Posterior Analytics
{"WorkMasterId":4933,"WpPageId":243291,"ParentWpPageId":189130,"Slug":"posterior-analytics","Url":"https://chrisdeasy.com/theos/humanities/philosophy/philosophers/aristotle-of-stagira/posterior-analytics/","RelativeUrl":"theos/humanities/philosophy/philosophers/aristotle-of-stagira/posterior-analytics/","HasFullText":true,"RawHtmlLength":268435,"CleanHtmlLength":211094,"Kicker":"Philosophy Work","Title":"Posterior Analytics","Deck":"Defines scientific knowledge as demonstrative understanding from true, primary, immediate, better-known explanatory principles.","BackLink":{"Text":"Back to Aristotle","Url":"https://chrisdeasy.com/theos/humanities/philosophy/philosophers/aristotle-of-stagira/"},"AuthorCard":{"Label":"Author","Title":"Aristotle","Url":"https://chrisdeasy.com/theos/humanities/philosophy/philosophers/aristotle-of-stagira/","MediaHref":"","ImageSrc":"https://chrisdeasy.com/wp-content/uploads/aristotle-01-palazzo-altemps-bust-3.jpg","ImageAlt":"Aristotle Bust in the Palazzo Altemps","FilterTerra":"Eastern Mediterranean","ClickText":"Aristotle","ClickHref":"https://chrisdeasy.com/theos/humanities/philosophy/philosophers/aristotle-of-stagira/","Copies":["384 BCE – 322 BCE","Stagira, Chalcidice","Greek philosopher from Stagira, student of Plato, tutor of Alexander, and founder of the Lyceum whose logic, metaphysics, psychology, ethics, politics, rhetoric, poetics, biology, and philosophy of science shaped later philosophy."]},"ContextCards":[{"Label":"Period","Key":"Period:1","Title":"Ancient History","DateText":"3000 BCE – 499 CE","Url":"https://chrisdeasy.com/theos/humanities/philosophy/eras-of-thought/philosophers-of-ancient-history/"},{"Label":"Era","Key":"Era:3","Title":"Classical Antiquity","DateText":"500 BCE – 499 CE","Url":"https://chrisdeasy.com/theos/humanities/philosophy/eras-of-thought/philosophers-of-ancient-history/philosophers-of-classical-antiquity/"},{"Label":"Composition","Title":"349 BCE","Url":"","DateText":""}],"DateNote":"Proxy chronology year for ordering the Aristotelian core corpus; it is not a documented composition date, and several treatises are composite lecture materials revised across Aristotle\u0027s career.","GeoCards":[{"Label":"Region","Key":"Region:1"},{"Label":"Terra Avita","Key":"TerraAvita:2"},{"Label":"Terra Avita Region","Key":"TerraAvitaRegion:8"},{"Label":"Modern Country","Key":"Country:GRC:2"}],"OriginalTitle":"Ἀναλυτικὰ Ὕστερα","Language":"Ancient Greek","DisciplineCards":[{"Label":"Primary Discipline","Key":"Discipline:epistemology"},{"Label":"Secondary Discipline","Key":"Discipline:logic"}],"Tradition":"Aristotelian philosophy","FullText":{"Title":"Full Text","Copy":"Full text from MIT Internet Classics Archive: Posterior Analytics .","Url":"","Label":"","Kicker":"","Cards":[]},"CoreThesis":["Defines scientific knowledge as demonstrative understanding from true, primary, immediate, better-known explanatory principles."],"Classification":{"AlternateTitles":"Analytica Posteriora","KeyConcepts":"demonstration; science; first principles; explanation; knowledge","Methodology":"Aristotelian analysis, definition, division, dialectical testing, causal explanation, and ordered inquiry.","Structure":"Treatise or lecture-material text within the traditional Aristotelian corpus."},"Arguments":["Develops a focused part of Aristotle\u0027s system through distinctions, examples, aporiai, definitions, and explanatory principles."],"Influence":{"InfluencedBy":"Plato; Socrates; Presocratic natural philosophy; Greek mathematics, rhetoric, medicine, and biological observation.","InfluenceOn":""},"Significance":["Core text in the Aristotelian corpus and a major source for later ancient, medieval, and modern philosophy.","Still used in research on logic, metaphysics, ethics, politics, psychology, language, science, rhetoric, poetics, and intellectual history."],"EvidenceNote":["Accepted for this Core Corpus pass as an Aristotle-authored or standard Aristotelian corpus work. Fragment-only works, pseudo-Aristotle, source/testimony pages, and excluded disputed works remain evidence rows rather than work pages."],"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\"\u003eMIT Internet Classics Archive\u003c/p\u003e\n \u003ch3 class=\"dz-philo__full-version-title\"\u003ePosterior Analytics\u003c/h3\u003e\n \u003cp class=\"dz-philo__full-version-meta\"\u003eHtmlText · LinkOnlyReady\u003c/p\u003e\n \u003ca class=\"dz-philo__full-version-link\" href=\"https://classics.mit.edu/Aristotle/posterior.html\"\u003eOpen full version\u003c/a\u003e\n \u003c/article\u003e\n \u003c/div\u003e"},{"Kind":"TextSection","Title":"Core Thesis","Paragraphs":["Defines scientific knowledge as demonstrative understanding from true, primary, immediate, better-known explanatory principles."]},{"Kind":"FieldSection","Title":"Classification","Fields":[{"Label":"Alternate Titles","Value":"Analytica Posteriora"},{"Label":"Key Concepts","Value":"demonstration; science; first principles; explanation; knowledge"},{"Label":"Methodology","Value":"Aristotelian analysis, definition, division, dialectical testing, causal explanation, and ordered inquiry."},{"Label":"Structure","Value":"Treatise or lecture-material text within the traditional Aristotelian corpus."}]},{"Kind":"TextSection","Title":"Arguments","Paragraphs":["Develops a focused part of Aristotle\u0027s system through distinctions, examples, aporiai, definitions, and explanatory principles."]},{"Kind":"FieldSection","Title":"Influence","Fields":[{"Label":"Influenced By","Value":"Plato; Socrates; Presocratic natural philosophy; Greek mathematics, rhetoric, medicine, and biological observation."},{"Label":"Influence On","Value":"Peripatetic philosophy; late antique commentary; Islamic, Jewish, and Christian Aristotelianism; scholastic philosophy; modern philosophical vocabulary."}]},{"Kind":"TextSection","Title":"Significance","Paragraphs":["Core text in the Aristotelian corpus and a major source for later ancient, medieval, and modern philosophy.","Still used in research on logic, metaphysics, ethics, politics, psychology, language, science, rhetoric, poetics, and intellectual history."]},{"Kind":"TextSection","Title":"Evidence Note","Paragraphs":["Accepted for this Core Corpus pass as an Aristotle-authored or standard Aristotelian corpus work. Fragment-only works, pseudo-Aristotle, source/testimony pages, and excluded disputed works remain evidence rows rather than work pages."]},{"Kind":"RawSection","Title":"Full Text","BodyHtml":"\u003cp class=\"dz-philo__section-copy dz-philo__full-text-source\"\u003eFull text from \u003ca href=\"https://classics.mit.edu/Aristotle/posterior.html\"\u003eMIT Internet Classics Archive: Posterior Analytics\u003c/a\u003e.\u003c/p\u003e\n \u003carticle class=\"dz-philo__full-text-body\"\u003e\n\u003chr\u003e\r\n\u003cHTML\u003e\n\n\u003cHEAD\u003e\n \n \n\u003cLINK REV=\"made\" HREF=\"mailto:classics@classics.mit.edu\"\u003e\n\u003cLINK REV=\"owns\" HREF=\"mailto:classics@classics.mit.edu\"\u003e\n \n\n \n\u003cMETA HTTP-EQUIV=\"Set-Cookie\" CONTENT=\"ICA_last_work=Aristotle.posterior; expires=1-Jan-102 00:00:00 GMT; path=/\"\u003e\n\u003cMETA NAME=\"description\" CONTENT=\"Posterior Analytics by Aristotle, part of the Internet Classics Archive\"\u003e\n\u003cMETA NAME=\"keywords\" CONTENT=\"classical, literature, classics, ancient, civilization, books, great books, philosophy, history, Greek, Latin, Roman, Persian, Chinese, Greece, Rome, commentary, pictures, bookstore, CD-ROM, Posterior Analytics, Aristotle, Aristotle\"\u003e\n\u003cTITLE\u003eThe Internet Classics Archive | Posterior Analytics by Aristotle\u003c/TITLE\u003e\n\u003c/HEAD\u003e\n\n\u003cBODY BGCOLOR=\"FFFFCC\" LINK=\"990033\" VLINK=\"990033\" TEXT=\"000000\"\u003e\n\n\u003cTABLE BORDER=\"0\" CELLSPACING=\"15\"\u003e\n\u003cTR ALIGN=\"CENTER\" VALIGN=\"CENTER\"\u003e\n\u003cTD ALIGN=\"CENTER\" VALIGN=\"BOTTOM\" NOWRAP\u003e\u003ca href=\"/index.html\"Go to home page\u0027; return true;\" TARGET=\"_top\"\u003e \u003c/A\u003e\n\u003cFONT SIZE=\"-1\"\u003e\u003cBR\u003e\u003ca href=\"/index.html\"Go to home page\u0027; return true;\" TARGET=\"_top\"\u003eHome\u003c/A\u003e\u003cBR\u003e\u0026nbsp;\u003c/FONT\u003e\u003c/TD\u003e\n\n\u003cTD ALIGN=\"CENTER\" VALIGN=\"BOTTOM\" NOWRAP\u003e\u003ca href=\"/Browse/index-Aristotle.html\"Browse a list of titles\u0027; return true;\" TARGET=\"_top\"\u003e \u003c/A\u003e\n\u003cFONT SIZE=\"-1\"\u003e\u003cBR\u003e\u003ca href=\"/Browse/index-Aristotle.html\"Browse a list of titles\u0027; return true;\" TARGET=\"_top\"\u003eBrowse and\u003cBR\u003eComment\u003c/A\u003e\u003c/FONT\u003e\u003c/TD\u003e\n\n\u003cTD ALIGN=\"CENTER\" VALIGN=\"BOTTOM\" NOWRAP\u003e\u003ca href=\"/Search/index.html\"Search texts\u0027; return true;\" TARGET=\"_top\"\u003e \u003c/A\u003e\n\u003cFONT SIZE=\"-1\"\u003e\u003cBR\u003e\u003ca href=\"/Search/index.html\"Search texts\u0027; return true;\" TARGET=\"_top\"\u003eSearch\u003c/A\u003e\u003cBR\u003e\u0026nbsp;\u003c/FONT\u003e\u003c/TD\u003e\n\n\u003cTD ALIGN=\"CENTER\" VALIGN=\"BOTTOM\" NOWRAP\u003e\u003ca href=\"/Buy/Aristotle.html\"Buy books and CD-ROMs\u0027; return true;\" TARGET=\"_top\"\u003e \u003c/A\u003e\n\u003cFONT SIZE=\"-1\"\u003e\u003cBR\u003e\u003ca href=\"/Buy/Aristotle.html\"Buy books and CD-ROMs\u0027; return true;\" TARGET=\"_top\"\u003eBuy Books and\u003cBR\u003eCD-ROMs\u003c/A\u003e\u003c/FONT\u003e\u003c/TD\u003e\n\n\u003cTD ALIGN=\"CENTER\" VALIGN=\"BOTTOM\" NOWRAP\u003e\u003ca href=\"/Help/general.html\"Get help\u0027; return true;\" TARGET=\"_top\"\u003e \u003c/A\u003e\n\u003cFONT SIZE=\"-1\"\u003e\u003cBR\u003e\u003ca href=\"/Help/general.html\"Get help\u0027; return true;\" TARGET=\"_top\"\u003eHelp\u003c/A\u003e\u003cBR\u003e\u0026nbsp;\u003c/FONT\u003e\u003c/TD\u003e\n\n\u003c/TR\u003e\n\u003c/TABLE\u003e\n\n\u003cHR SIZE=\"1\" COLOR=\"990033\" NOSHADE WIDTH=\"30%\"\u003e\n\u003cBR\u003e\n\u003cFONT SIZE=\"+2\"\u003e\u003cB\u003ePosterior Analytics\u003c/B\u003e\u003c/FONT\u003e\n\u003cFONT SIZE=\"+1\"\u003e\u003cBR\u003e\u003cBR\u003eBy Aristotle\u003c/FONT\u003e\n\n\u003cBLOCKQUOTE\u003e\u003cB\u003eCommentary:\u003c/B\u003e A few comments have been posted about\n\u003cU\u003ePosterior Analytics\u003c/U\u003e.\n\n\u003cBR\u003e\u003cBR\u003e\u003cB\u003eDownload:\u003c/B\u003e A \ntext-only version is \u003cA HREF=\"posterior.mb.txt\"Download text-only version\u0027; return true;\"\u003eavailable for download\u003c/A\u003e.\n\n\u003cBR\u003e\u003cHR SIZE=\"1\" COLOR=\"990033\" NOSHADE\u003e\u003cBR\u003e\n\n\u003cA NAME=\"1\"\u003e\u003c/A\u003e\u003cFONT SIZE=\"+1\"\u003e\u003cB\u003ePosterior Analytics\u003c/B\u003e\u003c/FONT\u003e\n\u003cA NAME=\"2\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eBy Aristotle\n\u003cA NAME=\"3\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWritten 350 B.C.E\n\u003cBR\u003e\u003cBR\u003eTranslated by G. R. G. Mure\n\n\u003cBR\u003e\u003cTABLE WIDTH=\"60%\" BORDER=\"0\"\u003e\n\u003cTR VALIGN=\"TOP\"\u003e\n\u003cTD ALIGN=\"LEFT\" WIDTH=\"30%\" NOWRAP\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u003c/TD\u003e\n\u003cTD ALIGN=\"CENTER\" NOWRAP\u003e\u003cA HREF=\"posterior.html\"Go to table of contents\u0027; return true;\"\u003eTable of Contents\u003c/A\u003e\n\u003cBR\u003e\u003cBR\u003e\u003cFONT SIZE=\"+1\"\u003e\u003cB\u003eBook I\u003c/B\u003e\u003c/FONT\u003e\u003c/TD\u003e\n\u003cTD ALIGN=\"RIGHT\" WIDTH=\"30%\" NOWRAP\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u003cA HREF=\"posterior.2.ii.html\"Book II\u0027; return true;\"\u003e \u003c/A\u003e\n\n\u003c/TD\u003e\n\u003c/TR\u003e\n\u003c/TABLE\u003e\n\u003cBR\u003e\n\u003cA NAME=\"start\"\u003e\u003c/A\u003e\n\n\u003cA NAME=\"10\"\u003e\u003c/A\u003e\u003cB\u003ePart 1\u003c/B\u003e\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"11\"\u003e\u003c/A\u003eAll instruction given or received by way of argument proceeds from pre-existent \n\u003cA NAME=\"12\"\u003e\u003c/A\u003eknowledge. This becomes evident upon a survey of all the species of such \n\u003cA NAME=\"13\"\u003e\u003c/A\u003einstruction. The mathematical sciences and all other speculative disciplines \n\u003cA NAME=\"14\"\u003e\u003c/A\u003eare acquired in this way, and so are the two forms of dialectical reasoning, \n\u003cA NAME=\"15\"\u003e\u003c/A\u003esyllogistic and inductive; for each of these latter make use of old knowledge \n\u003cA NAME=\"16\"\u003e\u003c/A\u003eto impart new, the syllogism assuming an audience that accepts its premisses, \n\u003cA NAME=\"17\"\u003e\u003c/A\u003einduction exhibiting the universal as implicit in the clearly known particular. \n\u003cA NAME=\"18\"\u003e\u003c/A\u003eAgain, the persuasion exerted by rhetorical arguments is in principle the \n\u003cA NAME=\"19\"\u003e\u003c/A\u003esame, since they use either example, a kind of induction, or enthymeme, \n\u003cA NAME=\"20\"\u003e\u003c/A\u003ea form of syllogism.