels\u003c/i\u003e the effect in some sense in which the effect\r\ndoes not compel the cause.\" This belief seems largely operative in the\r\ndislike of determinism; but, as a matter of fact, it is connected with\r\nour second maxim, and falls as soon as that is abandoned. We may\r\ndefine \"compulsion\" as follows: \"Any set of circumstances is said to\r\ncompel A when A desires to do something which the circumstances\r\nprevent, or to abstain from something which the circumstances cause.\"\r\nThis presupposes that some meaning has been found for the word\r\n\"cause\"\u0026mdash;a point to which I shall return later. What I want to make\r\nclear at present is that compulsion is a very complex notion,\r\ninvolving thwarted desire. So long as a person does what he wishes to\r\ndo, there is no compulsion, however much his wishes may be calculable\r\nby the help of earlier events. And where desire does not come in,\r\nthere can be no question of compulsion. Hence it is, in general,\r\nmisleading to regard the cause as compelling the effect.\u003c/p\u003e\r\n\r\n\u003cp\u003eA vaguer form of the same maxim substitutes the word \"determine\" for\r\nthe word \"compel\"; we are told that the cause \u003ci\u003edetermines\u003c/i\u003e the effect\r\nin a sense in which the effect does not \u003ci\u003edetermine\u003c/i\u003e the cause. It is\r\nnot quite clear what is meant by \"determining\"; the only precise\r\nsense, so far as I know, is that of a function or one-many relation.\r\nIf we admit plurality of causes, but not of effects, that is, if we\r\nsuppose that, given the cause, the effect must be such and such, but,\r\ngiven the effect, the \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_191\" id=\"Page_191\"\u003e[191]\u003c/a\u003e\u003c/span\u003ecause may have been one of many alternatives,\r\nthen we may say that the cause determines the effect, but not the\r\neffect the cause. Plurality of causes, however, results only from\r\nconceiving the effect vaguely and narrowly and the cause precisely and\r\nwidely. Many antecedents may \"cause\" a man\u0027s death, because his death\r\nis vague and narrow. But if we adopt the opposite course, taking as\r\nthe \"cause\" the drinking of a dose of arsenic, and as the \"effect\" the\r\nwhole state of the world five minutes later, we shall have plurality\r\nof effects instead of plurality of causes. Thus the supposed lack of\r\nsymmetry between \"cause\" and \"effect\" is illusory.\u003c/p\u003e\r\n\r\n\u003cp\u003e(4) \"A cause cannot operate when it has ceased to exist, because what\r\nhas ceased to exist is nothing.\" This is a common maxim, and a still\r\nmore common unexpressed prejudice. It has, I fancy, a good deal to do\r\nwith the attractiveness of Bergson\u0027s \"\u003ci\u003edur\u0026eacute;e\u003c/i\u003e\": since the past has\r\neffects now, it must still exist in some sense. The mistake in this\r\nmaxim consists in the supposition that causes \"operate\" at all. A\r\nvolition \"operates\" when what it wills takes place; but nothing can\r\noperate except a volition. The belief that causes \"operate\" results\r\nfrom assimilating them, consciously or unconsciously, to volitions. We\r\nhave already seen that, if there are causes at all, they must be\r\nseparated by a finite interval of time from their effects, and thus\r\ncause their effects after they have ceased to exist.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt may be objected to the above definition of a volition \"operating\"\r\nthat it only operates when it \"causes\" what it wills, not when it\r\nmerely happens to be followed by what it wills. This certainly\r\nrepresents the usual view of what is meant by a volition \"operating,\"\r\nbut as it involves the very view of causation which we are engaged in\r\ncombating, it is not open to us as a definition. We \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_192\" id=\"Page_192\"\u003e[192]\u003c/a\u003e\u003c/span\u003emay say that a\r\nvolition \"operates\" when there is some law in virtue of which a\r\nsimilar volition in rather similar circumstances will usually be\r\nfollowed by what it wills. But this is a vague conception, and\r\nintroduces ideas which we have not yet considered. What is chiefly\r\nimportant to notice is that the usual notion of \"operating\" is not\r\nopen to us if we reject, as I contend that we should, the usual notion\r\nof causation.\u003c/p\u003e\r\n\r\n\u003cp\u003e(5) \"A cause cannot operate except where it is.\" This maxim is very\r\nwidespread; it was urged against Newton, and has remained a source of\r\nprejudice against \"action at a distance.\" In philosophy it has led to\r\na denial of transient action, and thence to monism or Leibnizian\r\nmonadism. Like the analogous maxim concerning temporal contiguity, it\r\nrests upon the assumption that causes \"operate,\" i.e. that they are in\r\nsome obscure way analogous to volitions. And, as in the case of\r\ntemporal contiguity, the inferences drawn from this maxim are wholly\r\ngroundless.\u003c/p\u003e\r\n\r\n\u003cp\u003eI return now to the question, What law or laws can be found to take\r\nthe place of the supposed law of causality?\u003c/p\u003e\r\n\r\n\u003cp\u003eFirst, without passing beyond such uniformities of sequence as are\r\ncontemplated by the traditional law, we may admit that, if any such\r\nsequence has been observed in a great many cases, and has never been\r\nfound to fail, there is an inductive probability that it will be found\r\nto hold in future cases. If stones have hitherto been found to break\r\nwindows, it is probable that they will continue to do so. This, of\r\ncourse, assumes the inductive principle, of which the truth may\r\nreasonably be questioned; but as this principle is not our present\r\nconcern, I shall in this discussion treat it as indubitable. We may\r\nthen say, in the case of any such frequently observed sequence, that\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_193\" id=\"Page_193\"\u003e[193]\u003c/a\u003e\u003c/span\u003ethe earlier event is the \u003ci\u003ecause\u003c/i\u003e and the later event the \u003ci\u003eeffect\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003eSeveral considerations, however, make such special sequences very\r\ndifferent from the traditional relation of cause and effect. In the\r\nfirst place, the sequence, in any hitherto unobserved instance, is no\r\nmore than probable, whereas the relation of cause and effect was\r\nsupposed to be necessary. I do not mean by this merely that we are not\r\nsure of having discovered a true case of cause and effect; I mean\r\nthat, even when we have a case of cause and effect in our present\r\nsense, all that is meant is that on grounds of observation, it is\r\nprobable that when one occurs the other will also occur. Thus in our\r\npresent sense, A may be the cause of B even if there actually are\r\ncases where B does not follow A. Striking a match will be the cause of\r\nits igniting, in spite of the fact that some matches are damp and fail\r\nto ignite.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn the second place, it will not be assumed that \u003ci\u003eevery\u003c/i\u003e event has\r\nsome antecedent which is its cause in this sense; we shall only\r\nbelieve in causal sequences where we find them, without any\r\npresumption that they always are to be found.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn the third place, \u003ci\u003eany\u003c/i\u003e case of sufficiently frequent sequence will\r\nbe causal in our present sense; for example, we shall not refuse to\r\nsay that night is the cause of day. Our repugnance to saying this\r\narises from the ease with which we can imagine the sequence to fail,\r\nbut owing to the fact that cause and effect must be separated by a\r\nfinite interval of time, \u003ci\u003eany\u003c/i\u003e such sequence \u003ci\u003emight\u003c/i\u003e fail through the\r\ninterposition of other circumstances in the interval. Mill, discussing\r\nthis instance of night and day, says:\u0026mdash;\u003c/p\u003e\r\n\r\n\u003cp\u003e\"It is necessary to our using the word cause, that we should believe\r\nnot only that the antecedent always \u003ci\u003ehas\u003c/i\u003e \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_194\" id=\"Page_194\"\u003e[194]\u003c/a\u003e\u003c/span\u003ebeen followed by the\r\nconsequent, but that as long as the present constitution of things\r\nendures, it always \u003ci\u003ewill\u003c/i\u003e be so.\"\u003ca name=\"FNanchor_39_39\" id=\"FNanchor_39_39\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_39_39\" class=\"fnanchor\"\u003e[39]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eIn this sense, we shall have to give up the hope of finding causal\r\nlaws such as Mill contemplated; any causal sequence which we have\r\nobserved may at any moment be falsified without a falsification of any\r\nlaws of the kind that the more advanced sciences aim at establishing.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn the fourth place, such laws of probable sequence, though useful in\r\ndaily life and in the infancy of a science, tend to be displaced by\r\nquite different laws as soon as a science is successful. The law of\r\ngravitation will illustrate what occurs in any advanced science. In\r\nthe motions of mutually gravitating bodies, there is nothing that can\r\nbe called a cause, and nothing that can be called an effect; there is\r\nmerely a formula. Certain differential equations can be found, which\r\nhold at every instant for every particle of the system, and which,\r\ngiven the configuration and velocities at one instant, or the\r\nconfigurations at two instants, render the configuration at any other\r\nearlier or later instant theoretically calculable. That is to say, the\r\nconfiguration at any instant is a function of that instant and the\r\nconfigurations at two given instants. This statement holds throughout\r\nphysics, and not only in the special case of gravitation. But there is\r\nnothing that could be properly called \"cause\" and nothing that could\r\nbe properly called \"effect\" in such a system.\u003c/p\u003e\r\n\r\n\u003cp\u003eNo doubt the reason why the old \"law of causality\" has so long\r\ncontinued to pervade the books of philosophers is simply that the idea\r\nof a function is unfamiliar to most of them, and therefore they seek\r\nan unduly simplified statement. There is no question of repetitions of\r\nthe \"same\" cause producing the \"same\" effect; it \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_195\" id=\"Page_195\"\u003e[195]\u003c/a\u003e\u003c/span\u003eis not in any\r\nsameness of causes and effects that the constancy of scientific law\r\nconsists, but in sameness of relations. And even \"sameness of\r\nrelations\" is too simple a phrase; \"sameness of differential\r\nequations\" is the only correct phrase. It is impossible to state this\r\naccurately in non-mathematical language; the nearest approach would be\r\nas follows: \"There is a constant relation between the state of the\r\nuniverse at any instant and the rate of change in the rate at which\r\nany part of the universe is changing at that instant, and this\r\nrelation is many-one, i.e. such that the rate of change in the rate of\r\nchange is determinate when the state of the universe is given.\" If the\r\n\"law of causality\" is to be something actually discoverable in the\r\npractice of science, the above proposition has a better right to the\r\nname than any \"law of causality\" to be found in the books of\r\nphilosophers.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn regard to the above principle, several observations must be made\u0026mdash;\u003c/p\u003e\r\n\r\n\u003cp\u003e(1) No one can pretend that the above principle is \u003ci\u003ea priori\u003c/i\u003e or\r\nself-evident or a \"necessity of thought.\" Nor is it, in any sense, a\r\npremiss of science: it is an empirical generalisation from a number of\r\nlaws which are themselves empirical generalisations.\u003c/p\u003e\r\n\r\n\u003cp\u003e(2) The law makes no difference between past and future: the future\r\n\"determines\" the past in exactly the same sense in which the past\r\n\"determines\" the future. The word \"determine,\" here, has a purely\r\nlogical significance: a certain number of variables \"determine\"\r\nanother variable if that other variable is a function of them.\u003c/p\u003e\r\n\r\n\u003cp\u003e(3) The law will not be empirically verifiable unless the course of\r\nevents within some sufficiently small volume \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_196\" id=\"Page_196\"\u003e[196]\u003c/a\u003e\u003c/span\u003ewill be approximately\r\nthe same in any two states of the universe which only differ in regard\r\nto what is at a considerable distance from the small volume in\r\nquestion. For example, motions of planets in the solar system must be\r\napproximately the same however the fixed stars may be distributed,\r\nprovided that all the fixed stars are very much farther from the sun\r\nthan the planets are. If gravitation varied directly as the distance,\r\nso that the most remote stars made the most difference to the motions\r\nof the planets, the world might be just as regular and just as much\r\nsubject to mathematical laws as it is at present, but we could never\r\ndiscover the fact.\u003c/p\u003e\r\n\r\n\u003cp\u003e(4) Although the old \"law of causality\" is not assumed by science,\r\nsomething which we may call the \"uniformity of nature\" is assumed, or\r\nrather is accepted on inductive grounds. The uniformity of nature does\r\nnot assert the trivial principle \"same cause, same effect,\" but the\r\nprinciple of the permanence of laws. That is to say, when a law\r\nexhibiting, e.g. an acceleration as a function of the configuration\r\nhas been found to hold throughout the observable past, it is expected\r\nthat it will continue to hold in the future, or that, if it does not\r\nitself hold, there is some other law, agreeing with the supposed law\r\nas regards the past, which will hold for the future. The ground of\r\nthis principle is simply the inductive ground that it has been found\r\nto be true in very many instances; hence the principle cannot be\r\nconsidered certain, but only probable to a degree which cannot be\r\naccurately estimated.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe uniformity of nature, in the above sense, although it is assumed\r\nin the practice of science, must not, in its generality, be regarded\r\nas a kind of major premiss, without which all scientific reasoning\r\nwould be in error. The assumption that \u003ci\u003eall\u003c/i\u003e laws of nature are\r\npermanent has, of \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_197\" id=\"Page_197\"\u003e[197]\u003c/a\u003e\u003c/span\u003ecourse, less probability than the assumption that\r\nthis or that particular law is permanent; and the assumption that a\r\nparticular law is permanent for all time has less probability than the\r\nassumption that it will be valid up to such and such a date. Science,\r\nin any given case, will assume what the case requires, but no more. In\r\nconstructing the \u003ci\u003eNautical Almanac\u003c/i\u003e for 1915 it will assume that the\r\nlaw of gravitation will remain true up to the end of that year; but it\r\nwill make no assumption as to 1916 until it comes to the next volume\r\nof the almanac. This procedure is, of course, dictated by the fact\r\nthat the uniformity of nature is not known \u003ci\u003ea priori\u003c/i\u003e, but is an\r\nempirical generalisation, like \"all men are mortal.\" In all such\r\ncases, it is better to argue immediately from the given particular\r\ninstances to the new instance, than to argue by way of a major\r\npremiss; the conclusion is only probable in either case, but acquires\r\na higher probability by the former method than by the latter.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn all science we have to distinguish two sorts of laws: first, those\r\nthat are empirically verifiable but probably only approximate;\r\nsecondly, those that are not verifiable, but may be exact. The law of\r\ngravitation, for example, in its applications to the solar system, is\r\nonly empirically verifiable when it is assumed that matter outside the\r\nsolar system may be ignored for such purposes; we believe this to be\r\nonly approximately true, but we cannot empirically verify the law of\r\nuniversal gravitation which we believe to be exact. This point is very\r\nimportant in connection with what we may call \"relatively isolated\r\nsystems.\" These may be defined as follows:\u0026mdash;\u003c/p\u003e\r\n\r\n\u003cp\u003eA system relatively isolated during a given period is one which,\r\nwithin some assignable margin of error, will behave in the same way\r\nthroughout that period, however the rest of the universe may be\r\nconstituted.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_198\" id=\"Page_198\"\u003e[198]\u003c/a\u003e\u003c/span\u003eA system may be called \"practically isolated\" during a given period\r\nif, although there \u003ci\u003emight\u003c/i\u003e be states of the rest of the universe which\r\nwould produce more than the assigned margin of error, there is reason\r\nto believe that such states do not in fact occur.\u003c/p\u003e\r\n\r\n\u003cp\u003eStrictly speaking, we ought to specify the respect in which the system\r\nis relatively isolated. For example, the earth is relatively isolated\r\nas regards falling bodies, but not as regards tides; it is\r\n\u003ci\u003epractically\u003c/i\u003e isolated as regards economic phenomena, although, if\r\nJevons\u0027 sunspot theory of commercial crises had been true, it would\r\nnot have been even practically isolated in this respect.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt will be observed that we cannot prove in advance that a system is\r\nisolated. This will be inferred from the observed fact that\r\napproximate uniformities can be stated for this system alone. If the\r\ncomplete laws for the whole universe were known, the isolation of a\r\nsystem could be deduced from them; assuming, for example, the law of\r\nuniversal gravitation, the practical isolation of the solar system in\r\nthis respect can be deduced by the help of the fact that there is very\r\nlittle matter in its neighbourhood. But it should be observed that\r\nisolated systems are only important as providing a possibility of\r\n\u003ci\u003ediscovering\u003c/i\u003e scientific laws; they have no theoretical importance in\r\nthe finished structure of a science.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe case where one event A is said to \"cause\" another event B, which\r\nphilosophers take as fundamental, is really only the most simplified\r\ninstance of a practically isolated system. It may happen that, as a\r\nresult of general scientific laws, whenever A occurs throughout a\r\ncertain period, it is followed by B; in that case, A and B form a\r\nsystem which is practically isolated throughout that period. It is,\r\nhowever, to be regarded as a piece of good fortune if this occurs; it\r\nwill always be due to special \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_199\" id=\"Page_199\"\u003e[199]\u003c/a\u003e\u003c/span\u003ecircumstances, and would not have been\r\ntrue if the rest of the universe had been different though subject to\r\nthe same laws.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe essential function which causality has been supposed to perform is\r\nthe possibility of inferring the future from the past, or, more\r\ngenerally, events at any time from events at certain assigned times.\r\nAny system in which such inference is possible may be called a\r\n\"deterministic\" system. We may define a deterministic system as\r\nfollows:\u0026mdash;\u003c/p\u003e\r\n\r\n\u003cdiv class=\"block\"\u003e\u003cp\u003eA system is said to be \"deterministic\" when, given certain data,\r\n\u003ci\u003ee\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e, \u003ci\u003ee\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e, …, \u003ci\u003ee\u003c/i\u003e\u003csub\u003en\u003c/sub\u003e, at times \u003ci\u003et\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e, \u003ci\u003et\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e, …, \u003ci\u003et\u003c/i\u003e\u003csub\u003en\u003c/sub\u003e\r\nrespectively, concerning this system, if E\u003csub\u003e\u003ci\u003et\u003c/i\u003e\u003c/sub\u003e is the state of the\r\nsystem at any time \u003ci\u003et\u003c/i\u003e, there is a functional relation of the form\u003c/p\u003e\r\n\r\n\u003cdiv class=\"block\"\u003e\r\n\u003cp\u003eE\u003csub\u003et\u003c/sub\u003e = \u003ci\u003ef\u003c/i\u003e (\u003ci\u003ee\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e, \u003ci\u003et\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e, \u003ci\u003ee\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e, \u003ci\u003et\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e, …, \u003ci\u003ee\u003c/i\u003e\u003csub\u003en\u003c/sub\u003e, \u003ci\u003et\u003c/i\u003e\u003csub\u003en\u003c/sub\u003e, \u003ci\u003et\u003c/i\u003e). \u0026nbsp;\u0026nbsp;\u0026nbsp; (A)\u003c/p\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eThe system will be \"deterministic throughout a given period\" if\r\n\u003ci\u003et\u003c/i\u003e, in the above formula, may be any time within that period,\r\nthough outside that period the formula may be no longer true. If\r\nthe universe, as a whole, is such a system, determinism is true of\r\nthe universe; if not, not. A system which is part of a\r\ndeterministic system I shall call \"determined\"; one which is not\r\npart of any such system I shall call \"capricious.\"\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cp\u003eThe events \u003ci\u003ee\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e, \u003ci\u003ee\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e, …, \u003ci\u003ee\u003c/i\u003e\u003csub\u003en\u003c/sub\u003e I shall call \"determinants\" of the\r\nsystem. It is to be observed that a system which has one set of\r\ndeterminants will in general have many. In the case of the motions of\r\nthe planets, for example, the configurations of the solar system at\r\nany two given times will be determinants.\u003c/p\u003e\r\n\r\n\u003cp\u003eWe may take another illustration from the hypothesis of\r\npsycho-physical parallelism. Let us assume, for the purposes of this\r\nillustration, that to a given state of brain \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_200\" id=\"Page_200\"\u003e[200]\u003c/a\u003e\u003c/span\u003ea given state of mind\r\nalways corresponds, and vice versa, i.e. that there is a one-one\r\nrelation between them, so that each is a function of the other. We may\r\nalso assume, what is practically certain, that to a given state of a\r\ncertain brain a given state of the whole material universe\r\ncorresponds, since it is highly improbable that a given brain is ever\r\ntwice in exactly the same state. Hence there will be a one-one\r\nrelation between the state of a given person\u0027s mind and the state of\r\nthe whole material universe. It follows that, if \u003ci\u003en\u003c/i\u003e states of the\r\nmaterial universe are determinants of the material universe, then \u003ci\u003en\u003c/i\u003e\r\nstates of a given man\u0027s mind are determinants of the whole material\r\nand mental universe\u0026mdash;assuming, that is to say, that psycho-physical\r\nparallelism is true.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe above illustration is important in connection with a certain\r\nconfusion which seems to have beset those who have philosophised on\r\nthe relation of mind and matter. It is often thought that, if the\r\nstate of the mind is determinate when the state of the brain is given,\r\nand if the material world forms a deterministic system, then mind is\r\n\"subject\" to matter in some sense in which matter is not \"subject\" to\r\nmind. But if the state of the brain is also determinate when the state\r\nof the mind is given, it must be exactly as true to regard matter as\r\nsubject to mind as it would be to regard mind as subject to matter. We\r\ncould, theoretically, work out the history of mind without ever\r\nmentioning matter, and then, at the end, deduce that matter must\r\nmeanwhile have gone through the corresponding history. It is true that\r\nif the relation of brain to mind were many-one, not one-one, there\r\nwould be a one-sided dependence of mind on brain, while conversely, if\r\nthe relation were one-many, as Bergson supposes, there would be a\r\none-aided dependence of brain on mind. But the dependence involved is,\r\nin any case, only \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_201\" id=\"Page_201\"\u003e[201]\u003c/a\u003e\u003c/span\u003elogical; it does not mean that we shall be\r\ncompelled to do things we desire not to do, which is what people\r\ninstinctively imagine it to mean.\u003c/p\u003e\r\n\r\n\u003cp\u003eAs another illustration we may take the case of mechanism and\r\nteleology. A system may be defined as \"mechanical\" when it has a set\r\nof determinants that are purely material, such as the positions of\r\ncertain pieces of matter at certain times. It is an open question\r\nwhether the world of mind and matter, as we know it, is a mechanical\r\nsystem or not; let us suppose, for the sake of argument, that it is a\r\nmechanical system. This supposition\u0026mdash;so I contend\u0026mdash;throws no light\r\nwhatever on the question whether the universe is or is not a\r\n\"teleological\" system. It is difficult to define accurately what is\r\nmeant by a \"teleological\" system, but the argument is not much\r\naffected by the particular definition we adopt. Broadly, a\r\nteleological system is one in which purposes are realised, i.e. in\r\nwhich certain desires\u0026mdash;those that are deeper or nobler or more\r\nfundamental or more universal or what not\u0026mdash;are followed by their\r\nrealisation. Now the fact\u0026mdash;if it be a fact\u0026mdash;that the universe is\r\nmechanical has no bearing whatever on the question whether it is\r\nteleological in the above sense. There might be a mechanical system in\r\nwhich all wishes were realised, and there might be one in which all\r\nwishes were thwarted. The question whether, or how far, our actual\r\nworld is teleological, cannot, therefore, be settled by proving that\r\nit is mechanical, and the desire that it should be teleological is no\r\nground for wishing it to be not mechanical.\u003c/p\u003e\r\n\r\n\u003cp\u003eThere is, in all these questions, a very great difficulty in avoiding\r\nconfusion between what we can infer and what is in fact determined.\r\nLet us consider, for a moment, the various senses in which the future\r\nmay be \"determined.\" There is one sense\u0026mdash;and a very important \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_202\" id=\"Page_202\"\u003e[202]\u003c/a\u003e\u003c/span\u003eone\u0026mdash;in\r\nwhich it is determined quite independently of scientific laws, namely,\r\nthe sense that it will be what it will be. We all regard the past as\r\ndetermined simply by the fact that it has happened; but for the\r\naccident that memory works backward and not forward, we should regard\r\nthe future as equally determined by the fact that it will happen.\r\n\"But,\" we are told, \"you cannot alter the past, while you can to some\r\nextent alter the future.\" This view seems to me to rest upon just\r\nthose errors in regard to causation which it has been my object to\r\nremove. You cannot make the past other than it was\u0026mdash;true, but this is\r\na mere application of the law of contradiction. If you already know\r\nwhat the past was, obviously it is useless to wish it different. But\r\nalso you cannot make the future other than it will be; this again is\r\nan application of the law of contradiction. And if you happen to know\r\nthe future\u0026mdash;e.g. in the case of a forthcoming eclipse\u0026mdash;it is just as\r\nuseless to wish it different as to wish the past different. \"But,\" it\r\nwill be rejoined, \"our wishes can \u003ci\u003ecause\u003c/i\u003e the future, sometimes, to be\r\ndifferent from what it would be if they did not exist, and they can\r\nhave no such effect upon the past.\" This, again, is a mere tautology.\r\nAn effect being \u003ci\u003edefined\u003c/i\u003e as something subsequent to its cause,\r\nobviously we can have no \u003ci\u003eeffect\u003c/i\u003e upon the past. But that does not\r\nmean that the past would not have been different if our present wishes\r\nhad been different. Obviously, our present wishes are conditioned by\r\nthe past, and therefore could not have been different unless the past\r\nhad been different; therefore, if our present wishes were different,\r\nthe past would be different. Of course, the past cannot be different\r\nfrom what it was, but no more can our present wishes be different from\r\nwhat they are; this again is merely the law of contradiction. The\r\nfacts seem to be merely (1) that wishing generally \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_203\" id=\"Page_203\"\u003e[203]\u003c/a\u003e\u003c/span\u003edepends upon\r\nignorance, and is therefore commoner in regard to the future than in\r\nregard to the past; (2) that where a wish concerns the future, it and\r\nits realisation very often form a \"practically independent system,\"\r\ni.e. many wishes regarding the future are realised. But there seems no\r\ndoubt that the main difference in our feelings arises from the\r\naccidental fact that the past but not the future can be known by\r\nmemory.