\n\u003cA NAME=\"21\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThe pre-existent knowledge required is of two kinds. In some cases \n\u003cA NAME=\"22\"\u003e\u003c/A\u003eadmission of the fact must be assumed, in others comprehension of the meaning \n\u003cA NAME=\"23\"\u003e\u003c/A\u003eof the term used, and sometimes both assumptions are essential. Thus, we \n\u003cA NAME=\"24\"\u003e\u003c/A\u003eassume that every predicate can be either truly affirmed or truly denied \n\u003cA NAME=\"25\"\u003e\u003c/A\u003eof any subject, and that \u0027triangle\u0027 means so and so; as regards \u0027unit\u0027 \n\u003cA NAME=\"26\"\u003e\u003c/A\u003ewe have to make the double assumption of the meaning of the word and the \n\u003cA NAME=\"27\"\u003e\u003c/A\u003eexistence of the thing. The reason is that these several objects are not \n\u003cA NAME=\"28\"\u003e\u003c/A\u003eequally obvious to us. Recognition of a truth may in some cases contain \n\u003cA NAME=\"29\"\u003e\u003c/A\u003eas factors both previous knowledge and also knowledge acquired simultaneously \n\u003cA NAME=\"30\"\u003e\u003c/A\u003ewith that recognition-knowledge, this latter, of the particulars actually \n\u003cA NAME=\"31\"\u003e\u003c/A\u003efalling under the universal and therein already virtually known. For example, \n\u003cA NAME=\"32\"\u003e\u003c/A\u003ethe student knew beforehand that the angles of every triangle are equal \n\u003cA NAME=\"33\"\u003e\u003c/A\u003eto two right angles; but it was only at the actual moment at which he was \n\u003cA NAME=\"34\"\u003e\u003c/A\u003ebeing led on to recognize this as true in the instance before him that \n\u003cA NAME=\"35\"\u003e\u003c/A\u003ehe came to know \u0027this figure inscribed in the semicircle\u0027 to be a triangle. \n\u003cA NAME=\"36\"\u003e\u003c/A\u003eFor some things (viz. the singulars finally reached which are not predicable \n\u003cA NAME=\"37\"\u003e\u003c/A\u003eof anything else as subject) are only learnt in this way, i.e. there is \n\u003cA NAME=\"38\"\u003e\u003c/A\u003ehere no recognition through a middle of a minor term as subject to a major. \n\u003cA NAME=\"39\"\u003e\u003c/A\u003eBefore he was led on to recognition or before he actually drew a conclusion, \n\u003cA NAME=\"40\"\u003e\u003c/A\u003ewe should perhaps say that in a manner he knew, in a manner \n\u003cA NAME=\"41\"\u003e\u003c/A\u003enot.\n\u003cA NAME=\"42\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIf he did not in an unqualified sense of the term know the existence \n\u003cA NAME=\"43\"\u003e\u003c/A\u003eof this triangle, how could he know without qualification that its angles \n\u003cA NAME=\"44\"\u003e\u003c/A\u003ewere equal to two right angles? No: clearly he knows not without qualification \n\u003cA NAME=\"45\"\u003e\u003c/A\u003ebut only in the sense that he knows universally. If this distinction is \n\u003cA NAME=\"46\"\u003e\u003c/A\u003enot drawn, we are faced with the dilemma in the Meno: either a man will \n\u003cA NAME=\"47\"\u003e\u003c/A\u003elearn nothing or what he already knows; for we cannot accept the solution \n\u003cA NAME=\"48\"\u003e\u003c/A\u003ewhich some people offer. A man is asked, \u0027Do you, or do you not, know that \n\u003cA NAME=\"49\"\u003e\u003c/A\u003eevery pair is even?\u0027 He says he does know it. The questioner then produces \n\u003cA NAME=\"50\"\u003e\u003c/A\u003ea particular pair, of the existence, and so a fortiori of the evenness, \n\u003cA NAME=\"51\"\u003e\u003c/A\u003eof which he was unaware. The solution which some people offer is to assert \n\u003cA NAME=\"52\"\u003e\u003c/A\u003ethat they do not know that every pair is even, but only that everything \n\u003cA NAME=\"53\"\u003e\u003c/A\u003ewhich they know to be a pair is even: yet what they know to be even is \n\u003cA NAME=\"54\"\u003e\u003c/A\u003ethat of which they have demonstrated evenness, i.e. what they made the \n\u003cA NAME=\"55\"\u003e\u003c/A\u003esubject of their premiss, viz. not merely every triangle or number which \n\u003cA NAME=\"56\"\u003e\u003c/A\u003ethey know to be such, but any and every number or triangle without reservation. \n\u003cA NAME=\"57\"\u003e\u003c/A\u003eFor no premiss is ever couched in the form \u0027every number which you know \n\u003cA NAME=\"58\"\u003e\u003c/A\u003eto be such\u0027, or \u0027every rectilinear figure which you know to be such\u0027: the \n\u003cA NAME=\"59\"\u003e\u003c/A\u003epredicate is always construed as applicable to any and every instance of \n\u003cA NAME=\"60\"\u003e\u003c/A\u003ethe thing. On the other hand, I imagine there is nothing to prevent a man \n\u003cA NAME=\"61\"\u003e\u003c/A\u003ein one sense knowing what he is learning, in another not knowing it. The \n\u003cA NAME=\"62\"\u003e\u003c/A\u003estrange thing would be, not if in some sense he knew what he was learning, \n\u003cA NAME=\"63\"\u003e\u003c/A\u003ebut if he were to know it in that precise sense and manner in which he \n\u003cA NAME=\"64\"\u003e\u003c/A\u003ewas learning it.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"65\"\u003e\u003c/A\u003e\u003cB\u003ePart 2\u003c/B\u003e\n\n\u003cA NAME=\"66\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWe suppose ourselves to possess unqualified scientific knowledge \n\u003cA NAME=\"67\"\u003e\u003c/A\u003eof a thing, as opposed to knowing it in the accidental way in which the \n\u003cA NAME=\"68\"\u003e\u003c/A\u003esophist knows, when we think that we know the cause on which the fact depends, \n\u003cA NAME=\"69\"\u003e\u003c/A\u003eas the cause of that fact and of no other, and, further, that the fact \n\u003cA NAME=\"70\"\u003e\u003c/A\u003ecould not be other than it is. Now that scientific knowing is something \n\u003cA NAME=\"71\"\u003e\u003c/A\u003eof this sort is evident-witness both those who falsely claim it and those \n\u003cA NAME=\"72\"\u003e\u003c/A\u003ewho actually possess it, since the former merely imagine themselves to \n\u003cA NAME=\"73\"\u003e\u003c/A\u003ebe, while the latter are also actually, in the condition described. Consequently \n\u003cA NAME=\"74\"\u003e\u003c/A\u003ethe proper object of unqualified scientific knowledge is something which \n\u003cA NAME=\"75\"\u003e\u003c/A\u003ecannot be other than it is.\n\u003cA NAME=\"76\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThere may be another manner of knowing as well-that will be discussed \n\u003cA NAME=\"77\"\u003e\u003c/A\u003elater. What I now assert is that at all events we do know by demonstration. \n\u003cA NAME=\"78\"\u003e\u003c/A\u003eBy demonstration I mean a syllogism productive of scientific knowledge, \n\u003cA NAME=\"79\"\u003e\u003c/A\u003ea syllogism, that is, the grasp of which is eo ipso such knowledge. Assuming \n\u003cA NAME=\"80\"\u003e\u003c/A\u003ethen that my thesis as to the nature of scientific knowing is correct, \n\u003cA NAME=\"81\"\u003e\u003c/A\u003ethe premisses of demonstrated knowledge must be true, primary, immediate, \n\u003cA NAME=\"82\"\u003e\u003c/A\u003ebetter known than and prior to the conclusion, which is further related \n\u003cA NAME=\"83\"\u003e\u003c/A\u003eto them as effect to cause. Unless these conditions are satisfied, the \n\u003cA NAME=\"84\"\u003e\u003c/A\u003ebasic truths will not be \u0027appropriate\u0027 to the conclusion. Syllogism there \n\u003cA NAME=\"85\"\u003e\u003c/A\u003emay indeed be without these conditions, but such syllogism, not being productive \n\u003cA NAME=\"86\"\u003e\u003c/A\u003eof scientific knowledge, will not be demonstration. The premisses must \n\u003cA NAME=\"87\"\u003e\u003c/A\u003ebe true: for that which is non-existent cannot be known-we cannot know, \n\u003cA NAME=\"88\"\u003e\u003c/A\u003ee.g. that the diagonal of a square is commensurate with its side. The premisses \n\u003cA NAME=\"89\"\u003e\u003c/A\u003emust be primary and indemonstrable; otherwise they will require demonstration \n\u003cA NAME=\"90\"\u003e\u003c/A\u003ein order to be known, since to have knowledge, if it be not accidental \n\u003cA NAME=\"91\"\u003e\u003c/A\u003eknowledge, of things which are demonstrable, means precisely to have a \n\u003cA NAME=\"92\"\u003e\u003c/A\u003edemonstration of them. The premisses must be the causes of the conclusion, \n\u003cA NAME=\"93\"\u003e\u003c/A\u003ebetter known than it, and prior to it; its causes, since we possess scientific \n\u003cA NAME=\"94\"\u003e\u003c/A\u003eknowledge of a thing only when we know its cause; prior, in order to be \n\u003cA NAME=\"95\"\u003e\u003c/A\u003ecauses; antecedently known, this antecedent knowledge being not our mere \n\u003cA NAME=\"96\"\u003e\u003c/A\u003eunderstanding of the meaning, but knowledge of the fact as well. Now \u0027prior\u0027 \n\u003cA NAME=\"97\"\u003e\u003c/A\u003eand \u0027better known\u0027 are ambiguous terms, for there is a difference between \n\u003cA NAME=\"98\"\u003e\u003c/A\u003ewhat is prior and better known in the order of being and what is prior \n\u003cA NAME=\"99\"\u003e\u003c/A\u003eand better known to man. I mean that objects nearer to sense are prior \n\u003cA NAME=\"100\"\u003e\u003c/A\u003eand better known to man; objects without qualification prior and better \n\u003cA NAME=\"101\"\u003e\u003c/A\u003eknown are those further from sense. Now the most universal causes are furthest \n\u003cA NAME=\"102\"\u003e\u003c/A\u003efrom sense and particular causes are nearest to sense, and they are thus \n\u003cA NAME=\"103\"\u003e\u003c/A\u003eexactly opposed to one another. In saying that the premisses of demonstrated \n\u003cA NAME=\"104\"\u003e\u003c/A\u003eknowledge must be primary, I mean that they must be the \u0027appropriate\u0027 basic \n\u003cA NAME=\"105\"\u003e\u003c/A\u003etruths, for I identify primary premiss and basic truth. A \u0027basic truth\u0027 \n\u003cA NAME=\"106\"\u003e\u003c/A\u003ein a demonstration is an immediate proposition. An immediate proposition \n\u003cA NAME=\"107\"\u003e\u003c/A\u003eis one which has no other proposition prior to it. A proposition is either \n\u003cA NAME=\"108\"\u003e\u003c/A\u003epart of an enunciation, i.e. it predicates a single attribute of a single \n\u003cA NAME=\"109\"\u003e\u003c/A\u003esubject. If a proposition is dialectical, it assumes either part indifferently; \n\u003cA NAME=\"110\"\u003e\u003c/A\u003eif it is demonstrative, it lays down one part to the definite exclusion \n\u003cA NAME=\"111\"\u003e\u003c/A\u003eof the other because that part is true. The term \u0027enunciation\u0027 denotes \n\u003cA NAME=\"112\"\u003e\u003c/A\u003eeither part of a contradiction indifferently. A contradiction is an opposition \n\u003cA NAME=\"113\"\u003e\u003c/A\u003ewhich of its own nature excludes a middle. The part of a contradiction \n\u003cA NAME=\"114\"\u003e\u003c/A\u003ewhich conjoins a predicate with a subject is an affirmation; the part disjoining \n\u003cA NAME=\"115\"\u003e\u003c/A\u003ethem is a negation. I call an immediate basic truth of syllogism a \u0027thesis\u0027 \n\u003cA NAME=\"116\"\u003e\u003c/A\u003ewhen, though it is not susceptible of proof by the teacher, yet ignorance \n\u003cA NAME=\"117\"\u003e\u003c/A\u003eof it does not constitute a total bar to progress on the part of the pupil: \n\u003cA NAME=\"118\"\u003e\u003c/A\u003eone which the pupil must know if he is to learn anything whatever is an \n\u003cA NAME=\"119\"\u003e\u003c/A\u003eaxiom. I call it an axiom because there are such truths and we give them \n\u003cA NAME=\"120\"\u003e\u003c/A\u003ethe name of axioms par excellence. If a thesis assumes one part or the \n\u003cA NAME=\"121\"\u003e\u003c/A\u003eother of an enunciation, i.e. asserts either the existence or the non-existence \n\u003cA NAME=\"122\"\u003e\u003c/A\u003eof a subject, it is a hypothesis; if it does not so assert, it is a definition. \n\u003cA NAME=\"123\"\u003e\u003c/A\u003eDefinition is a \u0027thesis\u0027 or a \u0027laying something down\u0027, since the arithmetician \n\u003cA NAME=\"124\"\u003e\u003c/A\u003elays it down that to be a unit is to be quantitatively indivisible; but \n\u003cA NAME=\"125\"\u003e\u003c/A\u003eit is not a hypothesis, for to define what a unit is is not the same as \n\u003cA NAME=\"126\"\u003e\u003c/A\u003eto affirm its existence.\n\u003cA NAME=\"127\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eNow since the required ground of our knowledge-i.e. of our conviction-of \n\u003cA NAME=\"128\"\u003e\u003c/A\u003ea fact is the possession of such a syllogism as we call demonstration, \n\u003cA NAME=\"129\"\u003e\u003c/A\u003eand the ground of the syllogism is the facts constituting its premisses, \n\u003cA NAME=\"130\"\u003e\u003c/A\u003ewe must not only know the primary premisses-some if not all of them-beforehand, \n\u003cA NAME=\"131\"\u003e\u003c/A\u003ebut know them better than the conclusion: for the cause of an attribute\u0027s \n\u003cA NAME=\"132\"\u003e\u003c/A\u003einherence in a subject always itself inheres in the subject more firmly \n\u003cA NAME=\"133\"\u003e\u003c/A\u003ethan that attribute; e.g. the cause of our loving anything is dearer to \n\u003cA NAME=\"134\"\u003e\u003c/A\u003eus than the object of our love. So since the primary premisses are the \n\u003cA NAME=\"135\"\u003e\u003c/A\u003ecause of our knowledge-i.e. of our conviction-it follows that we know them \n\u003cA NAME=\"136\"\u003e\u003c/A\u003ebetter-that is, are more convinced of them-than their consequences, precisely \n\u003cA NAME=\"137\"\u003e\u003c/A\u003ebecause of our knowledge of the latter is the effect of our knowledge of \n\u003cA NAME=\"138\"\u003e\u003c/A\u003ethe premisses. Now a man cannot believe in anything more than in the things \n\u003cA NAME=\"139\"\u003e\u003c/A\u003ehe knows, unless he has either actual knowledge of it or something better \n\u003cA NAME=\"140\"\u003e\u003c/A\u003ethan actual knowledge. But we are faced with this paradox if a student \n\u003cA NAME=\"141\"\u003e\u003c/A\u003ewhose belief rests on demonstration has not prior knowledge; a man must \n\u003cA NAME=\"142\"\u003e\u003c/A\u003ebelieve in some, if not in all, of the basic truths more than in the conclusion. \n\u003cA NAME=\"143\"\u003e\u003c/A\u003eMoreover, if a man sets out to acquire the scientific knowledge that comes \n\u003cA NAME=\"144\"\u003e\u003c/A\u003ethrough demonstration, he must not only have a better knowledge of the \n\u003cA NAME=\"145\"\u003e\u003c/A\u003ebasic truths and a firmer conviction of them than of the connexion which \n\u003cA NAME=\"146\"\u003e\u003c/A\u003eis being demonstrated: more than this, nothing must be more certain or \n\u003cA NAME=\"147\"\u003e\u003c/A\u003ebetter known to him than these basic truths in their character as contradicting \n\u003cA NAME=\"148\"\u003e\u003c/A\u003ethe fundamental premisses which lead to the opposed and erroneous conclusion. \n\u003cA NAME=\"149\"\u003e\u003c/A\u003eFor indeed the conviction of pure science must be unshakable.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"150\"\u003e\u003c/A\u003e\u003cB\u003ePart 3\u003c/B\u003e\n\n\u003cA NAME=\"151\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eSome hold that, owing to the necessity of knowing the primary premisses, \n\u003cA NAME=\"152\"\u003e\u003c/A\u003ethere is no scientific knowledge. Others think there is, but that all truths \n\u003cA NAME=\"153\"\u003e\u003c/A\u003eare demonstrable. Neither doctrine is either true or a necessary deduction \n\u003cA NAME=\"154\"\u003e\u003c/A\u003efrom the premisses. The first school, assuming that there is no way of \n\u003cA NAME=\"155\"\u003e\u003c/A\u003eknowing other than by demonstration, maintain that an infinite regress \n\u003cA NAME=\"156\"\u003e\u003c/A\u003eis involved, on the ground that if behind the prior stands no primary, \n\u003cA NAME=\"157\"\u003e\u003c/A\u003ewe could not know the posterior through the prior (wherein they are right, \n\u003cA NAME=\"158\"\u003e\u003c/A\u003efor one cannot traverse an infinite series): if on the other hand-they \n\u003cA NAME=\"159\"\u003e\u003c/A\u003esay-the series terminates and there are primary premisses, yet these are \n\u003cA NAME=\"160\"\u003e\u003c/A\u003eunknowable because incapable of demonstration, which according to them \n\u003cA NAME=\"161\"\u003e\u003c/A\u003eis the only form of knowledge. And since thus one cannot know the primary \n\u003cA NAME=\"162\"\u003e\u003c/A\u003epremisses, knowledge of the conclusions which follow from them is not pure \n\u003cA NAME=\"163\"\u003e\u003c/A\u003escientific knowledge nor properly knowing at all, but rests on the mere \n\u003cA NAME=\"164\"\u003e\u003c/A\u003esupposition that the premisses are true. The other party agree with them \n\u003cA NAME=\"165\"\u003e\u003c/A\u003eas regards knowing, holding that it is only possible by demonstration, \n\u003cA NAME=\"166\"\u003e\u003c/A\u003ebut they see no difficulty in holding that all truths are demonstrated, \n\u003cA NAME=\"167\"\u003e\u003c/A\u003eon the ground that demonstration may be circular and \n\u003cA NAME=\"168\"\u003e\u003c/A\u003ereciprocal.\n\u003cA NAME=\"169\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eOur own doctrine is that not all knowledge is demonstrative: on \n\u003cA NAME=\"170\"\u003e\u003c/A\u003ethe contrary, knowledge of the immediate premisses is independent of demonstration. \n\u003cA NAME=\"171\"\u003e\u003c/A\u003e(The necessity of this is obvious; for since we must know the prior premisses \n\u003cA NAME=\"172\"\u003e\u003c/A\u003efrom which the demonstration is drawn, and since the regress must end in \n\u003cA NAME=\"173\"\u003e\u003c/A\u003eimmediate truths, those truths must be indemonstrable.) Such, then, is \n\u003cA NAME=\"174\"\u003e\u003c/A\u003eour doctrine, and in addition we maintain that besides scientific knowledge \n\u003cA NAME=\"175\"\u003e\u003c/A\u003ethere is its originative source which enables us to recognize the \n\u003cA NAME=\"176\"\u003e\u003c/A\u003edefinitions.\n\u003cA NAME=\"177\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eNow demonstration must be based on premisses prior to and better \n\u003cA NAME=\"178\"\u003e\u003c/A\u003eknown than the conclusion; and the same things cannot simultaneously be \n\u003cA NAME=\"179\"\u003e\u003c/A\u003eboth prior and posterior to one another: so circular demonstration is clearly \n\u003cA NAME=\"180\"\u003e\u003c/A\u003enot possible in the unqualified sense of \u0027demonstration\u0027, but only possible \n\u003cA NAME=\"181\"\u003e\u003c/A\u003eif \u0027demonstration\u0027 be extended to include that other method of argument \n\u003cA NAME=\"182\"\u003e\u003c/A\u003ewhich rests on a distinction between truths prior to us and truths without \n\u003cA NAME=\"183\"\u003e\u003c/A\u003equalification prior, i.e. the method by which induction produces knowledge. \n\u003cA NAME=\"184\"\u003e\u003c/A\u003eBut if we accept this extension of its meaning, our definition of unqualified \n\u003cA NAME=\"185\"\u003e\u003c/A\u003eknowledge will prove faulty; for there seem to be two kinds of it. Perhaps, \n\u003cA NAME=\"186\"\u003e\u003c/A\u003ehowever, the second form of demonstration, that which proceeds from truths \n\u003cA NAME=\"187\"\u003e\u003c/A\u003ebetter known to us, is not demonstration in the unqualified sense of the \n\u003cA NAME=\"188\"\u003e\u003c/A\u003eterm.\n\u003cA NAME=\"189\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThe advocates of circular demonstration are not only faced with \n\u003cA NAME=\"190\"\u003e\u003c/A\u003ethe difficulty we have just stated: in addition their theory reduces to \n\u003cA NAME=\"191\"\u003e\u003c/A\u003ethe mere statement that if a thing exists, then it does exist-an easy way \n\u003cA NAME=\"192\"\u003e\u003c/A\u003eof proving anything. That this is so can be clearly shown by taking three \n\u003cA NAME=\"193\"\u003e\u003c/A\u003eterms, for to constitute the circle it makes no difference whether many \n\u003cA NAME=\"194\"\u003e\u003c/A\u003eterms or few or even only two are taken. Thus by direct proof, if A is, \n\u003cA NAME=\"195\"\u003e\u003c/A\u003eB must be; if B is, C must be; therefore if A is, C must be. Since then-by \n\u003cA NAME=\"196\"\u003e\u003c/A\u003ethe circular proof-if A is, B must be, and if B is, A must be, A may be \n\u003cA NAME=\"197\"\u003e\u003c/A\u003esubstituted for C above. Then \u0027if B is, A must be\u0027=\u0027if B is, C must be\u0027, \n\u003cA NAME=\"198\"\u003e\u003c/A\u003ewhich above gave the conclusion \u0027if A is, C must be\u0027: but C and A have \n\u003cA NAME=\"199\"\u003e\u003c/A\u003ebeen identified. Consequently the upholders of circular demonstration are \n\u003cA NAME=\"200\"\u003e\u003c/A\u003ein the position of saying that if A is, A must be-a simple way of proving \n\u003cA NAME=\"201\"\u003e\u003c/A\u003eanything. Moreover, even such circular demonstration is impossible except \n\u003cA NAME=\"202\"\u003e\u003c/A\u003ein the case of attributes that imply one another, viz. \u0027peculiar\u0027 \n\u003cA NAME=\"203\"\u003e\u003c/A\u003eproperties.\n\u003cA NAME=\"204\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eNow, it has been shown that the positing of one thing-be it one \n\u003cA NAME=\"205\"\u003e\u003c/A\u003eterm or one premiss-never involves a necessary consequent: two premisses \n\u003cA NAME=\"206\"\u003e\u003c/A\u003econstitute the first and smallest foundation for drawing a conclusion at \n\u003cA NAME=\"207\"\u003e\u003c/A\u003eall and therefore a fortiori for the demonstrative syllogism of science. \n\u003cA NAME=\"208\"\u003e\u003c/A\u003eIf, then, A is implied in B and C, and B and C are reciprocally implied \n\u003cA NAME=\"209\"\u003e\u003c/A\u003ein one another and in A, it is possible, as has been shown in my writings \n\u003cA NAME=\"210\"\u003e\u003c/A\u003eon the syllogism, to prove all the assumptions on which the original conclusion \n\u003cA NAME=\"211\"\u003e\u003c/A\u003erested, by circular demonstration in the first figure. But it has also \n\u003cA NAME=\"212\"\u003e\u003c/A\u003ebeen shown that in the other figures either no conclusion is possible, \n\u003cA NAME=\"213\"\u003e\u003c/A\u003eor at least none which proves both the original premisses. Propositions \n\u003cA NAME=\"214\"\u003e\u003c/A\u003ethe terms of which are not convertible cannot be circularly demonstrated \n\u003cA NAME=\"215\"\u003e\u003c/A\u003eat all, and since convertible terms occur rarely in actual demonstrations, \n\u003cA NAME=\"216\"\u003e\u003c/A\u003eit is clearly frivolous and impossible to say that demonstration is reciprocal \n\u003cA NAME=\"217\"\u003e\u003c/A\u003eand that therefore everything can be demonstrated.