\u003c/p\u003e\r\n\r\n\u003cp\u003eAlthough the sense of \"determined\" in which the future is determined\r\nby the mere fact that it will be what it will be is sufficient (at\r\nleast so it seems to me) to refute some opponents of determinism,\r\nnotably M. Bergson and the pragmatists, yet it is not what most people\r\nhave in mind when they speak of the future as determined. What they\r\nhave in mind is a formula by means of which the future can be\r\nexhibited, and at least theoretically calculated, as a function of the\r\npast. But at this point we meet with a great difficulty, which besets\r\nwhat has been said above about deterministic systems, as well as what\r\nis said by others.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf formul\u0026aelig; of any degree of complexity, however great, are admitted,\r\nit would seem that any system, whose state at a given moment is a\r\nfunction of certain measurable quantities, must be a deterministic\r\nsystem. Let us consider, in illustration, a single material particle,\r\nwhose co-ordinates at time \u003ci\u003et\u003c/i\u003e are \u003ci\u003ex\u003c/i\u003e\u003csub\u003et\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub\u003et\u003c/sub\u003e, \u003ci\u003ez\u003c/i\u003e\u003csub\u003et\u003c/sub\u003e. Then,\r\nhowever, the particle moves, there must be, theoretically, functions\r\n\u003ci\u003ef\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e, \u003ci\u003ef\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e, \u003ci\u003ef\u003c/i\u003e\u003csub\u003e3\u003c/sub\u003e, such that\u003c/p\u003e\r\n\r\n\u003cdiv class=\"block\"\u003e\r\n\u003cp\u003e\u003ci\u003ex\u003c/i\u003e\u003csub\u003et\u003c/sub\u003e = \u003ci\u003ef\u003c/i\u003e\u003csub\u003et\u003c/sub\u003e\u0026nbsp;(\u003ci\u003et\u003c/i\u003e), \u0026nbsp;\u0026nbsp;\u0026nbsp; \u003ci\u003ey\u003c/i\u003e\u003csub\u003et\u003c/sub\u003e = \u003ci\u003ef\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e\u0026nbsp;(\u003ci\u003et\u003c/i\u003e), \u0026nbsp;\u0026nbsp;\u0026nbsp; \u003ci\u003ez\u003c/i\u003e\u003csub\u003et\u003c/sub\u003e = \u003ci\u003ef\u003c/i\u003e\u003csub\u003e3\u003c/sub\u003e\u0026nbsp;(\u003ci\u003et\u003c/i\u003e).\u003c/p\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eIt follows that, theoretically, the whole state of the material\r\nuniverse at time \u003ci\u003et\u003c/i\u003e must be capable of being exhibited as a function\r\nof \u003ci\u003et\u003c/i\u003e. Hence our universe will be deterministic in the sense defined\r\nabove. But if this be \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_204\" id=\"Page_204\"\u003e[204]\u003c/a\u003e\u003c/span\u003etrue, no information is conveyed about the\r\nuniverse in stating that it is deterministic. It is true that the\r\nformul\u0026aelig; involved may be of strictly infinite complexity, and therefore\r\nnot practically capable of being written down or apprehended. But\r\nexcept from the point of view of our knowledge, this might seem to be\r\na detail: in itself, if the above considerations are sound, the\r\nmaterial universe \u003ci\u003emust\u003c/i\u003e be deterministic, \u003ci\u003emust\u003c/i\u003e be subject to laws.\u003c/p\u003e\r\n\r\n\u003cp\u003eThis, however, is plainly not what was intended. The difference\r\nbetween this view and the view intended may be seen as follows. Given\r\nsome formula which fits the facts hitherto\u0026mdash;say the law of\r\ngravitation\u0026mdash;there will be an infinite number of other formul\u0026aelig;, not\r\nempirically distinguishable from it in the past, but diverging from it\r\nmore and more in the future. Hence, even assuming that there are\r\npersistent laws, we shall have no reason for assuming that the law of\r\nthe inverse square will hold in future; it may be some other hitherto\r\nindistinguishable law that will hold. We cannot say that \u003ci\u003eevery\u003c/i\u003e law\r\nwhich has held hitherto must hold in the future, because past facts\r\nwhich obey one law will also obey others, hitherto indistinguishable\r\nbut diverging in future. Hence there must, at every moment, be laws\r\nhitherto unbroken which are now broken for the first time. What\r\nscience does, in fact, is to select the \u003ci\u003esimplest\u003c/i\u003e formula that will\r\nfit the facts. But this, quite obviously, is merely a methodological\r\nprecept, not a law of Nature. If the simplest formula ceases, after a\r\ntime, to be applicable, the simplest formula that remains applicable\r\nis selected, and science has no sense that an axiom has been\r\nfalsified. We are thus left with the brute fact that, in many\r\ndepartments of science, quite simple laws have hitherto been found to\r\nhold. This fact cannot be regarded as having any \u003ci\u003ea priori\u003c/i\u003e ground,\r\nnor can it be used to support inductively the opinion that \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_205\" id=\"Page_205\"\u003e[205]\u003c/a\u003e\u003c/span\u003ethe same\r\nlaws will continue; for at every moment laws hitherto true are being\r\nfalsified, though in the advanced sciences these laws are less simple\r\nthan those that have remained true. Moreover it would be fallacious to\r\nargue inductively from the state of the advanced sciences to the\r\nfuture state of the others, for it may well be that the advanced\r\nsciences are advanced simply because, hitherto, their subject-matter\r\nhas obeyed simple and easily ascertainable laws, while the\r\nsubject-matter of other sciences has not done so.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe difficulty we have been considering seems to be met partly, if not\r\nwholly, by the principle that the \u003ci\u003etime\u003c/i\u003e must not enter explicitly\r\ninto our formul\u0026aelig;. All mechanical laws exhibit acceleration as a\r\nfunction of configuration, not of configuration and time jointly; and\r\nthis principle of the irrelevance of the time may be extended to all\r\nscientific laws. In fact we might interpret the \"uniformity of nature\"\r\nas meaning just this, that no scientific law involves the time as an\r\nargument, unless, of course, it is given in an integrated form, in\r\nwhich case \u003ci\u003elapse\u003c/i\u003e of time, though not absolute time, may appear in\r\nour formul\u0026aelig;. Whether this consideration suffices to overcome our\r\ndifficulty completely, I do not know; but in any case it does much to\r\ndiminish it.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt will serve to illustrate what has been said if we apply it to the\r\nquestion of free will.\u003c/p\u003e\r\n\r\n\u003cp\u003e(1) Determinism in regard to the will is the doctrine that our\r\nvolitions belong to some deterministic system, i.e. are \"determined\"\r\nin the sense defined above. Whether this doctrine is true or false, is\r\na mere question of fact; no \u003ci\u003ea priori\u003c/i\u003e considerations (if our previous\r\ndiscussions have been correct) can exist on either side. On the one\r\nhand, there is no \u003ci\u003ea priori\u003c/i\u003e category of causality, but merely certain\r\nobserved uniformities. As a matter \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_206\" id=\"Page_206\"\u003e[206]\u003c/a\u003e\u003c/span\u003eof fact, there are observed\r\nuniformities in regard to volitions; thus there is some empirical\r\nevidence that volitions are determined. But it would be very rash to\r\nmaintain that the evidence is overwhelming, and it is quite possible\r\nthat some volitions, as well as some other things, are not determined,\r\nexcept in the sense in which we found that everything must be\r\ndetermined.\u003c/p\u003e\r\n\r\n\u003cp\u003e(2) But, on the other hand, the subjective sense of freedom, sometimes\r\nalleged against determinism, has no bearing on the question whatever.\r\nThe view that it has a bearing rests upon the belief that causes\r\ncompel their effects, or that nature enforces obedience to its laws as\r\ngovernments do. These are mere anthropomorphic superstitions, due to\r\nassimilation of causes with volitions and of natural laws with human\r\nedicts. We feel that our will is not compelled, but that only means\r\nthat it is not other than we choose it to be. It is one of the\r\ndemerits of the traditional theory of causality that it has created an\r\nartificial opposition between determinism and the freedom of which we\r\nare introspectively conscious.\u003c/p\u003e\r\n\r\n\u003cp\u003e(3) Besides the general question whether volitions are determined,\r\nthere is the further question whether they are \u003ci\u003emechanically\u003c/i\u003e\r\ndetermined, i.e. whether they are part of what was above defined as a\r\nmechanical system. This is the question whether they form part of a\r\nsystem with purely material determinants, i.e. whether there are laws\r\nwhich, given certain material data, make all volitions functions of\r\nthose data. Here again, there is empirical evidence up to a point, but\r\nit is not conclusive in regard to all volitions. It is important to\r\nobserve, however that even if volitions are part of a mechanical\r\nsystem, this by no means implies any supremacy of matter over mind. It\r\nmay well be that the same system which is \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_207\" id=\"Page_207\"\u003e[207]\u003c/a\u003e\u003c/span\u003esusceptible of material\r\ndeterminants is also susceptible of mental determinants; thus a\r\nmechanical system may be determined by sets of volitions, as well as\r\nby sets of material facts. It would seem, therefore, that the reasons\r\nwhich make people dislike the view that volitions are mechanically\r\ndetermined are fallacious.\u003c/p\u003e\r\n\r\n\u003cp\u003e(4) The notion of \u003ci\u003enecessity\u003c/i\u003e, which is often associated with\r\ndeterminism, is a confused notion not legitimately deducible from\r\ndeterminism. Three meanings are commonly confounded when necessity is\r\nspoken of:\u0026mdash;\u003c/p\u003e\r\n\r\n\u003cp\u003e(\u0026alpha;) An \u003ci\u003eaction\u003c/i\u003e is necessary when it will be performed\r\nhowever much the agent may wish to do otherwise. Determinism does not\r\nimply that actions are necessary in this sense.\u003c/p\u003e\r\n\r\n\u003cp\u003e(\u0026beta;) A \u003ci\u003epropositional function\u003c/i\u003e is necessary when all its\r\nvalues are true. This sense is not relevant to our present discussion.\u003c/p\u003e\r\n\r\n\u003cp\u003e(\u0026gamma;) A \u003ci\u003eproposition\u003c/i\u003e is necessary with respect to a given\r\nconstituent when it is the value, with that constituent as argument,\r\nof a necessary propositional function, in other words, when it remains\r\ntrue however that constituent may be varied. In this sense, in a\r\ndeterministic system, the connection of a volition with its\r\ndeterminants is necessary, if the time at which the determinants occur\r\nbe taken as the constituent to be varied, the time-interval between\r\nthe determinants and the volition being kept constant. But this sense\r\nof necessity is purely logical, and has no emotional importance.\u003c/p\u003e\r\n\r\n\u003cp\u003eWe may now sum up our discussion of causality. We found first that the\r\nlaw of causality, as usually stated by philosophers, is false, and is\r\nnot employed in science. We then considered the nature of scientific\r\nlaws, and found that, instead of stating that one event A is always\r\nfollowed \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_208\" id=\"Page_208\"\u003e[208]\u003c/a\u003e\u003c/span\u003eby another event B, they stated functional relations between\r\ncertain events at certain times, which we called determinants, and\r\nother events at earlier or later times or at the same time. We were\r\nunable to find any \u003ci\u003ea priori\u003c/i\u003e category involved: the existence of\r\nscientific laws appeared as a purely empirical fact, not necessarily\r\nuniversal, except in a trivial and scientifically useless form. We\r\nfound that a system with one set of determinants may very likely have\r\nother sets of a quite different kind, that, for example, a\r\nmechanically determined system may also be teleologically or\r\nvolitionally determined. Finally we considered the problem of free\r\nwill: here we found that the reasons for supposing volitions to be\r\ndetermined are strong but not conclusive, and we decided that even if\r\nvolitions are mechanically determined, that is no reason for denying\r\nfreedom in the sense revealed by introspection, or for supposing that\r\nmechanical events are not determined by volitions. The problem of free\r\nwill \u003ci\u003eversus\u003c/i\u003e determinism is therefore, if we were right, mainly\r\nillusory, but in part not yet capable of being decisively solved.\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\u003chr style=\"width: 15%;\" /\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003ch4\u003eFOOTNOTES:\u003c/h4\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_35_35\" id=\"Footnote_35_35\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_35_35\"\u003e\u003cspan class=\"label\"\u003e[35]\u003c/span\u003e\u003c/a\u003e A propositional function is an expression containing a\r\nvariable, or undetermined constituent, and becoming a proposition as\r\nsoon as a definite value is assigned to the variable. Examples are: \"A\r\nis A,\" \"\u003ci\u003ex\u003c/i\u003e is a number.\" The variable is called the \u003ci\u003eargument\u003c/i\u003e of the\r\nfunction.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_36_36\" id=\"Footnote_36_36\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_36_36\"\u003e\u003cspan class=\"label\"\u003e[36]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eLogic\u003c/i\u003e, Bk. III, Chap. V, \u0026sect; 2.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_37_37\" id=\"Footnote_37_37\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_37_37\"\u003e\u003cspan class=\"label\"\u003e[37]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eTime and Free Will\u003c/i\u003e, p. 199.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_38_38\" id=\"Footnote_38_38\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_38_38\"\u003e\u003cspan class=\"label\"\u003e[38]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eTime and Free Will.\u003c/i\u003e p. 202.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_39_39\" id=\"Footnote_39_39\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_39_39\"\u003e\u003cspan class=\"label\"\u003e[39]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eLoc. cit.\u003c/i\u003e, \u0026sect; 6\u003c/p\u003e\u003c/div\u003e\r\n\r\n\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003ca name=\"X\" id=\"X\"\u003e\u003c/a\u003e\u003chr /\u003e\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_209\" id=\"Page_209\"\u003e[209]\u003c/a\u003e\u003c/span\u003e\u003cbr /\u003e\r\n\r\n\u003ch3\u003eX\u003cspan class=\"totoc\"\u003e\u003ca href=\"#toc\"\u003eToC\u003c/a\u003e\u003c/span\u003e\u003c/h3\u003e\r\n\r\n\u003ch4\u003eKNOWLEDGE BY ACQUAINTANCE AND KNOWLEDGE BY DESCRIPTION\u003c/h4\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003cp\u003eThe object of the following paper is to consider what it is that we\r\nknow in cases where we know propositions about \"the so-and-so\" without\r\nknowing who or what the so-and-so is. For example, I know that the\r\ncandidate who gets most votes will be elected, though I do not know\r\nwho is the candidate who will get most votes. The problem I wish to\r\nconsider is: What do we know in these cases, where the subject is\r\nmerely described? I have considered this problem elsewhere\u003ca name=\"FNanchor_40_40\" id=\"FNanchor_40_40\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_40_40\" class=\"fnanchor\"\u003e[40]\u003c/a\u003e from a\r\npurely logical point of view; but in what follows I wish to consider\r\nthe question in relation to theory of knowledge as well as in relation\r\nto logic, and in view of the above-mentioned logical discussions, I\r\nshall in this paper make the logical portion as brief as possible.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn order to make clear the antithesis between \"acquaintance\" and\r\n\"description,\" I shall first of all try to explain what I mean by\r\n\"acquaintance.\" I say that I am \u003ci\u003eacquainted\u003c/i\u003e with an object when I\r\nhave a direct cognitive relation to that object, i.e. when I am\r\ndirectly aware of the object itself. When I speak of a cognitive\r\nrelation here, I do not mean the sort of relation which constitutes\r\njudgment, but the sort which constitutes presentation. In fact, I\r\nthink the relation of subject and \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_210\" id=\"Page_210\"\u003e[210]\u003c/a\u003e\u003c/span\u003eobject which I call acquaintance is\r\nsimply the converse of the relation of object and subject which\r\nconstitutes presentation. That is, to say that S has acquaintance with\r\nO is essentially the same thing as to say that O is presented to S.\r\nBut the associations and natural extensions of the word \u003ci\u003eacquaintance\u003c/i\u003e\r\nare different from those of the word \u003ci\u003epresentation\u003c/i\u003e. To begin with, as\r\nin most cognitive words, it is natural to say that I am acquainted\r\nwith an object even at moments when it is not actually before my mind,\r\nprovided it has been before my mind, and will be again whenever\r\noccasion arises. This is the same sense in which I am said to know\r\nthat 2+2=4 even when I am thinking of something else. In the second\r\nplace, the word \u003ci\u003eacquaintance\u003c/i\u003e is designed to emphasise, more than the\r\nword \u003ci\u003epresentation\u003c/i\u003e, the relational character of the fact with which\r\nwe are concerned. There is, to my mind, a danger that, in speaking of\r\npresentation, we may so emphasise the object as to lose sight of the\r\nsubject. The result of this is either to lead to the view that there\r\nis no subject, whence we arrive at materialism; or to lead to the view\r\nthat what is presented is part of the subject, whence we arrive at\r\nidealism, and should arrive at solipsism but for the most desperate\r\ncontortions. Now I wish to preserve the dualism of subject and object\r\nin my terminology, because this dualism seems to me a fundamental fact\r\nconcerning cognition. Hence I prefer the word \u003ci\u003eacquaintance\u003c/i\u003e because\r\nit emphasises the need of a subject which is acquainted.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhen we ask what are the kinds of objects with which we are\r\nacquainted, the first and most obvious example is \u003ci\u003esense-data\u003c/i\u003e. When I\r\nsee a colour or hear a noise, I have direct acquaintance with the\r\ncolour or the noise. The sense-datum with which I am acquainted in\r\nthese cases is generally, if not always, complex. This is\r\nparticularly \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_211\" id=\"Page_211\"\u003e[211]\u003c/a\u003e\u003c/span\u003eobvious in the case of sight. I do not mean, of course,\r\nmerely that the supposed physical object is complex, but that the\r\ndirect sensible object is complex and contains parts with spatial\r\nrelations. Whether it is possible to be aware of a complex without\r\nbeing aware of its constituents is not an easy question, but on the\r\nwhole it would seem that there is no reason why it should not be\r\npossible. This question arises in an acute form in connection with\r\nself-consciousness, which we must now briefly consider.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn introspection, we seem to be immediately aware of varying\r\ncomplexes, consisting of objects in various cognitive and conative\r\nrelations to ourselves. When I see the sun, it often happens that I am\r\naware of my seeing the sun, in addition to being aware of the sun; and\r\nwhen I desire food, it often happens that I am aware of my desire for\r\nfood. But it is hard to discover any state of mind in which I am aware\r\nof myself alone, as opposed to a complex of which I am a constituent.\r\nThe question of the nature of self-consciousness is too large and too\r\nslightly connected with our subject, to be argued at length here. It\r\nis difficult, but probably not impossible, to account for plain facts\r\nif we assume that we do not have acquaintance with ourselves. It is\r\nplain that we are not only \u003ci\u003eacquainted\u003c/i\u003e with the complex\r\n\"Self-acquainted-with-A,\" but we also \u003ci\u003eknow\u003c/i\u003e the proposition \"I am\r\nacquainted with A.\" Now here the complex has been analysed, and if \"I\"\r\ndoes not stand for something which is a direct object of acquaintance,\r\nwe shall have to suppose that \"I\" is something known by description.\r\nIf we wished to maintain the view that there is no acquaintance with\r\nSelf, we might argue as follows: We are acquainted with\r\n\u003ci\u003eacquaintance\u003c/i\u003e, and we know that it is a relation. Also we are\r\nacquainted with a complex in which we perceive that acquaintance \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_212\" id=\"Page_212\"\u003e[212]\u003c/a\u003e\u003c/span\u003eis\r\nthe relating relation. Hence we know that this complex must have a\r\nconstituent which is that which is acquainted, i.e. must have a\r\nsubject-term as well as an object-term. This subject-term we define as\r\n\"I.\" Thus \"I\" means \"the subject-term in awarenesses of which \u003ci\u003eI\u003c/i\u003e am\r\naware.\" But as a definition this cannot be regarded as a happy effort.\r\nIt would seem necessary, therefore, either to suppose that I am\r\nacquainted with myself, and that \"I,\" therefore, requires no\r\ndefinition, being merely the proper name of a certain object, or to\r\nfind some other analysis of self-consciousness. Thus\r\nself-consciousness cannot be regarded as throwing light on the\r\nquestion whether we can know a complex without knowing its\r\nconstituents. This question, however, is not important for our present\r\npurposes, and I shall therefore not discuss it further.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe awarenesses we have considered so far have all been awarenesses of\r\nparticular existents, and might all in a large sense be called\r\nsense-data. For, from the point of view of theory of knowledge,\r\nintrospective knowledge is exactly on a level with knowledge derived\r\nfrom sight or hearing. But, in addition to awareness of the above kind\r\nof objects, which may be called awareness of \u003ci\u003eparticulars\u003c/i\u003e; we have\r\nalso (though not quite in the same sense) what may be called awareness\r\nof \u003ci\u003euniversals\u003c/i\u003e. Awareness of universals is called \u003ci\u003econceiving\u003c/i\u003e, and a\r\nuniversal of which we are aware is called a \u003ci\u003econcept\u003c/i\u003e. Not only are we\r\naware of particular yellows, but if we have seen a sufficient number\r\nof yellows and have sufficient intelligence, we are aware of the\r\nuniversal \u003ci\u003eyellow\u003c/i\u003e; this universal is the subject in such judgments as\r\n\"yellow differs from blue\" or \"yellow resembles blue less than green\r\ndoes.\" And the universal yellow is the predicate in such judgments as\r\n\"this is yellow,\" where \"this\" is a particular sense-datum. And\r\nuniversal relations, too, \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_213\" id=\"Page_213\"\u003e[213]\u003c/a\u003e\u003c/span\u003eare objects of awarenesses; up and down,\r\nbefore and after, resemblance, desire, awareness itself, and so on,\r\nwould seem to be all of them objects of which we can be aware.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn regard to relations, it might be urged that we are never aware of\r\nthe universal relation itself, but only of complexes in which it is a\r\nconstituent. For example, it may be said that we do not know directly\r\nsuch a relation as \u003ci\u003ebefore\u003c/i\u003e, though we understand such a proposition\r\nas \"this is before that,\" and may be directly aware of such a complex\r\nas \"this being before that.\" This view, however, is difficult to\r\nreconcile with the fact that we often know propositions in which the\r\nrelation is the subject, or in which the relata are not definite given\r\nobjects, but \"anything.\" For example, we know that if one thing is\r\nbefore another, and the other before a third, then the first is before\r\nthe third; and here the things concerned are not definite things, but\r\n\"anything.\" It is hard to see how we could know such a fact about\r\n\"before\" unless we were acquainted with \"before,\" and not merely with\r\nactual particular cases of one given object being before another given\r\nobject. And more directly: A judgment such as \"this is before that,\"\r\nwhere this judgment is derived from awareness of a complex,\r\nconstitutes an analysis, and we should not understand the analysis if\r\nwe were not acquainted with the meaning of the terms employed. Thus we\r\nmust suppose that we are acquainted with the meaning of \"before,\" and\r\nnot merely with instances of it.\u003c/p\u003e\r\n\r\n\u003cp\u003eThere are thus at least two sorts of objects of which we are aware,\r\nnamely, particulars and universals. Among particulars I include all\r\nexistents, and all complexes of which one or more constituents are\r\nexistents, such as this-before-that, this-above-that,\r\nthe-yellowness-of-this. \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_214\" id=\"Page_214\"\u003e[214]\u003c/a\u003e\u003c/span\u003eAmong universals I include all objects of\r\nwhich no particular is a constituent. Thus the disjunction\r\n\"universal-particular\" includes all objects. We might also call it the\r\ndisjunction \"abstract-concrete.\" It is not quite parallel with the\r\nopposition \"concept-percept,\" because things remembered or imagined\r\nbelong with particulars, but can hardly be called percepts. (On the\r\nother hand, universals with which we are acquainted may be identified\r\nwith concepts.)\u003c/p\u003e\r\n\r\n\u003cp\u003eIt will be seen that among the objects with which we are acquainted\r\nare not included physical objects (as opposed to sense-data), nor\r\nother people\u0027s minds. These things are known to us by what I call\r\n\"knowledge by description,\" which we must now consider.\u003c/p\u003e\r\n\r\n\u003cp\u003eBy a \"description\" I mean any phrase of the form \"a so-and-so\" or \"the\r\nso-and-so.\" A phrase of the form \"a so-and-so\" I shall call an\r\n\"ambiguous\" description; a phrase of the form \"the so-and-so\" (in the\r\nsingular) I shall call a \"definite\" description. Thus \"a man\" is an\r\nambiguous description, and \"the man with the iron mask\" is a definite\r\ndescription. There are various problems connected with ambiguous\r\ndescriptions, but I pass them by, since they do not directly concern\r\nthe matter I wish to discuss. What I wish to discuss is the nature of\r\nour knowledge concerning objects in cases where we know that there is\r\nan object answering to a definite description, though we are not\r\n\u003ci\u003eacquainted\u003c/i\u003e with any such object. This is a matter which is concerned\r\nexclusively with \u003ci\u003edefinite\u003c/i\u003e descriptions. I shall, therefore, in the\r\nsequel, speak simply of \"descriptions\" when I mean \"definite\r\ndescriptions.\" Thus a description will mean any phrase of the form\r\n\"the so-and-so\" in the singular.\u003c/p\u003e\r\n\r\n\u003cp\u003eI shall say that an object is \"known by description\" when we know that\r\nit is \"\u003ci\u003ethe\u003c/i\u003e so-and-so,\" i.e. when we \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_215\" id=\"Page_215\"\u003e[215]\u003c/a\u003e\u003c/span\u003eknow that there is one object,\r\nand no more, having a certain property; and it will generally be\r\nimplied that we do not have knowledge of the same object by\r\nacquaintance. We know that the man with the iron mask existed, and\r\nmany propositions are known about him; but we do not know who he was.\r\nWe know that the candidate who gets most votes will be elected, and in\r\nthis case we are very likely also acquainted (in the only sense in\r\nwhich one can be acquainted with some one else) with the man who is,\r\nin fact, the candidate who will get most votes, but we do not know\r\nwhich of the candidates he is, i.e. we do not know any proposition of\r\nthe form \"A is the candidate who will get most votes\" where A is one\r\nof the candidates by name. We shall say that we have \"\u003ci\u003emerely\u003c/i\u003e\r\ndescriptive knowledge\" of the so-and-so when, although we know that\r\nthe so-and-so exists, and although we may possibly be acquainted with\r\nthe object which is, in fact, the so-and-so, yet we do not know any\r\nproposition \"\u003ci\u003ea\u003c/i\u003e is the so-and-so,\" where \u003ci\u003ea\u003c/i\u003e is something with which\r\nwe are acquainted.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhen we say \"the so-and-so exists,\" we mean that there is just one\r\nobject which is the so-and-so. The proposition \"\u003ci\u003ea\u003c/i\u003e is the so-and-so\"\r\nmeans that \u003ci\u003ea\u003c/i\u003e has the property so-and-so, and nothing else has. \"Sir\r\nJoseph Larmor is the Unionist candidate\" means \"Sir Joseph Larmor is a\r\nUnionist candidate, and no one else is.\" \"The Unionist candidate\r\nexists\" means \"some one is a Unionist candidate, and no one else is.