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"218\"\u003e\u003c/A\u003e\u003cB\u003ePart 4\u003c/B\u003e\n\n\u003cA NAME=\"219\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eSince the object of pure scientific knowledge cannot be other than \n\u003cA NAME=\"220\"\u003e\u003c/A\u003eit is, the truth obtained by demonstrative knowledge will be necessary. \n\u003cA NAME=\"221\"\u003e\u003c/A\u003eAnd since demonstrative knowledge is only present when we have a demonstration, \n\u003cA NAME=\"222\"\u003e\u003c/A\u003eit follows that demonstration is an inference from necessary premisses. \n\u003cA NAME=\"223\"\u003e\u003c/A\u003eSo we must consider what are the premisses of demonstration-i.e. what is \n\u003cA NAME=\"224\"\u003e\u003c/A\u003etheir character: and as a preliminary, let us define what we mean by an \n\u003cA NAME=\"225\"\u003e\u003c/A\u003eattribute \u0027true in every instance of its subject\u0027, an \u0027essential\u0027 attribute, \n\u003cA NAME=\"226\"\u003e\u003c/A\u003eand a \u0027commensurate and universal\u0027 attribute. I call \u0027true in every instance\u0027 \n\u003cA NAME=\"227\"\u003e\u003c/A\u003ewhat is truly predicable of all instances-not of one to the exclusion of \n\u003cA NAME=\"228\"\u003e\u003c/A\u003eothers-and at all times, not at this or that time only; e.g. if animal \n\u003cA NAME=\"229\"\u003e\u003c/A\u003eis truly predicable of every instance of man, then if it be true to say \n\u003cA NAME=\"230\"\u003e\u003c/A\u003e\u0027this is a man\u0027, \u0027this is an animal\u0027 is also true, and if the one be true \n\u003cA NAME=\"231\"\u003e\u003c/A\u003enow the other is true now. A corresponding account holds if point is in \n\u003cA NAME=\"232\"\u003e\u003c/A\u003eevery instance predicable as contained in line. There is evidence for this \n\u003cA NAME=\"233\"\u003e\u003c/A\u003ein the fact that the objection we raise against a proposition put to us \n\u003cA NAME=\"234\"\u003e\u003c/A\u003eas true in every instance is either an instance in which, or an occasion \n\u003cA NAME=\"235\"\u003e\u003c/A\u003eon which, it is not true. Essential attributes are (1) such as belong to \n\u003cA NAME=\"236\"\u003e\u003c/A\u003etheir subject as elements in its essential nature (e.g. line thus belongs \n\u003cA NAME=\"237\"\u003e\u003c/A\u003eto triangle, point to line; for the very being or \u0027substance\u0027 of triangle \n\u003cA NAME=\"238\"\u003e\u003c/A\u003eand line is composed of these elements, which are contained in the formulae \n\u003cA NAME=\"239\"\u003e\u003c/A\u003edefining triangle and line): (2) such that, while they belong to certain \n\u003cA NAME=\"240\"\u003e\u003c/A\u003esubjects, the subjects to which they belong are contained in the attribute\u0027s \n\u003cA NAME=\"241\"\u003e\u003c/A\u003eown defining formula. Thus straight and curved belong to line, odd and \n\u003cA NAME=\"242\"\u003e\u003c/A\u003eeven, prime and compound, square and oblong, to number; and also the formula \n\u003cA NAME=\"243\"\u003e\u003c/A\u003edefining any one of these attributes contains its subject-e.g. line or \n\u003cA NAME=\"244\"\u003e\u003c/A\u003enumber as the case may be.\n\u003cA NAME=\"245\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eExtending this classification to all other attributes, I distinguish \n\u003cA NAME=\"246\"\u003e\u003c/A\u003ethose that answer the above description as belonging essentially to their \n\u003cA NAME=\"247\"\u003e\u003c/A\u003erespective subjects; whereas attributes related in neither of these two \n\u003cA NAME=\"248\"\u003e\u003c/A\u003eways to their subjects I call accidents or \u0027coincidents\u0027; e.g. musical \n\u003cA NAME=\"249\"\u003e\u003c/A\u003eor white is a \u0027coincident\u0027 of animal.\n\u003cA NAME=\"250\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eFurther (a) that is essential which is not predicated of a subject \n\u003cA NAME=\"251\"\u003e\u003c/A\u003eother than itself: e.g. \u0027the walking [thing]\u0027 walks and is white in virtue \n\u003cA NAME=\"252\"\u003e\u003c/A\u003eof being something else besides; whereas substance, in the sense of whatever \n\u003cA NAME=\"253\"\u003e\u003c/A\u003esignifies a \u0027this somewhat\u0027, is not what it is in virtue of being something \n\u003cA NAME=\"254\"\u003e\u003c/A\u003eelse besides. Things, then, not predicated of a subject I call essential; \n\u003cA NAME=\"255\"\u003e\u003c/A\u003ethings predicated of a subject I call accidental or \n\u003cA NAME=\"256\"\u003e\u003c/A\u003e\u0027coincidental\u0027.\n\u003cA NAME=\"257\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIn another sense again (b) a thing consequentially connected with \n\u003cA NAME=\"258\"\u003e\u003c/A\u003eanything is essential; one not so connected is \u0027coincidental\u0027. An example \n\u003cA NAME=\"259\"\u003e\u003c/A\u003eof the latter is \u0027While he was walking it lightened\u0027: the lightning was \n\u003cA NAME=\"260\"\u003e\u003c/A\u003enot due to his walking; it was, we should say, a coincidence. If, on the \n\u003cA NAME=\"261\"\u003e\u003c/A\u003eother hand, there is a consequential connexion, the predication is essential; \n\u003cA NAME=\"262\"\u003e\u003c/A\u003ee.g. if a beast dies when its throat is being cut, then its death is also \n\u003cA NAME=\"263\"\u003e\u003c/A\u003eessentially connected with the cutting, because the cutting was the cause \n\u003cA NAME=\"264\"\u003e\u003c/A\u003eof death, not death a \u0027coincident\u0027 of the cutting.\n\u003cA NAME=\"265\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eSo far then as concerns the sphere of connexions scientifically \n\u003cA NAME=\"266\"\u003e\u003c/A\u003eknown in the unqualified sense of that term, all attributes which (within \n\u003cA NAME=\"267\"\u003e\u003c/A\u003ethat sphere) are essential either in the sense that their subjects are \n\u003cA NAME=\"268\"\u003e\u003c/A\u003econtained in them, or in the sense that they are contained in their subjects, \n\u003cA NAME=\"269\"\u003e\u003c/A\u003eare necessary as well as consequentially connected with their subjects. \n\u003cA NAME=\"270\"\u003e\u003c/A\u003eFor it is impossible for them not to inhere in their subjects either simply \n\u003cA NAME=\"271\"\u003e\u003c/A\u003eor in the qualified sense that one or other of a pair of opposites must \n\u003cA NAME=\"272\"\u003e\u003c/A\u003einhere in the subject; e.g. in line must be either straightness or curvature, \n\u003cA NAME=\"273\"\u003e\u003c/A\u003ein number either oddness or evenness. For within a single identical genus \n\u003cA NAME=\"274\"\u003e\u003c/A\u003ethe contrary of a given attribute is either its privative or its contradictory; \n\u003cA NAME=\"275\"\u003e\u003c/A\u003ee.g. within number what is not odd is even, inasmuch as within this sphere \n\u003cA NAME=\"276\"\u003e\u003c/A\u003eeven is a necessary consequent of not-odd. So, since any given predicate \n\u003cA NAME=\"277\"\u003e\u003c/A\u003emust be either affirmed or denied of any subject, essential attributes \n\u003cA NAME=\"278\"\u003e\u003c/A\u003emust inhere in their subjects of necessity.\n\u003cA NAME=\"279\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThus, then, we have established the distinction between the attribute \n\u003cA NAME=\"280\"\u003e\u003c/A\u003ewhich is \u0027true in every instance\u0027 and the \u0027essential\u0027 \n\u003cA NAME=\"281\"\u003e\u003c/A\u003eattribute.\n\u003cA NAME=\"282\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eI term \u0027commensurately universal\u0027 an attribute which belongs to \n\u003cA NAME=\"283\"\u003e\u003c/A\u003eevery instance of its subject, and to every instance essentially and as \n\u003cA NAME=\"284\"\u003e\u003c/A\u003esuch; from which it clearly follows that all commensurate universals inhere \n\u003cA NAME=\"285\"\u003e\u003c/A\u003enecessarily in their subjects. The essential attribute, and the attribute \n\u003cA NAME=\"286\"\u003e\u003c/A\u003ethat belongs to its subject as such, are identical. E.g. point and straight \n\u003cA NAME=\"287\"\u003e\u003c/A\u003ebelong to line essentially, for they belong to line as such; and triangle \n\u003cA NAME=\"288\"\u003e\u003c/A\u003eas such has two right angles, for it is essentially equal to two right \n\u003cA NAME=\"289\"\u003e\u003c/A\u003eangles.\n\u003cA NAME=\"290\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eAn attribute belongs commensurately and universally to a subject \n\u003cA NAME=\"291\"\u003e\u003c/A\u003ewhen it can be shown to belong to any random instance of that subject and \n\u003cA NAME=\"292\"\u003e\u003c/A\u003ewhen the subject is the first thing to which it can be shown to belong. \n\u003cA NAME=\"293\"\u003e\u003c/A\u003eThus, e.g. (1) the equality of its angles to two right angles is not a \n\u003cA NAME=\"294\"\u003e\u003c/A\u003ecommensurately universal attribute of figure. For though it is possible \n\u003cA NAME=\"295\"\u003e\u003c/A\u003eto show that a figure has its angles equal to two right angles, this attribute \n\u003cA NAME=\"296\"\u003e\u003c/A\u003ecannot be demonstrated of any figure selected at haphazard, nor in demonstrating \n\u003cA NAME=\"297\"\u003e\u003c/A\u003edoes one take a figure at random-a square is a figure but its angles are \n\u003cA NAME=\"298\"\u003e\u003c/A\u003enot equal to two right angles. On the other hand, any isosceles triangle \n\u003cA NAME=\"299\"\u003e\u003c/A\u003ehas its angles equal to two right angles, yet isosceles triangle is not \n\u003cA NAME=\"300\"\u003e\u003c/A\u003ethe primary subject of this attribute but triangle is prior. So whatever \n\u003cA NAME=\"301\"\u003e\u003c/A\u003ecan be shown to have its angles equal to two right angles, or to possess \n\u003cA NAME=\"302\"\u003e\u003c/A\u003eany other attribute, in any random instance of itself and primarily-that \n\u003cA NAME=\"303\"\u003e\u003c/A\u003eis the first subject to which the predicate in question belongs commensurately \n\u003cA NAME=\"304\"\u003e\u003c/A\u003eand universally, and the demonstration, in the essential sense, of any \n\u003cA NAME=\"305\"\u003e\u003c/A\u003epredicate is the proof of it as belonging to this first subject commensurately \n\u003cA NAME=\"306\"\u003e\u003c/A\u003eand universally: while the proof of it as belonging to the other subjects \n\u003cA NAME=\"307\"\u003e\u003c/A\u003eto which it attaches is demonstration only in a secondary and unessential \n\u003cA NAME=\"308\"\u003e\u003c/A\u003esense. Nor again (2) is equality to two right angles a commensurately universal \n\u003cA NAME=\"309\"\u003e\u003c/A\u003eattribute of isosceles; it is of wider application.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"310\"\u003e\u003c/A\u003e\u003cB\u003ePart 5\u003c/B\u003e\n\n\u003cA NAME=\"311\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWe must not fail to observe that we often fall into error because \n\u003cA NAME=\"312\"\u003e\u003c/A\u003eour conclusion is not in fact primary and commensurately universal in the \n\u003cA NAME=\"313\"\u003e\u003c/A\u003esense in which we think we prove it so. We make this mistake (1) when the \n\u003cA NAME=\"314\"\u003e\u003c/A\u003esubject is an individual or individuals above which there is no universal \n\u003cA NAME=\"315\"\u003e\u003c/A\u003eto be found: (2) when the subjects belong to different species and there \n\u003cA NAME=\"316\"\u003e\u003c/A\u003eis a higher universal, but it has no name: (3) when the subject which the \n\u003cA NAME=\"317\"\u003e\u003c/A\u003edemonstrator takes as a whole is really only a part of a larger whole; \n\u003cA NAME=\"318\"\u003e\u003c/A\u003efor then the demonstration will be true of the individual instances within \n\u003cA NAME=\"319\"\u003e\u003c/A\u003ethe part and will hold in every instance of it, yet the demonstration will \n\u003cA NAME=\"320\"\u003e\u003c/A\u003enot be true of this subject primarily and commensurately and universally. \n\u003cA NAME=\"321\"\u003e\u003c/A\u003eWhen a demonstration is true of a subject primarily and commensurately \n\u003cA NAME=\"322\"\u003e\u003c/A\u003eand universally, that is to be taken to mean that it is true of a given \n\u003cA NAME=\"323\"\u003e\u003c/A\u003esubject primarily and as such. Case (3) may be thus exemplified. If a proof \n\u003cA NAME=\"324\"\u003e\u003c/A\u003ewere given that perpendiculars to the same line are parallel, it might \n\u003cA NAME=\"325\"\u003e\u003c/A\u003ebe supposed that lines thus perpendicular were the proper subject