\"\r\nThus, when we are acquainted with an object which we know to be the\r\nso-and-so, we know that the so-and-so exists but we may know that the\r\nso-and-so exists when we are not acquainted with any object which we\r\nknow to be the so-and-so, and even when we are not acquainted with any\r\nobject which, in fact, is the so-and-so.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_216\" id=\"Page_216\"\u003e[216]\u003c/a\u003e\u003c/span\u003eCommon words, even proper names, are usually really descriptions. That\r\nis to say, the thought in the mind of a person using a proper name\r\ncorrectly can generally only be expressed explicitly if we replace the\r\nproper name by a description. Moreover, the description required to\r\nexpress the thought will vary for different people, or for the same\r\nperson at different times. The only thing constant (so long as the\r\nname is rightly used) is the object to which the name applies. But so\r\nlong as this remains constant, the particular description involved\r\nusually makes no difference to the truth or falsehood of the\r\nproposition in which the name appears.\u003c/p\u003e\r\n\r\n\u003cp\u003eLet us take some illustrations. Suppose some statement made about\r\nBismarck. Assuming that there is such a thing as direct acquaintance\r\nwith oneself, Bismarck himself might have used his name directly to\r\ndesignate the particular person with whom he was acquainted. In this\r\ncase, if he made a judgment about himself, he himself might be a\r\nconstituent of the judgment. Here the proper name has the direct use\r\nwhich it always wishes to have, as simply standing for a certain\r\nobject, and not for a description of the object. But if a person who\r\nknew Bismarck made a judgment about him, the case is different. What\r\nthis person was acquainted with were certain sense-data which he\r\nconnected (rightly, we will suppose) with Bismarck\u0027s body. His body as\r\na physical object, and still more his mind, were only known as the\r\nbody and the mind connected with these sense-data. That is, they were\r\nknown by description. It is, of course, very much a matter of chance\r\nwhich characteristics of a man\u0027s appearance will come into a friend\u0027s\r\nmind when he thinks of him; thus the description actually in the\r\nfriend\u0027s mind is accidental. The essential point is that he knows that\r\nthe various descriptions all apply to the \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_217\" id=\"Page_217\"\u003e[217]\u003c/a\u003e\u003c/span\u003esame entity, in spite of\r\nnot being acquainted with the entity in question.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhen we, who did not know Bismarck, make a judgment about him, the\r\ndescription in our minds will probably be some more or less vague mass\r\nof historical knowledge\u0026mdash;far more, in most cases, than is required to\r\nidentify him. But, for the sake of illustration, let us assume that we\r\nthink of him as \"the first Chancellor of the German Empire.\" Here all\r\nthe words are abstract except \"German.\" The word \"German\" will again\r\nhave different meanings for different people. To some it will recall\r\ntravels in Germany, to some the look of Germany on the map, and so on.\r\nBut if we are to obtain a description which we know to be applicable,\r\nwe shall be compelled, at some point, to bring in a reference to a\r\nparticular with which we are acquainted. Such reference is involved in\r\nany mention of past, present, and future (as opposed to definite\r\ndates), or of here and there, or of what others have told us. Thus it\r\nwould seem that, in some way or other, a description known to be\r\napplicable to a particular must involve some reference to a particular\r\nwith which we are acquainted, if our knowledge about the thing\r\ndescribed is not to be merely what follows logically from the\r\ndescription. For example, \"the most long-lived of men\" is a\r\ndescription which must apply to some man, but we can make no judgments\r\nconcerning this man which involve knowledge about him beyond what the\r\ndescription gives. If, however, we say, \"the first Chancellor of the\r\nGerman Empire was an astute diplomatist,\" we can only be assured of\r\nthe truth of our judgment in virtue of something with which we are\r\nacquainted\u0026mdash;usually a testimony heard or read. Considered\r\npsychologically, apart from the information we convey to others, apart\r\nfrom the fact about the actual \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_218\" id=\"Page_218\"\u003e[218]\u003c/a\u003e\u003c/span\u003eBismarck, which gives importance to\r\nour judgment, the thought we really have contains the one or more\r\nparticulars involved, and otherwise consists wholly of concepts. All\r\nnames of places\u0026mdash;London, England, Europe, the earth, the Solar\r\nSystem\u0026mdash;similarly involve, when used, descriptions which start from\r\nsome one or more particulars with which we are acquainted. I suspect\r\nthat even the Universe, as considered by metaphysics, involves such a\r\nconnection with particulars. In logic, on the contrary, where we are\r\nconcerned not merely with what does exist, but with whatever might or\r\ncould exist or be, no reference to actual particulars is involved.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt would seem that, when we make a statement about something only\r\nknown by description, we often \u003ci\u003eintend\u003c/i\u003e to make our statement, not in\r\nthe form involving the description, but about the actual thing\r\ndescribed. That is to say, when we say anything about Bismarck, we\r\nshould like, if we could, to make the judgment which Bismarck alone\r\ncan make, namely, the judgment of which he himself is a constituent.\r\nIn this we are necessarily defeated, since the actual Bismarck is\r\nunknown to us. But we know that there is an object B called Bismarck,\r\nand that B was an astute diplomatist. We can thus \u003ci\u003edescribe\u003c/i\u003e the\r\nproposition we should like to affirm, namely, \"B was an astute\r\ndiplomatist,\" where B is the object which was Bismarck. What enables\r\nus to communicate in spite of the varying descriptions we employ is\r\nthat we know there is a true proposition concerning the actual\r\nBismarck, and that, however we may vary the description (so long as\r\nthe description is correct), the proposition described is still the\r\nsame. This proposition, which is described and is known to be true, is\r\nwhat interests us; but we are not acquainted with the proposition\r\nitself, and do not know \u003ci\u003eit\u003c/i\u003e, though we know it is true.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_219\" id=\"Page_219\"\u003e[219]\u003c/a\u003e\u003c/span\u003eIt will be seen that there are various stages in the removal from\r\nacquaintance with particulars: there is Bismarck to people who knew\r\nhim, Bismarck to those who only know of him through history, the man\r\nwith the iron mask, the longest-lived of men. These are progressively\r\nfurther removed from acquaintance with particulars, and there is a\r\nsimilar hierarchy in the region of universals. Many universals, like\r\nmany particulars, are only known to us by description. But here, as in\r\nthe case of particulars, knowledge concerning what is known by\r\ndescription is ultimately reducible to knowledge concerning what is\r\nknown by acquaintance.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe fundamental epistemological principle in the analysis of\r\npropositions containing descriptions is this: \u003ci\u003eEvery proposition which\r\nwe can understand must be composed wholly of constituents with which\r\nwe are acquainted.\u003c/i\u003e From what has been said already, it will be plain\r\nwhy I advocate this principle, and how I propose to meet the case of\r\npropositions which at first sight contravene it. Let us begin with the\r\nreasons for supposing the principle true.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe chief reason for supposing the principle true is that it seems\r\nscarcely possible to believe that we can make a judgment or entertain\r\na supposition without knowing what it is that we are judging or\r\nsupposing about. If we make a judgment about (say) Julius C\u0026aelig;sar, it is\r\nplain that the actual person who was Julius C\u0026aelig;sar is not a constituent\r\nof the judgment. But before going further, it may be well to explain\r\nwhat I mean when I say that this or that is a constituent of a\r\njudgment, or of a proposition which we understand. To begin with\r\njudgments: a judgment, as an occurrence, I take to be a relation of a\r\nmind to several entities, namely, the entities which compose what is\r\njudged. If, e.g. I judge \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_220\" id=\"Page_220\"\u003e[220]\u003c/a\u003e\u003c/span\u003ethat A loves B, the judgment as an event\r\nconsists in the existence, at a certain moment, of a specific\r\nfour-term relation, called \u003ci\u003ejudging\u003c/i\u003e, between me and A and love and B.\r\nThat is to say, at the time when I judge, there is a certain complex\r\nwhose terms are myself and A and love and B, and whose relating\r\nrelation is \u003ci\u003ejudging\u003c/i\u003e. My reasons for this view have been set forth\r\nelsewhere,\u003ca name=\"FNanchor_41_41\" id=\"FNanchor_41_41\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_41_41\" class=\"fnanchor\"\u003e[41]\u003c/a\u003e and I shall not repeat them here. Assuming this view of\r\njudgment, the constituents of the judgment are simply the constituents\r\nof the complex which is the judgment. Thus, in the above case, the\r\nconstituents are myself and A and love and B and judging. But myself\r\nand judging are constituents shared by all my judgments; thus the\r\n\u003ci\u003edistinctive\u003c/i\u003e constituents of the particular judgment in question are\r\nA and love and B. Coming now to what is meant by \"understanding a\r\nproposition,\" I should say that there is another relation possible\r\nbetween me and A and love and B, which is called my \u003ci\u003esupposing\u003c/i\u003e that A\r\nloves B.\u003ca name=\"FNanchor_42_42\" id=\"FNanchor_42_42\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_42_42\" class=\"fnanchor\"\u003e[42]\u003c/a\u003e When we can \u003ci\u003esuppose\u003c/i\u003e that A loves B, we \"understand the\r\nproposition\" \u003ci\u003eA loves B\u003c/i\u003e. Thus we often understand a proposition in\r\ncases where we have not enough knowledge to make a judgment.\r\nSupposing, like judging, is a many-term relation, of which a mind is\r\none term. The other terms of the relation are called the constituents\r\nof the proposition supposed. Thus the principle which I enunciated may\r\nbe re-stated as follows: \u003ci\u003eWhenever a \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_221\" id=\"Page_221\"\u003e[221]\u003c/a\u003e\u003c/span\u003erelation of supposing or judging\r\noccurs, the terms to which the supposing or judging mind is related by\r\nthe relation of supposing or judging must be terms with which the mind\r\nin question is acquainted.\u003c/i\u003e This is merely to say that we cannot make\r\na judgment or a supposition without knowing what it is that we are\r\nmaking our judgment or supposition about. It seems to me that the\r\ntruth of this principle is evident as soon as the principle is\r\nunderstood; I shall, therefore, in what follows, assume the principle,\r\nand use it as a guide in analysing judgments that contain\r\ndescriptions.\u003c/p\u003e\r\n\r\n\u003cp\u003eReturning now to Julius C\u0026aelig;sar, I assume that it will be admitted that\r\nhe himself is not a constituent of any judgment which I can make. But\r\nat this point it is necessary to examine the view that judgments are\r\ncomposed of something called \"ideas,\" and that it is the \"idea\" of\r\nJulius C\u0026aelig;sar that is a constituent of my judgment. I believe the\r\nplausibility of this view rests upon a failure to form a right theory\r\nof descriptions. We may mean by my \"idea\" of Julius C\u0026aelig;sar the things\r\nthat I know about him, e.g. that he conquered Gaul, was assassinated\r\non the Ides of March, and is a plague to schoolboys. Now I am\r\nadmitting, and indeed contending, that in order to discover what is\r\nactually in my mind when I judge about Julius C\u0026aelig;sar, we must\r\nsubstitute for the proper name a description made up of some of the\r\nthings I know about him. (A description which will often serve to\r\nexpress my thought is \"the man whose name was \u003ci\u003eJulius C\u0026aelig;sar\u003c/i\u003e.\" For\r\nwhatever else I may have forgotten about him, it is plain that when I\r\nmention him I have not forgotten that that was his name.) But although\r\nI think the theory that judgments consist of ideas may have been\r\nsuggested in some such way, yet I think the theory itself is\r\nfundamentally mistaken. The \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_222\" id=\"Page_222\"\u003e[222]\u003c/a\u003e\u003c/span\u003eview seems to be that there is some\r\nmental existent which may be called the \"idea\" of something outside\r\nthe mind of the person who has the idea, and that, since judgment is a\r\nmental event, its constituents must be constituents of the mind of the\r\nperson judging. But in this view ideas become a veil between us and\r\noutside things\u0026mdash;we never really, in knowledge, attain to the things we\r\nare supposed to be knowing about, but only to the ideas of those\r\nthings. The relation of mind, idea, and object, on this view, is\r\nutterly obscure, and, so far as I can see, nothing discoverable by\r\ninspection warrants the intrusion of the idea between the mind and the\r\nobject. I suspect that the view is fostered by the dislike of\r\nrelations, and that it is felt the mind could not know objects unless\r\nthere were something \"in\" the mind which could be called the state of\r\nknowing the object. Such a view, however, leads at once to a vicious\r\nendless regress, since the relation of idea to object will have to be\r\nexplained by supposing that the idea itself has an idea of the object,\r\nand so on \u003ci\u003ead infinitum\u003c/i\u003e. I therefore see no reason to believe that,\r\nwhen we are acquainted with an object, there is in us something which\r\ncan be called the \"idea\" of the object. On the contrary, I hold that\r\nacquaintance is wholly a relation, not demanding any such constituent\r\nof the mind as is supposed by advocates of \"ideas.\" This is, of\r\ncourse, a large question, and one which would take us far from our\r\nsubject if it were adequately discussed. I therefore content myself\r\nwith the above indications, and with the corollary that, in judging,\r\nthe actual objects concerning which we judge, rather than any supposed\r\npurely mental entities, are constituents of the complex which is the\r\njudgment.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhen, therefore, I say that we must substitute for \"Julius C\u0026aelig;sar\" some\r\ndescription of Julius C\u0026aelig;sar, in order \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_223\" id=\"Page_223\"\u003e[223]\u003c/a\u003e\u003c/span\u003eto discover the meaning of a\r\njudgment nominally about him, I am not saying that we must substitute\r\nan idea. Suppose our description is \"the man whose name was \u003ci\u003eJulius\r\nC\u0026aelig;sar\u003c/i\u003e.\" Let our judgment be \"Julius C\u0026aelig;sar was assassinated.\" Then it\r\nbecomes \"the man whose name was \u003ci\u003eJulius C\u0026aelig;sar\u003c/i\u003e was assassinated.\" Here\r\n\u003ci\u003eJulius C\u0026aelig;sar\u003c/i\u003e is a noise or shape with which we are acquainted, and\r\nall the other constituents of the judgment (neglecting the tense in\r\n\"was\") are \u003ci\u003econcepts\u003c/i\u003e with which we are acquainted. Thus our judgment\r\nis wholly reduced to constituents with which we are acquainted, but\r\nJulius C\u0026aelig;sar himself has ceased to be a constituent of our judgment.\r\nThis, however, requires a proviso, to be further explained shortly,\r\nnamely that \"the man whose name was \u003ci\u003eJulius C\u0026aelig;sar\u003c/i\u003e\" must not, as a\r\nwhole, be a constituent of our judgment, that is to say, this phrase\r\nmust not, as a whole, have a meaning which enters into the judgment.\r\nAny right analysis of the judgment, therefore, must break up this\r\nphrase, and not treat it as a subordinate complex which is part of the\r\njudgment. The judgment \"the man whose name was \u003ci\u003eJulius C\u0026aelig;sar\u003c/i\u003e was\r\nassassinated\" may be interpreted as meaning \"one and only one man was\r\ncalled \u003ci\u003eJulius C\u0026aelig;sar\u003c/i\u003e, and that one was assassinated.\" Here it is\r\nplain that there is no constituent corresponding to the phrase \"the\r\nman whose name was \u003ci\u003eJulius C\u0026aelig;sar\u003c/i\u003e.\" Thus there is no reason to regard\r\nthis phrase as expressing a constituent of the judgment, and we have\r\nseen that this phrase must be broken up if we are to be acquainted\r\nwith all the constituents of the judgment. This conclusion, which we\r\nhave reached from considerations concerned with the theory of\r\nknowledge, is also forced upon us by logical considerations, which\r\nmust now be briefly reviewed.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is common to distinguish two aspects, \u003ci\u003emeaning\u003c/i\u003e and \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_224\" id=\"Page_224\"\u003e[224]\u003c/a\u003e\u003c/span\u003e\u003ci\u003edenotation\u003c/i\u003e,\r\nsuch phrases as \"the author of Waverley.\" The meaning will be a\r\ncertain complex, consisting (at least) of authorship and Waverley with\r\nsome relation; the denotation will be Scott. Similarly \"featherless\r\nbipeds\" will have a complex meaning, containing as constituents the\r\npresence of two feet and the absence of feathers, while its denotation\r\nwill be the class of men. Thus when we say \"Scott is the author of\r\nWaverley\" or \"men are the same as featherless bipeds,\" we are\r\nasserting an identity of denotation, and this assertion is worth\r\nmaking because of the diversity of meaning.\u003ca name=\"FNanchor_43_43\" id=\"FNanchor_43_43\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_43_43\" class=\"fnanchor\"\u003e[43]\u003c/a\u003e I believe that the\r\nduality of meaning and denotation, though capable of a true\r\ninterpretation, is misleading if taken as fundamental. The denotation,\r\nI believe, is not a constituent of the proposition, except in the case\r\nof proper names, i.e. of words which do not assign a property to an\r\nobject, but merely and solely name it. And I should hold further that,\r\nin this sense, there are only two words which are strictly proper\r\nnames of particulars, namely, \"I\" and \"this.\"\u003ca name=\"FNanchor_44_44\" id=\"FNanchor_44_44\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_44_44\" class=\"fnanchor\"\u003e[44]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eOne reason for not believing the denotation to be a constituent of the\r\nproposition is that we may know the proposition even when we are not\r\nacquainted with the denotation. The proposition \"the author of\r\nWaverley is a novelist\" was known to people who did not know that \"the\r\nauthor of Waverley\" denoted Scott. This reason has been already\r\nsufficiently emphasised.\u003c/p\u003e\r\n\r\n\u003cp\u003eA second reason is that propositions concerning \"the so-and-so\" are\r\npossible even when \"the so-and-so\" has no denotation. Take, e.g. \"the\r\ngolden mountain does not exist\" or \"the round square is\r\nself-contradictory.\" \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_225\" id=\"Page_225\"\u003e[225]\u003c/a\u003e\u003c/span\u003eIf we are to preserve the duality of meaning and\r\ndenotation, we have to say, with Meinong, that there are such objects\r\nas the golden mountain and the round square, although these objects do\r\nnot have being. We even have to admit that the existent round square\r\nis existent, but does not exist.\u003ca name=\"FNanchor_45_45\" id=\"FNanchor_45_45\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_45_45\" class=\"fnanchor\"\u003e[45]\u003c/a\u003e Meinong does not regard this as a\r\ncontradiction, but I fail to see that it is not one. Indeed, it seems\r\nto me evident that the judgment \"there is no such object as the round\r\nsquare\" does not presuppose that there is such an object. If this is\r\nadmitted, however, we are led to the conclusion that, by parity of\r\nform, no judgment concerning \"the so-and-so\" actually involves the\r\nso-and-so as a constituent.\u003c/p\u003e\r\n\r\n\u003cp\u003eMiss Jones\u003ca name=\"FNanchor_46_46\" id=\"FNanchor_46_46\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_46_46\" class=\"fnanchor\"\u003e[46]\u003c/a\u003e contends that there is no difficulty in admitting\r\ncontradictory predicates concerning such an object as \"the present\r\nKing of France,\" on the ground that this object is in itself\r\ncontradictory. Now it might, of course, be argued that this object,\r\nunlike the round square, is not self-contradictory, but merely\r\nnon-existent. This, however, would not go to the root of the matter.\r\nThe real objection to such an argument is that the law of\r\ncontradiction ought not to be stated in the traditional form \"A is not\r\nboth B and not B,\" but in the form \"no proposition is both true and\r\nfalse.\" The traditional form only applies to certain propositions,\r\nnamely, to those which attribute a predicate to a subject. When the\r\nlaw is stated of propositions, instead of being stated concerning\r\nsubjects and predicates, it is at once evident that propositions about\r\nthe present King of France or the round square can form no exception,\r\nbut are just as incapable of being both true and false as other\r\npropositions. Miss Jones\u003ca name=\"FNanchor_47_47\" id=\"FNanchor_47_47\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_47_47\" class=\"fnanchor\"\u003e[47]\u003c/a\u003e argues that \"Scott is the author of\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_226\" id=\"Page_226\"\u003e[226]\u003c/a\u003e\u003c/span\u003eWaverley\" asserts identity of denotation between \u003ci\u003eScott\u003c/i\u003e and \u003ci\u003ethe\r\nauthor of Waverley\u003c/i\u003e. But there is some difficulty in choosing among\r\nalternative meanings of this contention. In the first place, it should\r\nbe observed that \u003ci\u003ethe author of Waverley\u003c/i\u003e is not a \u003ci\u003emere\u003c/i\u003e name, like\r\n\u003ci\u003eScott\u003c/i\u003e. \u003ci\u003eScott\u003c/i\u003e is merely a noise or shape conventionally used to\r\ndesignate a certain person; it gives us no information about that\r\nperson, and has nothing that can be called meaning as opposed to\r\ndenotation. (I neglect the fact, considered above, that even proper\r\nnames, as a rule, really stand for descriptions.) But \u003ci\u003ethe author of\r\nWaverley\u003c/i\u003e is not merely conventionally a name for Scott; the element\r\nof mere convention belongs here to the separate words, \u003ci\u003ethe\u003c/i\u003e and\r\n\u003ci\u003eauthor\u003c/i\u003e and \u003ci\u003eof\u003c/i\u003e and \u003ci\u003eWaverley\u003c/i\u003e. Given what these words stand for,\r\n\u003ci\u003ethe author of Waverley\u003c/i\u003e is no longer arbitrary. When it is said that\r\nScott is the author of Waverley, we are not stating that these are two\r\n\u003ci\u003enames\u003c/i\u003e for one man, as we should be if we said \"Scott is Sir Walter.\"\r\nA man\u0027s name is what he is called, but however much Scott had been\r\ncalled the author of Waverley, that would not have made him be the\r\nauthor; it was necessary for him actually to write Waverley, which was\r\na fact having nothing to do with names.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf, then, we are asserting identity of denotation, we must not mean by\r\n\u003ci\u003edenotation\u003c/i\u003e the mere relation of a name to the thing named. In fact,\r\nit would be nearer to the truth to say that the \u003ci\u003emeaning\u003c/i\u003e of \"Scott\"\r\nis the \u003ci\u003edenotation\u003c/i\u003e of \"the author of Waverley.\" The relation of\r\n\"Scott\" to Scott is that \"Scott\" means Scott, just as the relation of\r\n\"author\" to the concept which is so called is that \"author\" means this\r\nconcept. Thus if we distinguish meaning and denotation in \"the author\r\nof Waverley,\" we shall have to say that \"Scott\" has meaning but not\r\ndenotation. Also when we say \"Scott is the \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_227\" id=\"Page_227\"\u003e[227]\u003c/a\u003e\u003c/span\u003eauthor of Waverley,\" the\r\n\u003ci\u003emeaning\u003c/i\u003e of \"the author of Waverley\" is relevant to our assertion.\r\nFor if the denotation alone were relevant, any other phrase with the\r\nsame denotation would give the same proposition. Thus \"Scott is the\r\nauthor of Marmion\" would be the same proposition as \"Scott is the\r\nauthor of Waverley.\" But this is plainly not the case, since from the\r\nfirst we learn that Scott wrote Marmion and from the second we learn\r\nthat he wrote Waverley, but the first tells us nothing about Waverley\r\nand the second nothing about Marmion. Hence the meaning of \"the author\r\nof Waverley,\" as opposed to the denotation, is certainly relevant to\r\n\"Scott is the author of Waverley.\"\u003c/p\u003e\r\n\r\n\u003cp\u003eWe have thus agreed that \"the author of Waverley\" is not a mere name,\r\nand that its meaning is relevant in propositions in which it occurs.\r\nThus if we are to say, as Miss Jones does, that \"Scott is the author\r\nof Waverley\" asserts an identity of denotation, we must regard the\r\ndenotation of \"the author of Waverley\" as the denotation of what is\r\n\u003ci\u003emeant\u003c/i\u003e by \"the author of Waverley.\" Let us call the meaning of \"the\r\nauthor of Waverley\" M. Thus M is what \"the author of Waverley\" means.\r\nThen we are to suppose that \"Scott is the author of Waverley\" means\r\n\"Scott is the denotation of M.\" But here we are explaining our\r\nproposition by another of the same form, and thus we have made no\r\nprogress towards a real explanation. \"The denotation of M,\" like \"the\r\nauthor of Waverley,\" has both meaning and denotation, on the theory we\r\nare examining. If we call its meaning M\u0027, our proposition becomes\r\n\"Scott is the denotation of M\u0027.\" But this leads at once to an endless\r\nregress. Thus the attempt to regard our proposition as asserting\r\nidentity of denotation breaks down, and it becomes imperative to find\r\nsome other analysis. When this analysis has been \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_228\" id=\"Page_228\"\u003e[228]\u003c/a\u003e\u003c/span\u003ecompleted, we shall\r\nbe able to reinterpret the phrase \"identity of denotation,\" which\r\nremains obscure so long as it is taken as fundamental.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe first point to observe is that, in any proposition about \"the\r\nauthor of Waverley,\" provided Scott is not explicitly mentioned, the\r\ndenotation itself, i.e. Scott, does not occur, but only the concept of\r\ndenotation, which will be represented by a variable. Suppose we say\r\n\"the author of Waverley was the author of Marmion,\" we are certainly\r\nnot saying that both were Scott\u0026mdash;we may have forgotten that there was\r\nsuch a person as Scott. We are saying that there is some man who was\r\nthe author of Waverley and the author of Marmion. That is to say,\r\nthere is some one who wrote Waverley and Marmion, and no one else\r\nwrote them. Thus the identity is that of a variable, i.e. of an\r\nindefinite subject, \"some one.\" This is why we can understand\r\npropositions about \"the author of Waverley,\" without knowing who he\r\nwas. When we say \"the author of Waverley was a poet,\" we mean \"one and\r\nonly one man wrote Waverley, and he was a poet\"; when we say \"the\r\nauthor of Waverley was Scott\" we mean \"one and only one man wrote\r\nWaverley, and he was Scott.\" Here the identity is between a variable,\r\ni.e. an indeterminate subject (\"he\"), and Scott; \"the author of\r\nWaverley\" has been analysed away, and no longer appears as a\r\nconstituent of the proposition.\u003ca name=\"FNanchor_48_48\" id=\"FNanchor_48_48\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_48_48\" class=\"fnanchor\"\u003e[48]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eThe reason why it is imperative to analyse away the phrase \"the author\r\nof Waverley\" may be stated as follows. It is plain that when we say\r\n\"the author of Waverley is the author of Marmion,\" the \u003ci\u003eis\u003c/i\u003e expresses\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_229\" id=\"Page_229\"\u003e[229]\u003c/a\u003e\u003c/span\u003eidentity. We have seen also that the common \u003ci\u003edenotation\u003c/i\u003e, namely\r\nScott, is not a constituent of this proposition, while the \u003ci\u003emeanings\u003c/i\u003e\r\n(if any) of \"the author of Waverley\" and \"the author of Marmion\" are\r\nnot identical. We have seen also that, in any sense in which the\r\nmeaning of a word is a constituent of a proposition in whose verbal\r\nexpression the word occurs, \"Scott\" means the actual man Scott, in the\r\nsame sense (so far as concerns our present discussion) in which\r\n\"author\" means a certain universal. Thus, if \"the author of Waverley\"\r\nwere a subordinate complex in the above proposition, its \u003ci\u003emeaning\u003c/i\u003e\r\nwould have to be what was said to be identical with the \u003ci\u003emeaning\u003c/i\u003e of\r\n\"the author of Marmion.