of the \n\u003cA NAME=\"326\"\u003e\u003c/A\u003edemonstration because being parallel is true of every instance of them. \n\u003cA NAME=\"327\"\u003e\u003c/A\u003eBut it is not so, for the parallelism depends not on these angles being \n\u003cA NAME=\"328\"\u003e\u003c/A\u003eequal to one another because each is a right angle, but simply on their \n\u003cA NAME=\"329\"\u003e\u003c/A\u003ebeing equal to one another. An example of (1) would be as follows: if isosceles \n\u003cA NAME=\"330\"\u003e\u003c/A\u003ewere the only triangle, it would be thought to have its angles equal to \n\u003cA NAME=\"331\"\u003e\u003c/A\u003etwo right angles qua isosceles. An instance of (2) would be the law that \n\u003cA NAME=\"332\"\u003e\u003c/A\u003eproportionals alternate. Alternation used to be demonstrated separately \n\u003cA NAME=\"333\"\u003e\u003c/A\u003eof numbers, lines, solids, and durations, though it could have been proved \n\u003cA NAME=\"334\"\u003e\u003c/A\u003eof them all by a single demonstration. Because there was no single name \n\u003cA NAME=\"335\"\u003e\u003c/A\u003eto denote that in which numbers, lengths, durations, and solids are identical, \n\u003cA NAME=\"336\"\u003e\u003c/A\u003eand because they differed specifically from one another, this property \n\u003cA NAME=\"337\"\u003e\u003c/A\u003ewas proved of each of them separately. To-day, however, the proof is commensurately \n\u003cA NAME=\"338\"\u003e\u003c/A\u003euniversal, for they do not possess this attribute qua lines or qua numbers, \n\u003cA NAME=\"339\"\u003e\u003c/A\u003ebut qua manifesting this generic character which they are postulated as \n\u003cA NAME=\"340\"\u003e\u003c/A\u003epossessing universally. Hence, even if one prove of each kind of triangle \n\u003cA NAME=\"341\"\u003e\u003c/A\u003ethat its angles are equal to two right angles, whether by means of the \n\u003cA NAME=\"342\"\u003e\u003c/A\u003esame or different proofs; still, as long as one treats separately equilateral, \n\u003cA NAME=\"343\"\u003e\u003c/A\u003escalene, and isosceles, one does not yet know, except sophistically, that \n\u003cA NAME=\"344\"\u003e\u003c/A\u003etriangle has its angles equal to two right angles, nor does one yet know \n\u003cA NAME=\"345\"\u003e\u003c/A\u003ethat triangle has this property commensurately and universally, even if \n\u003cA NAME=\"346\"\u003e\u003c/A\u003ethere is no other species of triangle but these. For one does not know \n\u003cA NAME=\"347\"\u003e\u003c/A\u003ethat triangle as such has this property, nor even that \u0027all\u0027 triangles \n\u003cA NAME=\"348\"\u003e\u003c/A\u003ehave it-unless \u0027all\u0027 means \u0027each taken singly\u0027: if \u0027all\u0027 means \u0027as a whole \n\u003cA NAME=\"349\"\u003e\u003c/A\u003eclass\u0027, then, though there be none in which one does not recognize this \n\u003cA NAME=\"350\"\u003e\u003c/A\u003eproperty, one does not know it of \u0027all triangles\u0027.\n\u003cA NAME=\"351\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWhen, then, does our knowledge fail of commensurate universality, \n\u003cA NAME=\"352\"\u003e\u003c/A\u003eand when it is unqualified knowledge? If triangle be identical in essence \n\u003cA NAME=\"353\"\u003e\u003c/A\u003ewith equilateral, i.e. with each or all equilaterals, then clearly we have \n\u003cA NAME=\"354\"\u003e\u003c/A\u003eunqualified knowledge: if on the other hand it be not, and the attribute \n\u003cA NAME=\"355\"\u003e\u003c/A\u003ebelongs to equilateral qua triangle; then our knowledge fails of commensurate \n\u003cA NAME=\"356\"\u003e\u003c/A\u003euniversality. \u0027But\u0027, it will be asked, \u0027does this attribute belong to the \n\u003cA NAME=\"357\"\u003e\u003c/A\u003esubject of which it has been demonstrated qua triangle or qua isosceles? \n\u003cA NAME=\"358\"\u003e\u003c/A\u003eWhat is the point at which the subject. to which it belongs is primary? \n\u003cA NAME=\"359\"\u003e\u003c/A\u003e(i.e. to what subject can it be demonstrated as belonging commensurately \n\u003cA NAME=\"360\"\u003e\u003c/A\u003eand universally?)\u0027 Clearly this point is the first term in which it is \n\u003cA NAME=\"361\"\u003e\u003c/A\u003efound to inhere as the elimination of inferior differentiae proceeds. Thus \n\u003cA NAME=\"362\"\u003e\u003c/A\u003ethe angles of a brazen isosceles triangle are equal to two right angles: \n\u003cA NAME=\"363\"\u003e\u003c/A\u003ebut eliminate brazen and isosceles and the attribute remains. \u0027But\u0027-you \n\u003cA NAME=\"364\"\u003e\u003c/A\u003emay say-\u0027eliminate figure or limit, and the attribute vanishes.\u0027 True, \n\u003cA NAME=\"365\"\u003e\u003c/A\u003ebut figure and limit are not the first differentiae whose elimination destroys \n\u003cA NAME=\"366\"\u003e\u003c/A\u003ethe attribute. \u0027Then what is the first?\u0027 If it is triangle, it will be \n\u003cA NAME=\"367\"\u003e\u003c/A\u003ein virtue of triangle that the attribute belongs to all the other subjects \n\u003cA NAME=\"368\"\u003e\u003c/A\u003eof which it is predicable, and triangle is the subject to which it can \n\u003cA NAME=\"369\"\u003e\u003c/A\u003ebe demonstrated as belonging commensurately and universally.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"370\"\u003e\u003c/A\u003e\u003cB\u003ePart 6\u003c/B\u003e\n\n\u003cA NAME=\"371\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eDemonstrative knowledge must rest on necessary basic truths; for \n\u003cA NAME=\"372\"\u003e\u003c/A\u003ethe object of scientific knowledge cannot be other than it is. Now attributes \n\u003cA NAME=\"373\"\u003e\u003c/A\u003eattaching essentially to their subjects attach necessarily to them: for \n\u003cA NAME=\"374\"\u003e\u003c/A\u003eessential attributes are either elements in the essential nature of their \n\u003cA NAME=\"375\"\u003e\u003c/A\u003esubjects, or contain their subjects as elements in their own essential \n\u003cA NAME=\"376\"\u003e\u003c/A\u003enature. (The pairs of opposites which the latter class includes are necessary \n\u003cA NAME=\"377\"\u003e\u003c/A\u003ebecause one member or the other necessarily inheres.) It follows from this \n\u003cA NAME=\"378\"\u003e\u003c/A\u003ethat premisses of the demonstrative syllogism must be connexions essential \n\u003cA NAME=\"379\"\u003e\u003c/A\u003ein the sense explained: for all attributes must inhere essentially or else \n\u003cA NAME=\"380\"\u003e\u003c/A\u003ebe accidental, and accidental attributes are not necessary to their \n\u003cA NAME=\"381\"\u003e\u003c/A\u003esubjects.\n\u003cA NAME=\"382\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWe must either state the case thus, or else premise that the conclusion \n\u003cA NAME=\"383\"\u003e\u003c/A\u003eof demonstration is necessary and that a demonstrated conclusion cannot \n\u003cA NAME=\"384\"\u003e\u003c/A\u003ebe other than it is, and then infer that the conclusion must be developed \n\u003cA NAME=\"385\"\u003e\u003c/A\u003efrom necessary premisses. For though you may reason from true premisses \n\u003cA NAME=\"386\"\u003e\u003c/A\u003ewithout demonstrating, yet if your premisses are necessary you will assuredly \n\u003cA NAME=\"387\"\u003e\u003c/A\u003edemonstrate-in such necessity you have at once a distinctive character \n\u003cA NAME=\"388\"\u003e\u003c/A\u003eof demonstration. That demonstration proceeds from necessary premisses \n\u003cA NAME=\"389\"\u003e\u003c/A\u003eis also indicated by the fact that the objection we raise against a professed \n\u003cA NAME=\"390\"\u003e\u003c/A\u003edemonstration is that a premiss of it is not a necessary truth-whether \n\u003cA NAME=\"391\"\u003e\u003c/A\u003ewe think it altogether devoid of necessity, or at any rate so far as our \n\u003cA NAME=\"392\"\u003e\u003c/A\u003eopponent\u0027s previous argument goes. This shows how naive it is to suppose \n\u003cA NAME=\"393\"\u003e\u003c/A\u003eone\u0027s basic truths rightly chosen if one starts with a proposition which \n\u003cA NAME=\"394\"\u003e\u003c/A\u003eis (1) popularly accepted and (2) true, such as the sophists\u0027 assumption \n\u003cA NAME=\"395\"\u003e\u003c/A\u003ethat to know is the same as to possess knowledge. For (1) popular acceptance \n\u003cA NAME=\"396\"\u003e\u003c/A\u003eor rejection is no criterion of a basic truth, which can only be the primary \n\u003cA NAME=\"397\"\u003e\u003c/A\u003elaw of the genus constituting the subject matter of the demonstration; \n\u003cA NAME=\"398\"\u003e\u003c/A\u003eand (2) not all truth is \u0027appropriate\u0027.\n\u003cA NAME=\"399\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eA further proof that the conclusion must be the development of \n\u003cA NAME=\"400\"\u003e\u003c/A\u003enecessary premisses is as follows. Where demonstration is possible, one \n\u003cA NAME=\"401\"\u003e\u003c/A\u003ewho can give no account which includes the cause has no scientific knowledge. \n\u003cA NAME=\"402\"\u003e\u003c/A\u003eIf, then, we suppose a syllogism in which, though A necessarily inheres \n\u003cA NAME=\"403\"\u003e\u003c/A\u003ein C, yet B, the middle term of the demonstration, is not necessarily connected \n\u003cA NAME=\"404\"\u003e\u003c/A\u003ewith A and C, then the man who argues thus has no reasoned knowledge of \n\u003cA NAME=\"405\"\u003e\u003c/A\u003ethe conclusion, since this conclusion does not owe its necessity to the \n\u003cA NAME=\"406\"\u003e\u003c/A\u003emiddle term; for though the conclusion is necessary, the mediating link \n\u003cA NAME=\"407\"\u003e\u003c/A\u003eis a contingent fact. Or again, if a man is without knowledge now, though \n\u003cA NAME=\"408\"\u003e\u003c/A\u003ehe still retains the steps of the argument, though there is no change in \n\u003cA NAME=\"409\"\u003e\u003c/A\u003ehimself or in the fact and no lapse of memory on his part; then neither \n\u003cA NAME=\"410\"\u003e\u003c/A\u003ehad he knowledge previously. But the mediating link, not being necessary, \n\u003cA NAME=\"411\"\u003e\u003c/A\u003emay have perished in the interval; and if so, though there be no change \n\u003cA NAME=\"412\"\u003e\u003c/A\u003ein him nor in the fact, and though he will still retain the steps of the \n\u003cA NAME=\"413\"\u003e\u003c/A\u003eargument, yet he has not knowledge, and therefore had not knowledge before. \n\u003cA NAME=\"414\"\u003e\u003c/A\u003eEven if the link has not actually perished but is liable to perish, this \n\u003cA NAME=\"415\"\u003e\u003c/A\u003esituation is possible and might occur. But such a condition cannot be \n\u003cA NAME=\"416\"\u003e\u003c/A\u003eknowledge.\n\u003cA NAME=\"417\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWhen the conclusion is necessary, the middle through which it was \n\u003cA NAME=\"418\"\u003e\u003c/A\u003eproved may yet quite easily be non-necessary. You can in fact infer the \n\u003cA NAME=\"419\"\u003e\u003c/A\u003enecessary even from a non-necessary premiss, just as you can infer the \n\u003cA NAME=\"420\"\u003e\u003c/A\u003etrue from the not true. On the other hand, when the middle is necessary \n\u003cA NAME=\"421\"\u003e\u003c/A\u003ethe conclusion must be necessary; just as true premisses always give a \n\u003cA NAME=\"422\"\u003e\u003c/A\u003etrue conclusion. Thus, if A is necessarily predicated of B and B of C, \n\u003cA NAME=\"423\"\u003e\u003c/A\u003ethen A is necessarily predicated of C. But when the conclusion is nonnecessary \n\u003cA NAME=\"424\"\u003e\u003c/A\u003ethe middle cannot be necessary either. Thus: let A be predicated non-necessarily \n\u003cA NAME=\"425\"\u003e\u003c/A\u003eof C but necessarily of B, and let B be a necessary predicate of C; then \n\u003cA NAME=\"426\"\u003e\u003c/A\u003eA too will be a necessary predicate of C, which by hypothesis it is \n\u003cA NAME=\"427\"\u003e\u003c/A\u003enot.