\" This is plainly not the case; and the only\r\nescape is to say that \"the author of Waverley\" does not, by itself,\r\nhave a meaning, though phrases of which it is part do have a meaning.\r\nThat is, in a right analysis of the above proposition, \"the author of\r\nWaverley\" must disappear. This is effected when the above proposition\r\nis analysed as meaning: \"Some one wrote Waverley and no one else did,\r\nand that some one also wrote Marmion and no one else did.\" This may be\r\nmore simply expressed by saying that the propositional function \"\u003ci\u003ex\u003c/i\u003e\r\nwrote Waverley and Marmion, and no one else did\" is capable of truth,\r\ni.e. some value of \u003ci\u003ex\u003c/i\u003e makes it true, but no other value does. Thus\r\nthe true subject of our judgment is a propositional function, i.e. a\r\ncomplex containing an undetermined constituent, and becoming a\r\nproposition as soon as this constituent is determined.\u003c/p\u003e\r\n\r\n\u003cp\u003eWe may now define the denotation of a phrase. If we know that the\r\nproposition \"\u003ci\u003ea\u003c/i\u003e is the so-and-so\" is true, i.e. that \u003ci\u003ea\u003c/i\u003e is so-and-so\r\nand nothing else is, we call \u003ci\u003ea\u003c/i\u003e the denotation of the phrase \"the\r\nso-and-so.\" A very great many of the propositions we naturally make\r\nabout \"the \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_230\" id=\"Page_230\"\u003e[230]\u003c/a\u003e\u003c/span\u003eso-and-so\" will remain true or remain false if we\r\nsubstitute \u003ci\u003ea\u003c/i\u003e for \"the so-and-so,\" where \u003ci\u003ea\u003c/i\u003e is the denotation of\r\n\"the so-and-so.\" Such propositions will also remain true or remain\r\nfalse if we substitute for \"the so-and-so\" any other phrase having the\r\nsame denotation. Hence, as practical men, we become interested in the\r\ndenotation more than in the description, since the denotation decides\r\nas to the truth or falsehood of so many statements in which the\r\ndescription occurs. Moreover, as we saw earlier in considering the\r\nrelations of description and acquaintance, we often wish to reach the\r\ndenotation, and are only hindered by lack of acquaintance: in such\r\ncases the description is merely the means we employ to get as near as\r\npossible to the denotation. Hence it naturally comes to be supposed\r\nthat the denotation is part of the proposition in which the\r\ndescription occurs. But we have seen, both on logical and on\r\nepistemological grounds, that this is an error. The actual object (if\r\nany) which is the denotation is not (unless it is explicitly\r\nmentioned) a constituent of propositions in which descriptions occur;\r\nand this is the reason why, in order to understand such propositions,\r\nwe need acquaintance with the constituents of the description, but do\r\nnot need acquaintance with its denotation. The first result of\r\nanalysis, when applied to propositions whose grammatical subject is\r\n\"the so-and-so,\" is to substitute a variable as subject; i.e. we\r\nobtain a proposition of the form: \"There is \u003ci\u003esomething\u003c/i\u003e which alone is\r\nso-and-so, and that \u003ci\u003esomething\u003c/i\u003e is such-and-such.\" The further\r\nanalysis of propositions concerning \"the so-and-so\" is thus merged in\r\nthe problem of the nature of the variable, i.e. of the meanings of\r\n\u003ci\u003esome\u003c/i\u003e, \u003ci\u003eany\u003c/i\u003e, and \u003ci\u003eall\u003c/i\u003e. This is a difficult problem, concerning\r\nwhich I do not intend to say anything at present.\u003c/p\u003e\r\n\r\n\u003cp\u003eTo sum up our whole discussion. We began by \u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_231\" id=\"Page_231\"\u003e[231]\u003c/a\u003e\u003c/span\u003edistinguishing two sorts\r\nof knowledge of objects, namely, knowledge by \u003ci\u003eacquaintance\u003c/i\u003e and\r\nknowledge by \u003ci\u003edescription\u003c/i\u003e. Of these it is only the former that brings\r\nthe object itself before the mind. We have acquaintance with\r\nsense-data, with many universals, and possibly with ourselves, but not\r\nwith physical objects or other minds. We have \u003ci\u003edescriptive\u003c/i\u003e knowledge\r\nof an object when we know that it is \u003ci\u003ethe\u003c/i\u003e object having some property\r\nor properties with which we are acquainted; that is to say, when we\r\nknow that the property or properties in question belong to one object\r\nand no more, we are said to have knowledge of that one object by\r\ndescription, whether or not we are acquainted with the object. Our\r\nknowledge of physical objects and of other minds is only knowledge by\r\ndescription, the descriptions involved being usually such as involve\r\nsense-data. All propositions intelligible to us, whether or not they\r\nprimarily concern things only known to us by description, are composed\r\nwholly of constituents with which we are acquainted, for a constituent\r\nwith which we are not acquainted is unintelligible to us. A judgment,\r\nwe found, is not composed of mental constituents called \"ideas,\" but\r\nconsists of an occurrence whose constituents are a mind\u003ca name=\"FNanchor_49_49\" id=\"FNanchor_49_49\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_49_49\" class=\"fnanchor\"\u003e[49]\u003c/a\u003e and\r\ncertain objects, particulars or universals. (One at least must be a\r\nuniversal.) When a judgment is rightly analysed, the objects which are\r\nconstituents of it must all be objects with which the mind which is a\r\nconstituent of it is acquainted. This conclusion forces us to analyse\r\ndescriptive phrases occurring in propositions, and to say that the\r\nobjects denoted by such phrases are not constituents of judgments in\r\nwhich such phrases occur (unless these objects are explicitly\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_232\" id=\"Page_232\"\u003e[232]\u003c/a\u003e\u003c/span\u003ementioned). This leads us to the view (recommended also on purely\r\nlogical grounds) that when we say \"the author of Marmion was the\r\nauthor of Waverley,\" Scott himself is not a constituent of our\r\njudgment, and that the judgment cannot be explained by saying that it\r\naffirms identity of denotation with diversity of meaning. It also,\r\nplainly, does not assert identity of meaning. Such judgments,\r\ntherefore, can only be analysed by breaking up the descriptive\r\nphrases, introducing a variable, and making propositional functions\r\nthe ultimate subjects. In fact, \"the so-and-so is such-and-such\" will\r\nmean that \"\u003ci\u003ex\u003c/i\u003e is so-and-so and nothing else is, and \u003ci\u003ex\u003c/i\u003e is\r\nsuch-and-such\" is capable of truth. The analysis of such judgments\r\ninvolves many fresh problems, but the discussion of these problems is\r\nnot undertaken in the present paper.\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\u003chr style=\"width: 15%;\" /\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003ch4\u003eFOOTNOTES:\u003c/h4\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_40_40\" id=\"Footnote_40_40\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_40_40\"\u003e\u003cspan class=\"label\"\u003e[40]\u003c/span\u003e\u003c/a\u003e See references later.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_41_41\" id=\"Footnote_41_41\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_41_41\"\u003e\u003cspan class=\"label\"\u003e[41]\u003c/span\u003e\u003c/a\u003e \u003ci\u003ePhilosophical Essays\u003c/i\u003e, \"The Nature of Truth.\" I have\r\nbeen persuaded by Mr. Wittgenstein that this theory is somewhat unduly\r\nsimple, but the modification which I believe it to require does not\r\naffect the above argument [1917].\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_42_42\" id=\"Footnote_42_42\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_42_42\"\u003e\u003cspan class=\"label\"\u003e[42]\u003c/span\u003e\u003c/a\u003e Cf. Meinong, \u003ci\u003eUeber Annahmen\u003c/i\u003e, \u003ci\u003epassim\u003c/i\u003e. I formerly\r\nsupposed, contrary to Meinong\u0027s view, that the relationship of\r\nsupposing might be merely that of presentation. In this view I now\r\nthink I was mistaken, and Meinong is right. But my present view\r\ndepends upon the theory that both in judgment and in assumption there\r\nis no single Objective, but the several constituents of the judgment\r\nor assumption are in a many-term relation to the mind.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_43_43\" id=\"Footnote_43_43\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_43_43\"\u003e\u003cspan class=\"label\"\u003e[43]\u003c/span\u003e\u003c/a\u003e This view has been recently advocated by Miss E.E.C.\r\nJones. \"A New Law of Thought and its Implications,\" \u003ci\u003eMind\u003c/i\u003e, January,\r\n1911.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_44_44\" id=\"Footnote_44_44\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_44_44\"\u003e\u003cspan class=\"label\"\u003e[44]\u003c/span\u003e\u003c/a\u003e I should now exclude \"I\" from proper names in the strict\r\nsense, and retain only \"this\" [1917].\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_45_45\" id=\"Footnote_45_45\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_45_45\"\u003e\u003cspan class=\"label\"\u003e[45]\u003c/span\u003e\u003c/a\u003e Meinong, \u003ci\u003eUeber Annahmen\u003c/i\u003e, 2nd ed., Leipzig, 1910, p.\r\n141.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_46_46\" id=\"Footnote_46_46\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_46_46\"\u003e\u003cspan class=\"label\"\u003e[46]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eMind\u003c/i\u003e, July, 1910, p. 380.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_47_47\" id=\"Footnote_47_47\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_47_47\"\u003e\u003cspan class=\"label\"\u003e[47]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eMind\u003c/i\u003e, July, 1910, p. 379.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_48_48\" id=\"Footnote_48_48\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_48_48\"\u003e\u003cspan class=\"label\"\u003e[48]\u003c/span\u003e\u003c/a\u003e The theory which I am advocating is set forth fully,\r\nwith the logical grounds in its favour, in \u003ci\u003ePrincipia Mathematica\u003c/i\u003e,\r\nVol. I. Introduction, Chap. III; also, less fully, in \u003ci\u003eMind\u003c/i\u003e, October,\r\n1905.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp class=\"noin\"\u003e\u003ca name=\"Footnote_49_49\" id=\"Footnote_49_49\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_49_49\"\u003e\u003cspan class=\"label\"\u003e[49]\u003c/span\u003e\u003c/a\u003e I use this phrase merely to denote the something\r\npsychological which enters into judgment, without intending to\r\nprejudge the question as to what this something is.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003ca name=\"INDEX\" id=\"INDEX\"\u003e\u003c/a\u003e\u003chr /\u003e\r\n\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_233\" id=\"Page_233\"\u003e[233]\u003c/a\u003e\u003c/span\u003e\u003cbr /\u003e\r\n\r\n\u003ch3\u003eINDEX\u003cspan class=\"totoc\"\u003e\u003ca href=\"#toc\"\u003eToC\u003c/a\u003e\u003c/span\u003e\u003c/h3\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003cul\u003e\u003cli\u003eAchilles and the tortoise, \u003ca href=\"#Page_80\"\u003e80 ff\u003c/a\u003e, \u003ca href=\"#Page_89\"\u003e89 ff\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eAcquaintance, the relation of, \u003ca href=\"#Page_209\"\u003e209 ff\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eAlexander, \u003ca href=\"#Page_125\"\u003e125\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eAmerican Realists, the, \u003ca href=\"#Page_134\"\u003e134\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eAristotle, \u003ca href=\"#Page_42\"\u003e42\u003c/a\u003e, \u003ca href=\"#Page_76\"\u003e76\u003c/a\u003e, \u003ca href=\"#Page_97\"\u003e97\u003c/a\u003e\u003cbr /\u003e\u003cbr /\u003e\u003c/li\u003e\r\n\r\n\r\n\u003cli\u003eBacon, \u003ca href=\"#Page_41\"\u003e41\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eBergson, \u003ca href=\"#Page_14\"\u003e14 ff\u003c/a\u003e, \u003ca href=\"#Page_22\"\u003e22\u003c/a\u003e, \u003ca href=\"#Page_105\"\u003e105\u003c/a\u003e, \u003ca href=\"#Page_128\"\u003e128\u003c/a\u003e, \u003ca href=\"#Page_185\"\u003e185 ff\u003c/a\u003e, \u003ca href=\"#Page_203\"\u003e203\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eBerkeley, \u003ca href=\"#Page_97\"\u003e97\u003c/a\u003e, \u003ca href=\"#Page_132\"\u003e132\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eBlake, \u003ca href=\"#Page_1\"\u003e1\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eBosanquet, \u003ca href=\"#Page_99\"\u003e99\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eBroad, \u003ca href=\"#Page_89\"\u003e89 \u003ci\u003en\u003c/i\u003e\u003c/a\u003e\u003cbr /\u003e\u003cbr /\u003e\u003c/li\u003e\r\n\r\n\r\n\u003cli\u003eCalculus, the, \u003ca href=\"#Page_82\"\u003e82\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eCantor, Georg, \u003ca href=\"#Page_64\"\u003e64\u003c/a\u003e, \u003ca href=\"#Page_81\"\u003e81 ff\u003c/a\u003e, \u003ca href=\"#Page_85\"\u003e85\u003c/a\u003e, \u003ca href=\"#Page_91\"\u003e91\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eCarlyle, \u003ca href=\"#Page_50\"\u003e50\u003c/a\u003e, \u003ca href=\"#Page_82\"\u003e82\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eCause, the conception of, \u003ca href=\"#Page_135\"\u003e135 \u003ci\u003en\u003c/i\u003e\u003c/a\u003e, \u003ca href=\"#Page_180\"\u003e180 ff\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eChristianity and renunciation, \u003ca href=\"#Page_51\"\u003e51\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eChuang Tz\u0026#365;, \u003ca href=\"#Page_106\"\u003e106\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eConstruction of permanent things and matter, \u003ca href=\"#Page_169\"\u003e169 ff\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eConstructions, logical, \u003ca href=\"#Page_155\"\u003e155 ff\u003c/a\u003e\u003cbr /\u003e\u003cbr /\u003e\u003c/li\u003e\r\n\r\n\r\n\u003cli\u003eDarwin, \u003ca href=\"#Page_15\"\u003e15\u003c/a\u003e, \u003ca href=\"#Page_23\"\u003e23\u003c/a\u003e, \u003ca href=\"#Page_43\"\u003e43\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eDedekind, \u003ca href=\"#Page_64\"\u003e64\u003c/a\u003e, \u003ca href=\"#Page_81\"\u003e81 ff\u003c/a\u003e, \u003ca href=\"#Page_85\"\u003e85\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eDescartes, \u003ca href=\"#Page_97\"\u003e97\u003c/a\u003e, \u003ca href=\"#Page_126\"\u003e126\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eDescriptions, \u003ca href=\"#Page_175\"\u003e175\u003c/a\u003e, \u003ca href=\"#Page_214\"\u003e214 ff\u003c/a\u003e\u003cbr /\u003e\u003cbr /\u003e\u003c/li\u003e\r\n\r\n\r\n\u003cli\u003eEducation, \u003ca href=\"#Page_37\"\u003e37 ff\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eEuclid, \u003ca href=\"#Page_62\"\u003e62\u003c/a\u003e, \u003ca href=\"#Page_92\"\u003e92\u003c/a\u003e, \u003ca href=\"#Page_94\"\u003e94\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eEvolutionism, \u003ca href=\"#Page_23\"\u003e23 ff\u003c/a\u003e, \u003ca href=\"#Page_28\"\u003e28\u003c/a\u003e\u003cbr /\u003e\u003cbr /\u003e\u003c/li\u003e\r\n\r\n\r\n\u003cli\u003eFano, \u003ca href=\"#Page_93\"\u003e93\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eFaraday, \u003ca href=\"#Page_34\"\u003e34\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eFree will, \u003ca href=\"#Page_205\"\u003e205 ff\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eFrege, \u003ca href=\"#Page_78\"\u003e78 \u003ci\u003en\u003c/i\u003e\u003c/a\u003e\u003cbr /\u003e\u003cbr /\u003e\u003c/li\u003e\r\n\r\n\r\n\u003cli\u003eGalileo, \u003ca href=\"#Page_42\"\u003e42\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eGladstone, \u003ca href=\"#Page_177\"\u003e177\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eGood and evil, \u003ca href=\"#Page_26\"\u003e26 ff\u003c/a\u003e\u003cbr /\u003e\u003cbr /\u003e\u003c/li\u003e\r\n\r\n\r\n\u003cli\u003eHegel, \u003ca href=\"#Page_8\"\u003e8\u003c/a\u003e, \u003ca href=\"#Page_10\"\u003e10\u003c/a\u003e, \u003ca href=\"#Page_18\"\u003e18\u003c/a\u003e, \u003ca href=\"#Page_85\"\u003e85\u003c/a\u003e, \u003ca href=\"#Page_97\"\u003e97\u003c/a\u003e, \u003ca href=\"#Page_105\"\u003e105 ff\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eHeine, \u003ca href=\"#Page_113\"\u003e113\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eHeraclitus, \u003ca href=\"#Page_1\"\u003e1 ff\u003c/a\u003e, \u003ca href=\"#Page_10\"\u003e10\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eHertz, \u003ca href=\"#Page_34\"\u003e34\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eHolt, \u003ca href=\"#Page_177\"\u003e177 \u003ci\u003en\u003c/i\u003e\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eHume, \u003ca href=\"#Page_1\"\u003e1\u003c/a\u003e, \u003ca href=\"#Page_97\"\u003e97\u003c/a\u003e\u003cbr /\u003e\u003cbr /\u003e\u003c/li\u003e\r\n\r\n\r\n\u003cli\u003eInfinite, the mathematical, \u003ca href=\"#Page_84\"\u003e84 ff\u003c/a\u003e\u003cbr /\u003e\u003cbr /\u003e\u003c/li\u003e\r\n\r\n\r\n\u003cli\u003eJames, William, \u003ca href=\"#Page_100\"\u003e100\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eJones, Miss E.E.C., \u003ca href=\"#Page_224\"\u003e224 \u003ci\u003en\u003c/i\u003e\u003c/a\u003e, \u003ca href=\"#Page_225\"\u003e225\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eJudgment, \u003ca href=\"#Page_219\"\u003e219 ff\u003c/a\u003e\u003cbr /\u003e\u003cbr /\u003e\u003c/li\u003e\r\n\r\n\r\n\u003cli\u003eKant, \u003ca href=\"#Page_85\"\u003e85\u003c/a\u003e, \u003ca href=\"#Page_96\"\u003e96\u003c/a\u003e, \u003ca href=\"#Page_97\"\u003e97\u003c/a\u003e, \u003ca href=\"#Page_99\"\u003e99\u003c/a\u003e, \u003ca href=\"#Page_118\"\u003e118 ff\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eKnowledge by acquaintance, \u003ca href=\"#Page_209\"\u003e209 ff\u003c/a\u003e;\r\n \u003cul class=\"nest\"\u003e\r\n \u003cli\u003eby description, \u003ca href=\"#Page_214\"\u003e214 ff\u003c/a\u003e\u003c/li\u003e\r\n \u003c/ul\u003e\r\n\u003cbr /\u003e\u003c/li\u003e\r\n\r\n\r\n\u003cli\u003eLaplace, \u003ca href=\"#Page_23\"\u003e23\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eLeibniz, \u003ca href=\"#Page_76\"\u003e76\u003c/a\u003e, \u003ca href=\"#Page_79\"\u003e79\u003c/a\u003e, \u003ca href=\"#Page_82\"\u003e82 ff\u003c/a\u003e, \u003ca href=\"#Page_97\"\u003e97\u003c/a\u003e, \u003ca href=\"#Page_126\"\u003e126\u003c/a\u003e, \u003ca href=\"#Page_144\"\u003e144\u003c/a\u003e, \u003ca href=\"#Page_160\"\u003e160\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eLocke, \u003ca href=\"#Page_97\"\u003e97\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eLogic, the laws of, \u003ca href=\"#Page_68\"\u003e68 ff\u003c/a\u003e\u003cbr /\u003e\u003cbr /\u003e\u003c/li\u003e\r\n\r\n\r\n\u003cli\u003eMacaulay and Taylor\u0027s theorem, \u003ca href=\"#Page_95\"\u003e95\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eMalthus, \u003ca href=\"#Page_43\"\u003e43\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eMathematics, \u003ca href=\"#Page_58\"\u003e58 ff\u003c/a\u003e;\r\n \u003cul class=\"nest\"\u003e\r\n \u003cli\u003eand the Metaphysicians, \u003ca href=\"#Page_74\"\u003e74 ff\u003c/a\u003e;\u003c/li\u003e\r\n \u003cli\u003eand logic, \u003ca href=\"#Page_75\"\u003e75 ff\u003c/a\u003e;\u003c/li\u003e\r\n \u003cli\u003eand the infinitesimal, \u003ca href=\"#Page_82\"\u003e82 ff\u003c/a\u003e\u003c/li\u003e\r\n \u003c/ul\u003e\r\n\u003c/li\u003e\r\n\r\n\u003cli\u003eMatter, the nature of, \u003ca href=\"#Page_125\"\u003e125 ff\u003c/a\u003e;\r\n \u003cul class=\"nest\"\u003e\r\n \u003cli\u003edefinition of, \u003ca href=\"#Page_164\"\u003e164 ff\u003c/a\u003e\u003c/li\u003e\r\n \u003c/ul\u003e\r\n\u003c/li\u003e\r\n\r\n\u003cli\u003eMaxwell, \u003ca href=\"#Page_34\"\u003e34\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eMeaning and denotation, \u003ca href=\"#Page_223\"\u003e223 ff\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eMeinong, \u003ca href=\"#Page_174\"\u003e174\u003c/a\u003e, \u003ca href=\"#Page_220\"\u003e220 \u003ci\u003en\u003c/i\u003e\u003c/a\u003e, \u003ca href=\"#Page_225\"\u003e225\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eMilitarism, \u003ca href=\"#Page_50\"\u003e50\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eMill, \u003ca href=\"#Page_185\"\u003e185\u003c/a\u003e, \u003ca href=\"#Page_193\"\u003e193 ff\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eMysticism and logic, \u003ca href=\"#Page_1\"\u003e1 ff\u003c/a\u003e\u003cbr /\u003e\u003cbr /\u003e\u003c/li\u003e\r\n\r\n\r\n\u003cli\u003eNecessity, the notion of, \u003ca href=\"#Page_207\"\u003e207 ff\u003c/a\u003e\u003cspan class=\u0027pagenum\u0027\u003e\u003ca name=\"Page_234\" id=\"Page_234\"\u003e[234]\u003c/a\u003e\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eNietzsche, \u003ca href=\"#Page_22\"\u003e22\u003c/a\u003e, \u003ca href=\"#Page_50\"\u003e50\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eNunn, \u003ca href=\"#Page_125\"\u003e125\u003c/a\u003e, \u003ca href=\"#Page_137\"\u003e137 \u003ci\u003en\u003c/i\u003e\u003c/a\u003e, \u003ca href=\"#Page_153\"\u003e153\u003c/a\u003e\u003cbr /\u003e\u003cbr /\u003e\u003c/li\u003e\r\n\r\n\r\n\u003cli\u003eParmenides, \u003ca href=\"#Page_7\"\u003e7 ff\u003c/a\u003e, \u003ca href=\"#Page_18\"\u003e18\u003c/a\u003e, \u003ca href=\"#Page_21\"\u003e21\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eParticulars, awareness of, \u003ca href=\"#Page_210\"\u003e210 ff\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003ePeano, \u003ca href=\"#Page_78\"\u003e78 ff\u003c/a\u003e, \u003ca href=\"#Page_93\"\u003e93 ff\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003ePerspectives, \u003ca href=\"#Page_139\"\u003e139 ff\u003c/a\u003e;\r\n \u003cul class=\"nest\"\u003e\r\n \u003cli\u003ethe space of, \u003ca href=\"#Page_158\"\u003e158 ff\u003c/a\u003e\u003c/li\u003e\r\n \u003c/ul\u003e\r\n\u003c/li\u003e\r\n\r\n\u003cli\u003ePhilosophy and logic, \u003ca href=\"#Page_111\"\u003e111\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003ePhysics, sense-data and, \u003ca href=\"#Page_145\"\u003e145 ff\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003ePierce, \u003ca href=\"#Page_76\"\u003e76 \u003ci\u003en\u003c/i\u003e\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003ePlato, \u003ca href=\"#Page_1\"\u003e1 ff\u003c/a\u003e, \u003ca href=\"#Page_10\"\u003e10\u003c/a\u003e, \u003ca href=\"#Page_30\"\u003e30\u003c/a\u003e, \u003ca href=\"#Page_60\"\u003e60\u003c/a\u003e, \u003ca href=\"#Page_97\"\u003e97\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003ePragmatism, \u003ca href=\"#Page_22\"\u003e22\u003c/a\u003e, \u003ca href=\"#Page_105\"\u003e105\u003c/a\u003e\u003cbr /\u003e\u003cbr /\u003e\u003c/li\u003e\r\n\r\n\r\n\u003cli\u003eRealism and the analytic method, \u003ca href=\"#Page_120\"\u003e120 ff\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eReason and intuition, \u003ca href=\"#Page_12\"\u003e12 ff\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eRelatives, the logic of, \u003ca href=\"#Page_76\"\u003e76\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eRobb, \u003ca href=\"#Page_167\"\u003e167 \u003ci\u003en\u003c/i\u003e\u003c/a\u003e\u003cbr /\u003e\u003cbr /\u003e\u003c/li\u003e\r\n\r\n\r\n\u003cli\u003eSantayana, \u003ca href=\"#Page_20\"\u003e20\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eSense-data, \u003ca href=\"#Page_147\"\u003e147\u003c/a\u003e, \u003ca href=\"#Page_210\"\u003e210 ff\u003c/a\u003e;\r\n \u003cul class=\"nest\"\u003e\r\n \u003cli\u003eand physics, \u003ca href=\"#Page_145\"\u003e145 ff\u003c/a\u003e\u003c/li\u003e\r\n \u003c/ul\u003e\r\n\u003c/li\u003e\r\n\r\n\u003cli\u003eSensibilia, \u003ca href=\"#Page_148\"\u003e148 ff\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eSpace, \u003ca href=\"#Page_138\"\u003e138 ff\u003c/a\u003e;\r\n \u003cul class=\"nest\"\u003e\r\n \u003cli\u003eprivate, \u003ca href=\"#Page_158\"\u003e158 ff\u003c/a\u003e;\u003c/li\u003e\r\n \u003cli\u003ethe logical problem, \u003ca href=\"#Page_114\"\u003e114 ff\u003c/a\u003e;\u003c/li\u003e\r\n \u003cli\u003ethe problem in physics, \u003ca href=\"#Page_115\"\u003e115 ff\u003c/a\u003e;\u003c/li\u003e\r\n \u003cli\u003ethe epistemological problem, \u003ca href=\"#Page_118\"\u003e118 ff\u003c/a\u003e\u003c/li\u003e\r\n \u003c/ul\u003e\r\n\u003c/li\u003e\r\n\r\n\u003cli\u003eSystems, deterministic, \u003ca href=\"#Page_199\"\u003e199\u003c/a\u003e;\r\n \u003cul class=\"nest\"\u003e\r\n \u003cli\u003epractically isolated, \u003ca href=\"#Page_198\"\u003e198\u003c/a\u003e;\u003c/li\u003e\r\n \u003cli\u003erelatively isolated, \u003ca href=\"#Page_197\"\u003e197\u003c/a\u003e;\u003c/li\u003e\r\n \u003cli\u003emechanical, \u003ca href=\"#Page_201\"\u003e201\u003c/a\u003e\u003c/li\u003e\r\n \u003c/ul\u003e\r\n\u003cbr /\u003e\u003c/li\u003e\r\n\r\n\r\n\u003cli\u003eTime, \u003ca href=\"#Page_10\"\u003e10\u003c/a\u003e, \u003ca href=\"#Page_21\"\u003e21 ff\u003c/a\u003e, \u003ca href=\"#Page_141\"\u003e141 ff\u003c/a\u003e, \u003ca href=\"#Page_167\"\u003e167 ff\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eTristram Shandy, the paradox of, \u003ca href=\"#Page_90\"\u003e90 ff\u003c/a\u003e\u003cbr /\u003e\u003cbr /\u003e\u003c/li\u003e\r\n\r\n\r\n\u003cli\u003eUnity and Plurality, \u003ca href=\"#Page_18\"\u003e18 ff\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eUniversals, awareness of, \u003ca href=\"#Page_212\"\u003e212 ff\u003c/a\u003e\u003cbr /\u003e\u003cbr /\u003e\u003c/li\u003e\r\n\r\n\r\n\u003cli\u003eWard, \u003ca href=\"#Page_180\"\u003e180\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eWeierstrass, \u003ca href=\"#Page_80\"\u003e80\u003c/a\u003e, \u003ca href=\"#Page_82\"\u003e82\u003c/a\u003e, \u003ca href=\"#Page_95\"\u003e95\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eWhitehead, \u003ca href=\"#Page_117\"\u003e117\u003c/a\u003e, \u003ca href=\"#Page_157\"\u003e157\u003c/a\u003e, \u003ca href=\"#Page_175\"\u003e175\u003c/a\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eWolf, \u003ca href=\"#Page_173\"\u003e173\u003c/a\u003e\u003cbr /\u003e\u003cbr /\u003e\u003c/li\u003e\r\n\r\n\r\n\u003cli\u003eZeno the Eleatic, \u003ca href=\"#Page_64\"\u003e64\u003c/a\u003e, \u003ca href=\"#Page_80\"\u003e80\u003c/a\u003e, \u003ca href=\"#Page_84\"\u003e84\u003c/a\u003e, \u003ca href=\"#Page_89\"\u003e89 ff\u003c/a\u003e\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\r\n\u003cbr /\u003e\r\n\u003chr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003cdiv class=\"img\"\u003e\r\n\u003cimg border=\"0\" src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-mysticism-and-logic-and-other-essays-deco.png\" width=\"15%\" alt=\"Publisher\u0027s mark\" /\u003e\r\n\u003c/div\u003e\r\n\r\n\u003ch4\u003eGEORGE ALLEN \u0026amp; UNWIN LTD\u003c/h4\u003e\r\n\r\n\u003ch4\u003e\u003ci\u003eLondon: 40 Museum Street, W.C. 1\u003c/i\u003e\u003c/h4\u003e\r\n\r\n\u003cp class=\"cen\"\u003e\u003ci\u003eAuckland: 24 Wyndham Street\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eBombay: 15 Graham Road, Ballard Estate, Bombay 1\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eCalcutta: 17 Chittaranjan Avenue, Calcutta 13\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eCape Town: 109 Long Street\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eKarachi: Metherson\u0027s Estate, Wood Street, Karachi 2\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eNew Delhi: 13-14 Ajmeri Gate Extension, New Delhi 1\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eS\u0026atilde;o Paulo: Avenida 9 de Julho 1138\u0026mdash;Ap. 51\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eSingapore, South East Asia and Far East, 36c, Prinsep Street\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eSydney, N.S.W.: Bradbury House, 55 York Street\u003c/i\u003e\u003cbr /\u003e\r\n\u003ci\u003eToronto: 91 Wellington Street West\u003c/i\u003e\u003c/p\u003e\r\n\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003cbr /\u003e\r\n\u003chr /\u003e\r\n\u003cbr /\u003e\r\n\r\n\u003cdiv class=\"tr\"\u003e\r\n\u003cp class=\"cen\"\u003e\u003ca name=\"TN\" id=\"TN\"\u003e\u003c/a\u003eTypographical errors corrected in text:\u003c/p\u003e\r\n\u003cbr /\u003e\r\nPage 111: \u0026nbsp;charateristic replaced with characteristic\u003cbr /\u003e\r\nPage \u0026nbsp;\u0026nbsp;71: \u0026nbsp;inexpugnable replaced with inexpungable\u003cbr /\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cbr /\u003e\r\n\u003chr /\u003e\r\n\u003cbr /\u003e\r\n\u003c/article\u003e"}],"SectionSequence":["Back Link","Work Title","Deck","Author","Period","Era","Composition","Date Note","Region","Terra Avita","Terra Avita Region","Modern Country","Original Title","Language","Primary Discipline","Secondary Discipline","Tradition","Full Versions","Core Thesis","Classification","Arguments","Influence","Significance","Evidence Note","Full Text"],"Counts":{"ContextCards":3,"GeoCards":4,"DisciplineCards":2,"Links":11,"Sections":25,"Styles":3,"Scripts":1}}