\n\u003cA NAME=\"428\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eTo sum up, then: demonstrative knowledge must be knowledge of a \n\u003cA NAME=\"429\"\u003e\u003c/A\u003enecessary nexus, and therefore must clearly be obtained through a necessary \n\u003cA NAME=\"430\"\u003e\u003c/A\u003emiddle term; otherwise its possessor will know neither the cause nor the \n\u003cA NAME=\"431\"\u003e\u003c/A\u003efact that his conclusion is a necessary connexion. Either he will mistake \n\u003cA NAME=\"432\"\u003e\u003c/A\u003ethe non-necessary for the necessary and believe the necessity of the conclusion \n\u003cA NAME=\"433\"\u003e\u003c/A\u003ewithout knowing it, or else he will not even believe it-in which case he \n\u003cA NAME=\"434\"\u003e\u003c/A\u003ewill be equally ignorant, whether he actually infers the mere fact through \n\u003cA NAME=\"435\"\u003e\u003c/A\u003emiddle terms or the reasoned fact and from immediate \n\u003cA NAME=\"436\"\u003e\u003c/A\u003epremisses.\n\u003cA NAME=\"437\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eOf accidents that are not essential according to our definition \n\u003cA NAME=\"438\"\u003e\u003c/A\u003eof essential there is no demonstrative knowledge; for since an accident, \n\u003cA NAME=\"439\"\u003e\u003c/A\u003ein the sense in which I here speak of it, may also not inhere, it is impossible \n\u003cA NAME=\"440\"\u003e\u003c/A\u003eto prove its inherence as a necessary conclusion. A difficulty, however, \n\u003cA NAME=\"441\"\u003e\u003c/A\u003emight be raised as to why in dialectic, if the conclusion is not a necessary \n\u003cA NAME=\"442\"\u003e\u003c/A\u003econnexion, such and such determinate premisses should be proposed in order \n\u003cA NAME=\"443\"\u003e\u003c/A\u003eto deal with such and such determinate problems. Would not the result be \n\u003cA NAME=\"444\"\u003e\u003c/A\u003ethe same if one asked any questions whatever and then merely stated one\u0027s \n\u003cA NAME=\"445\"\u003e\u003c/A\u003econclusion? The solution is that determinate questions have to be put, \n\u003cA NAME=\"446\"\u003e\u003c/A\u003enot because the replies to them affirm facts which necessitate facts affirmed \n\u003cA NAME=\"447\"\u003e\u003c/A\u003eby the conclusion, but because these answers are propositions which if \n\u003cA NAME=\"448\"\u003e\u003c/A\u003ethe answerer affirm, he must affirm the conclusion and affirm it with truth \n\u003cA NAME=\"449\"\u003e\u003c/A\u003eif they are true.\n\u003cA NAME=\"450\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eSince it is just those attributes within every genus which are \n\u003cA NAME=\"451\"\u003e\u003c/A\u003eessential and possessed by their respective subjects as such that are necessary \n\u003cA NAME=\"452\"\u003e\u003c/A\u003eit is clear that both the conclusions and the premisses of demonstrations \n\u003cA NAME=\"453\"\u003e\u003c/A\u003ewhich produce scientific knowledge are essential. For accidents are not \n\u003cA NAME=\"454\"\u003e\u003c/A\u003enecessary: and, further, since accidents are not necessary one does not \n\u003cA NAME=\"455\"\u003e\u003c/A\u003enecessarily have reasoned knowledge of a conclusion drawn from them (this \n\u003cA NAME=\"456\"\u003e\u003c/A\u003eis so even if the accidental premisses are invariable but not essential, \n\u003cA NAME=\"457\"\u003e\u003c/A\u003eas in proofs through signs; for though the conclusion be actually essential, \n\u003cA NAME=\"458\"\u003e\u003c/A\u003eone will not know it as essential nor know its reason); but to have reasoned \n\u003cA NAME=\"459\"\u003e\u003c/A\u003eknowledge of a conclusion is to know it through its cause. We may conclude \n\u003cA NAME=\"460\"\u003e\u003c/A\u003ethat the middle must be consequentially connected with the minor, and the \n\u003cA NAME=\"461\"\u003e\u003c/A\u003emajor with the middle.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"462\"\u003e\u003c/A\u003e\u003cB\u003ePart 7\u003c/B\u003e\n\n\u003cA NAME=\"463\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt follows that we cannot in demonstrating pass from one genus \n\u003cA NAME=\"464\"\u003e\u003c/A\u003eto another. We cannot, for instance, prove geometrical truths by arithmetic. \n\u003cA NAME=\"465\"\u003e\u003c/A\u003eFor there are three elements in demonstration: (1) what is proved, the \n\u003cA NAME=\"466\"\u003e\u003c/A\u003econclusion-an attribute inhering essentially in a genus; (2) the axioms, \n\u003cA NAME=\"467\"\u003e\u003c/A\u003ei.e. axioms which are premisses of demonstration; (3) the subject-genus \n\u003cA NAME=\"468\"\u003e\u003c/A\u003ewhose attributes, i.e. essential properties, are revealed by the demonstration. \n\u003cA NAME=\"469\"\u003e\u003c/A\u003eThe axioms which are premisses of demonstration may be identical in two \n\u003cA NAME=\"470\"\u003e\u003c/A\u003eor more sciences: but in the case of two different genera such as arithmetic \n\u003cA NAME=\"471\"\u003e\u003c/A\u003eand geometry you cannot apply arithmetical demonstration to the properties \n\u003cA NAME=\"472\"\u003e\u003c/A\u003eof magnitudes unless the magnitudes in question are numbers. How in certain \n\u003cA NAME=\"473\"\u003e\u003c/A\u003ecases transference is possible I will explain later.\n\u003cA NAME=\"474\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eArithmetical demonstration and the other sciences likewise possess, \n\u003cA NAME=\"475\"\u003e\u003c/A\u003eeach of them, their own genera; so that if the demonstration is to pass \n\u003cA NAME=\"476\"\u003e\u003c/A\u003efrom one sphere to another, the genus must be either absolutely or to some \n\u003cA NAME=\"477\"\u003e\u003c/A\u003eextent the same. If this is not so, transference is clearly impossible, \n\u003cA NAME=\"478\"\u003e\u003c/A\u003ebecause the extreme and the middle terms must be drawn from the same genus: \n\u003cA NAME=\"479\"\u003e\u003c/A\u003eotherwise, as predicated, they will not be essential and will thus be accidents. \n\u003cA NAME=\"480\"\u003e\u003c/A\u003eThat is why it cannot be proved by geometry that opposites fall under one \n\u003cA NAME=\"481\"\u003e\u003c/A\u003escience, nor even that the product of two cubes is a cube. Nor can the \n\u003cA NAME=\"482\"\u003e\u003c/A\u003etheorem of any one science be demonstrated by means of another science, \n\u003cA NAME=\"483\"\u003e\u003c/A\u003eunless these theorems are related as subordinate to superior (e.g. as optical \n\u003cA NAME=\"484\"\u003e\u003c/A\u003etheorems to geometry or harmonic theorems to arithmetic). Geometry again \n\u003cA NAME=\"485\"\u003e\u003c/A\u003ecannot prove of lines any property which they do not possess qua lines, \n\u003cA NAME=\"486\"\u003e\u003c/A\u003ei.e. in virtue of the fundamental truths of their peculiar genus: it cannot \n\u003cA NAME=\"487\"\u003e\u003c/A\u003eshow, for example, that the straight line is the most beautiful of lines \n\u003cA NAME=\"488\"\u003e\u003c/A\u003eor the contrary of the circle; for these qualities do not belong to lines \n\u003cA NAME=\"489\"\u003e\u003c/A\u003ein virtue of their peculiar genus, but through some property which it shares \n\u003cA NAME=\"490\"\u003e\u003c/A\u003ewith other genera.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"491\"\u003e\u003c/A\u003e\u003cB\u003ePart 8\u003c/B\u003e\n\n\u003cA NAME=\"492\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is also clear that if the premisses from which the syllogism \n\u003cA NAME=\"493\"\u003e\u003c/A\u003eproceeds are commensurately universal, the conclusion of such i.e. in the \n\u003cA NAME=\"494\"\u003e\u003c/A\u003eunqualified sense-must also be eternal. Therefore no attribute can be demonstrated \n\u003cA NAME=\"495\"\u003e\u003c/A\u003enor known by strictly scientific knowledge to inhere in perishable things. \n\u003cA NAME=\"496\"\u003e\u003c/A\u003eThe proof can only be accidental, because the attribute\u0027s connexion with \n\u003cA NAME=\"497\"\u003e\u003c/A\u003eits perishable subject is not commensurately universal but temporary and \n\u003cA NAME=\"498\"\u003e\u003c/A\u003especial. If such a demonstration is made, one premiss must be perishable \n\u003cA NAME=\"499\"\u003e\u003c/A\u003eand not commensurately universal (perishable because only if it is perishable \n\u003cA NAME=\"500\"\u003e\u003c/A\u003ewill the conclusion be perishable; not commensurately universal, because \n\u003cA NAME=\"501\"\u003e\u003c/A\u003ethe predicate will be predicable of some instances of the subject and not \n\u003cA NAME=\"502\"\u003e\u003c/A\u003eof others); so that the conclusion can only be that a fact is true at the \n\u003cA NAME=\"503\"\u003e\u003c/A\u003emoment-not commensurately and universally. The same is true of definitions, \n\u003cA NAME=\"504\"\u003e\u003c/A\u003esince a definition is either a primary premiss or a conclusion of a demonstration, \n\u003cA NAME=\"505\"\u003e\u003c/A\u003eor else only differs from a demonstration in the order of its terms. Demonstration \n\u003cA NAME=\"506\"\u003e\u003c/A\u003eand science of merely frequent occurrences-e.g. of eclipse as happening \n\u003cA NAME=\"507\"\u003e\u003c/A\u003eto the moon-are, as such, clearly eternal: whereas so far as they are not \n\u003cA NAME=\"508\"\u003e\u003c/A\u003eeternal they are not fully commensurate. Other subjects too have properties \n\u003cA NAME=\"509\"\u003e\u003c/A\u003eattaching to them in the same way as eclipse attaches to the \n\u003cA NAME=\"510\"\u003e\u003c/A\u003emoon.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"511\"\u003e\u003c/A\u003e\u003cB\u003ePart 9\u003c/B\u003e\n\n\u003cA NAME=\"512\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is clear that if the conclusion is to show an attribute inhering \n\u003cA NAME=\"513\"\u003e\u003c/A\u003eas such, nothing can be demonstrated except from its \u0027appropriate\u0027 basic \n\u003cA NAME=\"514\"\u003e\u003c/A\u003etruths. Consequently a proof even from true, indemonstrable, and immediate \n\u003cA NAME=\"515\"\u003e\u003c/A\u003epremisses does not constitute knowledge. Such proofs are like Bryson\u0027s \n\u003cA NAME=\"516\"\u003e\u003c/A\u003emethod of squaring the circle; for they operate by taking as their middle \n\u003cA NAME=\"517\"\u003e\u003c/A\u003ea common character-a character, therefore, which the subject may share \n\u003cA NAME=\"518\"\u003e\u003c/A\u003ewith another-and consequently they apply equally to subjects different \n\u003cA NAME=\"519\"\u003e\u003c/A\u003ein kind. They therefore afford knowledge of an attribute only as inhering \n\u003cA NAME=\"520\"\u003e\u003c/A\u003eaccidentally, not as belonging to its subject as such: otherwise they would \n\u003cA NAME=\"521\"\u003e\u003c/A\u003enot have been applicable to another genus.\n\u003cA NAME=\"522\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eOur knowledge of any attribute\u0027s connexion with a subject is accidental \n\u003cA NAME=\"523\"\u003e\u003c/A\u003eunless we know that connexion through the middle term in virtue of which \n\u003cA NAME=\"524\"\u003e\u003c/A\u003eit inheres, and as an inference from basic premisses essential and \u0027appropriate\u0027 \n\u003cA NAME=\"525\"\u003e\u003c/A\u003eto the subject-unless we know, e.g. the property of possessing angles equal \n\u003cA NAME=\"526\"\u003e\u003c/A\u003eto two right angles as belonging to that subject in which it inheres essentially, \n\u003cA NAME=\"527\"\u003e\u003c/A\u003eand as inferred from basic premisses essential and \u0027appropriate\u0027 to that \n\u003cA NAME=\"528\"\u003e\u003c/A\u003esubject: so that if that middle term also belongs essentially to the minor, \n\u003cA NAME=\"529\"\u003e\u003c/A\u003ethe middle must belong to the same kind as the major and minor terms. The \n\u003cA NAME=\"530\"\u003e\u003c/A\u003eonly exceptions to this rule are such cases as theorems in harmonics which \n\u003cA NAME=\"531\"\u003e\u003c/A\u003eare demonstrable by arithmetic. Such theorems are proved by the same middle \n\u003cA NAME=\"532\"\u003e\u003c/A\u003eterms as arithmetical properties, but with a qualification-the fact falls \n\u003cA NAME=\"533\"\u003e\u003c/A\u003eunder a separate science (for the subject genus is separate), but the reasoned \n\u003cA NAME=\"534\"\u003e\u003c/A\u003efact concerns the superior science, to which the attributes essentially \n\u003cA NAME=\"535\"\u003e\u003c/A\u003ebelong. Thus, even these apparent exceptions show that no attribute is \n\u003cA NAME=\"536\"\u003e\u003c/A\u003estrictly demonstrable except from its \u0027appropriate\u0027 basic truths, which, \n\u003cA NAME=\"537\"\u003e\u003c/A\u003ehowever, in the case of these sciences have the requisite identity of \n\u003cA NAME=\"538\"\u003e\u003c/A\u003echaracter.\n\u003cA NAME=\"539\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is no less evident that the peculiar basic truths of each inhering \n\u003cA NAME=\"540\"\u003e\u003c/A\u003eattribute are indemonstrable; for basic truths from which they might be \n\u003cA NAME=\"541\"\u003e\u003c/A\u003ededuced would be basic truths of all that is, and the science to which \n\u003cA NAME=\"542\"\u003e\u003c/A\u003ethey belonged would possess universal sovereignty. This is so because he \n\u003cA NAME=\"543\"\u003e\u003c/A\u003eknows better whose knowledge is deduced from higher causes, for his knowledge \n\u003cA NAME=\"544\"\u003e\u003c/A\u003eis from prior premisses when it derives from causes themselves uncaused: \n\u003cA NAME=\"545\"\u003e\u003c/A\u003ehence, if he knows better than others or best of all, his knowledge would \n\u003cA NAME=\"546\"\u003e\u003c/A\u003ebe science in a higher or the highest degree. But, as things are, demonstration \n\u003cA NAME=\"547\"\u003e\u003c/A\u003eis not transferable to another genus, with such exceptions as we have mentioned \n\u003cA NAME=\"548\"\u003e\u003c/A\u003eof the application of geometrical demonstrations to theorems in mechanics \n\u003cA NAME=\"549\"\u003e\u003c/A\u003eor optics, or of arithmetical demonstrations to those of \n\u003cA NAME=\"550\"\u003e\u003c/A\u003eharmonics.\n\u003cA NAME=\"551\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is hard to be sure whether one knows or not; for it is hard \n\u003cA NAME=\"552\"\u003e\u003c/A\u003eto be sure whether one\u0027s knowledge is based on the basic truths appropriate \n\u003cA NAME=\"553\"\u003e\u003c/A\u003eto each attribute-the differentia of true knowledge. We think we have scientific \n\u003cA NAME=\"554\"\u003e\u003c/A\u003eknowledge if we have reasoned from true and primary premisses. But that \n\u003cA NAME=\"555\"\u003e\u003c/A\u003eis not so: the conclusion must be homogeneous with the basic facts of the \n\u003cA NAME=\"556\"\u003e\u003c/A\u003escience.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"557\"\u003e\u003c/A\u003e\u003cB\u003ePart 10\u003c/B\u003e\n\n\u003cA NAME=\"558\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eI call the basic truths of every genus those clements in it the \n\u003cA NAME=\"559\"\u003e\u003c/A\u003eexistence of which cannot be proved. As regards both these primary truths \n\u003cA NAME=\"560\"\u003e\u003c/A\u003eand the attributes dependent on them the meaning of the name is assumed. \n\u003cA NAME=\"561\"\u003e\u003c/A\u003eThe fact of their existence as regards the primary truths must be assumed; \n\u003cA NAME=\"562\"\u003e\u003c/A\u003ebut it has to be proved of the remainder, the attributes. Thus we assume \n\u003cA NAME=\"563\"\u003e\u003c/A\u003ethe meaning alike of unity, straight, and triangular; but while as regards \n\u003cA NAME=\"564\"\u003e\u003c/A\u003eunity and magnitude we assume also the fact of their existence, in the \n\u003cA NAME=\"565\"\u003e\u003c/A\u003ecase of the remainder proof is required.\n\u003cA NAME=\"566\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eOf the basic truths used in the demonstrative sciences some are \n\u003cA NAME=\"567\"\u003e\u003c/A\u003epeculiar to each science, and some are common, but common only in the sense \n\u003cA NAME=\"568\"\u003e\u003c/A\u003eof analogous, being of use only in so far as they fall within the genus \n\u003cA NAME=\"569\"\u003e\u003c/A\u003econstituting the province of the science in question.\n\u003cA NAME=\"570\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003ePeculiar truths are, e.g. the definitions of line and straight; \n\u003cA NAME=\"571\"\u003e\u003c/A\u003ecommon truths are such as \u0027take equals from equals and equals remain\u0027. \n\u003cA NAME=\"572\"\u003e\u003c/A\u003eOnly so much of these common truths is required as falls within the genus \n\u003cA NAME=\"573\"\u003e\u003c/A\u003ein question: for a truth of this kind will have the same force even if \n\u003cA NAME=\"574\"\u003e\u003c/A\u003enot used generally but applied by the geometer only to magnitudes, or by \n\u003cA NAME=\"575\"\u003e\u003c/A\u003ethe arithmetician only to numbers. Also peculiar to a science are the subjects \n\u003cA NAME=\"576\"\u003e\u003c/A\u003ethe existence as well as the meaning of which it assumes, and the essential \n\u003cA NAME=\"577\"\u003e\u003c/A\u003eattributes of which it investigates, e.g. in arithmetic units, in geometry \n\u003cA NAME=\"578\"\u003e\u003c/A\u003epoints and lines. Both the existence and the meaning of the subjects are \n\u003cA NAME=\"579\"\u003e\u003c/A\u003eassumed by these sciences; but of their essential attributes only the meaning \n\u003cA NAME=\"580\"\u003e\u003c/A\u003eis assumed. For example arithmetic assumes the meaning of odd and even, \n\u003cA NAME=\"581\"\u003e\u003c/A\u003esquare and cube, geometry that of incommensurable, or of deflection or \n\u003cA NAME=\"582\"\u003e\u003c/A\u003everging of lines, whereas the existence of these attributes is demonstrated \n\u003cA NAME=\"583\"\u003e\u003c/A\u003eby means of the axioms and from previous conclusions as premisses. Astronomy \n\u003cA NAME=\"584\"\u003e\u003c/A\u003etoo proceeds in the same way. For indeed every demonstrative science has \n\u003cA NAME=\"585\"\u003e\u003c/A\u003ethree elements: (1) that which it posits, the subject genus whose essential \n\u003cA NAME=\"586\"\u003e\u003c/A\u003eattributes it examines; (2) the so-called axioms, which are primary premisses \n\u003cA NAME=\"587\"\u003e\u003c/A\u003eof its demonstration; (3) the attributes, the meaning of which it assumes. \n\u003cA NAME=\"588\"\u003e\u003c/A\u003eYet some sciences may very well pass over some of these elements; e.g. \n\u003cA NAME=\"589\"\u003e\u003c/A\u003ewe might not expressly posit the existence of the genus if its existence \n\u003cA NAME=\"590\"\u003e\u003c/A\u003ewere obvious (for instance, the existence of hot and cold is more evident \n\u003cA NAME=\"591\"\u003e\u003c/A\u003ethan that of number); or we might omit to assume expressly the meaning \n\u003cA NAME=\"592\"\u003e\u003c/A\u003eof the attributes if it were well understood. In the way the meaning of \n\u003cA NAME=\"593\"\u003e\u003c/A\u003eaxioms, such as \u0027Take equals from equals and equals remain\u0027, is well known \n\u003cA NAME=\"594\"\u003e\u003c/A\u003eand so not expressly assumed. Nevertheless in the nature of the case the \n\u003cA NAME=\"595\"\u003e\u003c/A\u003eessential elements of demonstration are three: the subject, the attributes, \n\u003cA NAME=\"596\"\u003e\u003c/A\u003eand the basic premisses.\n\u003cA NAME=\"597\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThat which expresses necessary self-grounded fact, and which we \n\u003cA NAME=\"598\"\u003e\u003c/A\u003emust necessarily believe, is distinct both from the hypotheses of a science \n\u003cA NAME=\"599\"\u003e\u003c/A\u003eand from illegitimate postulate-I say \u0027must believe\u0027, because all syllogism, \n\u003cA NAME=\"600\"\u003e\u003c/A\u003eand therefore a fortiori demonstration, is addressed not to the spoken \n\u003cA NAME=\"601\"\u003e\u003c/A\u003eword, but to the discourse within the soul, and though we can always raise \n\u003cA NAME=\"602\"\u003e\u003c/A\u003eobjections to the spoken word, to the inward discourse we cannot always \n\u003cA NAME=\"603\"\u003e\u003c/A\u003eobject. That which is capable of proof but assumed by the teacher without \n\u003cA NAME=\"604\"\u003e\u003c/A\u003eproof is, if the pupil believes and accepts it, hypothesis, though only \n\u003cA NAME=\"605\"\u003e\u003c/A\u003ein a limited sense hypothesis-that is, relatively to the pupil; if the \n\u003cA NAME=\"606\"\u003e\u003c/A\u003epupil has no opinion or a contrary opinion on the matter, the same assumption \n\u003cA NAME=\"607\"\u003e\u003c/A\u003eis an illegitimate postulate. Therein lies the distinction between hypothesis \n\u003cA NAME=\"608\"\u003e\u003c/A\u003eand illegitimate postulate: the latter is the contrary of the pupil\u0027s opinion, \n\u003cA NAME=\"609\"\u003e\u003c/A\u003edemonstrable, but assumed and used without demonstration.\n\u003cA NAME=\"610\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThe definition-viz. those which are not expressed as statements \n\u003cA NAME=\"611\"\u003e\u003c/A\u003ethat anything is or is not-are not hypotheses: but it is in the premisses \n\u003cA NAME=\"612\"\u003e\u003c/A\u003eof a science that its hypotheses are contained. Definitions require only \n\u003cA NAME=\"613\"\u003e\u003c/A\u003eto be understood, and this is not hypothesis-unless it be contended that \n\u003cA NAME=\"614\"\u003e\u003c/A\u003ethe pupil\u0027s hearing is also an hypothesis required by the teacher. Hypotheses, \n\u003cA NAME=\"615\"\u003e\u003c/A\u003eon the contrary, postulate facts on the being of which depends the being \n\u003cA NAME=\"616\"\u003e\u003c/A\u003eof the fact inferred. Nor are the geometer\u0027s hypotheses false, as some \n\u003cA NAME=\"617\"\u003e\u003c/A\u003ehave held, urging that one must not employ falsehood and that the geometer \n\u003cA NAME=\"618\"\u003e\u003c/A\u003eis uttering falsehood in stating that the line which he draws is a foot \n\u003cA NAME=\"619\"\u003e\u003c/A\u003elong or straight, when it is actually neither. The truth is that the geometer \n\u003cA NAME=\"620\"\u003e\u003c/A\u003edoes not draw any conclusion from the being of the particular line of which \n\u003cA NAME=\"621\"\u003e\u003c/A\u003ehe speaks, but from what his diagrams symbolize. A further distinction \n\u003cA NAME=\"622\"\u003e\u003c/A\u003eis that all hypotheses and illegitimate postulates are either universal \n\u003cA NAME=\"623\"\u003e\u003c/A\u003eor particular, whereas a definition is neither.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"624\"\u003e\u003c/A\u003e\u003cB\u003ePart 11\u003c/B\u003e\n\n\u003cA NAME=\"625\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eSo demonstration does not necessarily imply the being of Forms \n\u003cA NAME=\"626\"\u003e\u003c/A\u003enor a One beside a Many, but it does necessarily imply the possibility \n\u003cA NAME=\"627\"\u003e\u003c/A\u003eof truly predicating one of many; since without this possibility we cannot \n\u003cA NAME=\"628\"\u003e\u003c/A\u003esave the universal, and if the universal goes, the middle term goes witb. \n\u003cA NAME=\"629\"\u003e\u003c/A\u003eit, and so demonstration becomes impossible. We conclude, then, that there \n\u003cA NAME=\"630\"\u003e\u003c/A\u003emust be a single identical term unequivocally predicable of a number of \n\u003cA NAME=\"631\"\u003e\u003c/A\u003eindividuals.\n\u003cA NAME=\"632\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThe law that it is impossible to affirm and deny simultaneously \n\u003cA NAME=\"633\"\u003e\u003c/A\u003ethe same predicate of the same subject is not expressly posited by any \n\u003cA NAME=\"634\"\u003e\u003c/A\u003edemonstration except when the conclusion also has to be expressed in that \n\u003cA NAME=\"635\"\u003e\u003c/A\u003eform; in which case the proof lays down as its major premiss that the major \n\u003cA NAME=\"636\"\u003e\u003c/A\u003eis truly affirmed of the middle but falsely denied. It makes no difference, \n\u003cA NAME=\"637\"\u003e\u003c/A\u003ehowever, if we add to the middle, or again to the minor term, the corresponding \n\u003cA NAME=\"638\"\u003e\u003c/A\u003enegative. For grant a minor term of which it is true to predicate man-even \n\u003cA NAME=\"639\"\u003e\u003c/A\u003eif it be also true to predicate not-man of it–still grant simply that \n\u003cA NAME=\"640\"\u003e\u003c/A\u003eman is animal and not not-animal, and the conclusion follows: for it will \n\u003cA NAME=\"641\"\u003e\u003c/A\u003estill be true to say that Callias–even if it be also true to say that \n\u003cA NAME=\"642\"\u003e\u003c/A\u003enot-Callias–is animal and not not-animal. The reason is that the major \n\u003cA NAME=\"643\"\u003e\u003c/A\u003eterm is predicable not only of the middle, but of something other than \n\u003cA NAME=\"644\"\u003e\u003c/A\u003ethe middle as well, being of wider application; so that the conclusion \n\u003cA NAME=\"645\"\u003e\u003c/A\u003eis not affected even if the middle is extended to cover the original middle \n\u003cA NAME=\"646\"\u003e\u003c/A\u003eterm and also what is not the original middle term.\n\u003cA NAME=\"647\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThe law that every predicate can be either truly affirmed or truly \n\u003cA NAME=\"648\"\u003e\u003c/A\u003edenied of every subject is posited by such demonstration as uses reductio \n\u003cA NAME=\"649\"\u003e\u003c/A\u003ead impossibile, and then not always universally, but so far as it is requisite; \n\u003cA NAME=\"650\"\u003e\u003c/A\u003ewithin the limits, that is, of the genus-the genus, I mean (as I have already \n\u003cA NAME=\"651\"\u003e\u003c/A\u003eexplained), to which the man of science applies his demonstrations. In \n\u003cA NAME=\"652\"\u003e\u003c/A\u003evirtue of the common elements of demonstration-I mean the common axioms \n\u003cA NAME=\"653\"\u003e\u003c/A\u003ewhich are used as premisses of demonstration, not the subjects nor the \n\u003cA NAME=\"654\"\u003e\u003c/A\u003eattributes demonstrated as belonging to them-all the sciences have communion \n\u003cA NAME=\"655\"\u003e\u003c/A\u003ewith one another, and in communion with them all is dialectic and any science \n\u003cA NAME=\"656\"\u003e\u003c/A\u003ewhich might attempt a universal proof of axioms such as the law of excluded \n\u003cA NAME=\"657\"\u003e\u003c/A\u003emiddle, the law that the subtraction of equals from equals leaves equal \n\u003cA NAME=\"658\"\u003e\u003c/A\u003eremainders, or other axioms of the same kind. Dialectic has no definite \n\u003cA NAME=\"659\"\u003e\u003c/A\u003esphere of this kind, not being confined to a single genus. Otherwise its \n\u003cA NAME=\"660\"\u003e\u003c/A\u003emethod would not be interrogative; for the interrogative method is barred \n\u003cA NAME=\"661\"\u003e\u003c/A\u003eto the demonstrator, who cannot use the opposite facts to prove the same \n\u003cA NAME=\"662\"\u003e\u003c/A\u003enexus. This was shown in my work on the syllogism.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"663\"\u003e\u003c/A\u003e\u003cB\u003ePart 12\u003c/B\u003e\n\n\u003cA NAME=\"664\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIf a syllogistic question is equivalent to a proposition embodying \n\u003cA NAME=\"665\"\u003e\u003c/A\u003eone of the two sides of a contradiction, and if each science has its peculiar \n\u003cA NAME=\"666\"\u003e\u003c/A\u003epropositions from which its peculiar conclusion is developed, then there \n\u003cA NAME=\"667\"\u003e\u003c/A\u003eis such a thing as a distinctively scientific question, and it is the interrogative \n\u003cA NAME=\"668\"\u003e\u003c/A\u003eform of the premisses from which the \u0027appropriate\u0027 conclusion of each science \n\u003cA NAME=\"669\"\u003e\u003c/A\u003eis developed. Hence it is clear that not every question will be relevant \n\u003cA NAME=\"670\"\u003e\u003c/A\u003eto geometry, nor to medicine, nor to any other science: only those questions \n\u003cA NAME=\"671\"\u003e\u003c/A\u003ewill be geometrical which form premisses for the proof of the theorems \n\u003cA NAME=\"672\"\u003e\u003c/A\u003eof geometry or of any other science, such as optics, which uses the same \n\u003cA NAME=\"673\"\u003e\u003c/A\u003ebasic truths as geometry. Of the other sciences the like is true. Of these \n\u003cA NAME=\"674\"\u003e\u003c/A\u003equestions the geometer is bound to give his account, using the basic truths \n\u003cA NAME=\"675\"\u003e\u003c/A\u003eof geometry in conjunction with his previous conclusions; of the basic \n\u003cA NAME=\"676\"\u003e\u003c/A\u003etruths the geometer, as such, is not bound to give any account. The like \n\u003cA NAME=\"677\"\u003e\u003c/A\u003eis true of the other sciences. There is a limit, then, to the questions \n\u003cA NAME=\"678\"\u003e\u003c/A\u003ewhich we may put to each man of science; nor is each man of science bound \n\u003cA NAME=\"679\"\u003e\u003c/A\u003eto answer all inquiries on each several subject, but only such as fall \n\u003cA NAME=\"680\"\u003e\u003c/A\u003ewithin the defined field of his own science. If, then, in controversy with \n\u003cA NAME=\"681\"\u003e\u003c/A\u003ea geometer qua geometer the disputant confines himself to geometry and \n\u003cA NAME=\"682\"\u003e\u003c/A\u003eproves anything from geometrical premisses, he is clearly to be applauded; \n\u003cA NAME=\"683\"\u003e\u003c/A\u003eif he goes outside these he will be at fault, and obviously cannot even \n\u003cA NAME=\"684\"\u003e\u003c/A\u003erefute the geometer except accidentally. One should therefore not discuss \n\u003cA NAME=\"685\"\u003e\u003c/A\u003egeometry among those who are not geometers, for in such a company an unsound \n\u003cA NAME=\"686\"\u003e\u003c/A\u003eargument will pass unnoticed. This is correspondingly true in the other \n\u003cA NAME=\"687\"\u003e\u003c/A\u003esciences.\n\u003cA NAME=\"688\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eSince there are \u0027geometrical\u0027 questions, does it follow that there \n\u003cA NAME=\"689\"\u003e\u003c/A\u003eare also distinctively \u0027ungeometrical\u0027 questions? Further, in each special \n\u003cA NAME=\"690\"\u003e\u003c/A\u003escience-geometry for instance-what kind of error is it that may vitiate \n\u003cA NAME=\"691\"\u003e\u003c/A\u003equestions, and yet not exclude them from that science? Again, is the erroneous \n\u003cA NAME=\"692\"\u003e\u003c/A\u003econclusion one constructed from premisses opposite to the true premisses, \n\u003cA NAME=\"693\"\u003e\u003c/A\u003eor is it formal fallacy though drawn from geometrical premisses? Or, perhaps, \n\u003cA NAME=\"694\"\u003e\u003c/A\u003ethe erroneous conclusion is due to the drawing of premisses from another \n\u003cA NAME=\"695\"\u003e\u003c/A\u003escience; e.g. in a geometrical controversy a musical question is distinctively \n\u003cA NAME=\"696\"\u003e\u003c/A\u003eungeometrical, whereas the notion that parallels meet is in one sense geometrical, \n\u003cA NAME=\"697\"\u003e\u003c/A\u003ebeing ungeometrical in a different fashion: the reason being that \u0027ungeometrical\u0027, \n\u003cA NAME=\"698\"\u003e\u003c/A\u003elike \u0027unrhythmical\u0027, is equivocal, meaning in the one case not geometry \n\u003cA NAME=\"699\"\u003e\u003c/A\u003eat all, in the other bad geometry? It is this error, i.e. error based on \n\u003cA NAME=\"700\"\u003e\u003c/A\u003epremisses of this kind-\u0027of\u0027 the science but false-that is the contrary \n\u003cA NAME=\"701\"\u003e\u003c/A\u003eof science. In mathematics the formal fallacy is not so common, because \n\u003cA NAME=\"702\"\u003e\u003c/A\u003eit is the middle term in which the ambiguity lies, since the major is predicated \n\u003cA NAME=\"703\"\u003e\u003c/A\u003eof the whole of the middle and the middle of the whole of the minor (the \n\u003cA NAME=\"704\"\u003e\u003c/A\u003epredicate of course never has the prefix \u0027all\u0027); and in mathematics one \n\u003cA NAME=\"705\"\u003e\u003c/A\u003ecan, so to speak, see these middle terms with an intellectual vision, while \n\u003cA NAME=\"706\"\u003e\u003c/A\u003ein dialectic the ambiguity may escape detection. E.g. \u0027Is every circle \n\u003cA NAME=\"707\"\u003e\u003c/A\u003ea figure?\u0027 A diagram shows that this is so, but the minor premiss \u0027Are \n\u003cA NAME=\"708\"\u003e\u003c/A\u003eepics circles?\u0027 is shown by the diagram to be false.\n\u003cA NAME=\"709\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIf a proof has an inductive minor premiss, one should not bring \n\u003cA NAME=\"710\"\u003e\u003c/A\u003ean \u0027objection\u0027 against it. For since every premiss must be applicable to \n\u003cA NAME=\"711\"\u003e\u003c/A\u003ea number of cases (otherwise it will not be true in every instance, which, \n\u003cA NAME=\"712\"\u003e\u003c/A\u003esince the syllogism proceeds from universals, it must be), then assuredly \n\u003cA NAME=\"713\"\u003e\u003c/A\u003ethe same is true of an \u0027objection\u0027; since premisses and \u0027objections\u0027 are \n\u003cA NAME=\"714\"\u003e\u003c/A\u003eso far the same that anything which can be validly advanced as an \u0027objection\u0027 \n\u003cA NAME=\"715\"\u003e\u003c/A\u003emust be such that it could take the form of a premiss, either demonstrative \n\u003cA NAME=\"716\"\u003e\u003c/A\u003eor dialectical. On the other hand, arguments formally illogical do sometimes \n\u003cA NAME=\"717\"\u003e\u003c/A\u003eoccur through taking as middles mere attributes of the major and minor \n\u003cA NAME=\"718\"\u003e\u003c/A\u003eterms. An instance of this is Caeneus\u0027 proof that fire increases in geometrical \n\u003cA NAME=\"719\"\u003e\u003c/A\u003eproportion: \u0027Fire\u0027, he argues, \u0027increases rapidly, and so does geometrical \n\u003cA NAME=\"720\"\u003e\u003c/A\u003eproportion\u0027. There is no syllogism so, but there is a syllogism if the \n\u003cA NAME=\"721\"\u003e\u003c/A\u003emost rapidly increasing proportion is geometrical and the most rapidly \n\u003cA NAME=\"722\"\u003e\u003c/A\u003eincreasing proportion is attributable to fire in its motion. Sometimes, \n\u003cA NAME=\"723\"\u003e\u003c/A\u003eno doubt, it is impossible to reason from premisses predicating mere attributes: \n\u003cA NAME=\"724\"\u003e\u003c/A\u003ebut sometimes it is possible, though the possibility is overlooked. If \n\u003cA NAME=\"725\"\u003e\u003c/A\u003efalse premisses could never give true conclusions \u0027resolution\u0027 would be \n\u003cA NAME=\"726\"\u003e\u003c/A\u003eeasy, for premisses and conclusion would in that case inevitably reciprocate. \n\u003cA NAME=\"727\"\u003e\u003c/A\u003eI might then argue thus: let A be an existing fact; let the existence of \n\u003cA NAME=\"728\"\u003e\u003c/A\u003eA imply such and such facts actually known to me to exist, which we may \n\u003cA NAME=\"729\"\u003e\u003c/A\u003ecall B. I can now, since they reciprocate, infer A from \n\u003cA NAME=\"730\"\u003e\u003c/A\u003eB.\n\u003cA NAME=\"731\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eReciprocation of premisses and conclusion is more frequent in mathematics, \n\u003cA NAME=\"732\"\u003e\u003c/A\u003ebecause mathematics takes definitions, but never an accident, for its premisses-a \n\u003cA NAME=\"733\"\u003e\u003c/A\u003esecond characteristic distinguishing mathematical reasoning from dialectical \n\u003cA NAME=\"734\"\u003e\u003c/A\u003edisputations.\n\u003cA NAME=\"735\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eA science expands not by the interposition of fresh middle terms, \n\u003cA NAME=\"736\"\u003e\u003c/A\u003ebut by the apposition of fresh extreme terms. E.g. A is predicated of B, \n\u003cA NAME=\"737\"\u003e\u003c/A\u003eB of C, C of D, and so indefinitely. Or the expansion may be lateral: e.g. \n\u003cA NAME=\"738\"\u003e\u003c/A\u003eone major A, may be proved of two minors, C and E. Thus let A represent \n\u003cA NAME=\"739\"\u003e\u003c/A\u003enumber-a number or number taken indeterminately; B determinate odd number; \n\u003cA NAME=\"740\"\u003e\u003c/A\u003eC any particular odd number. We can then predicate A of C. Next let D represent \n\u003cA NAME=\"741\"\u003e\u003c/A\u003edeterminate even number, and E even number. Then A is predicable of \n\u003cA NAME=\"742\"\u003e\u003c/A\u003eE.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"743\"\u003e\u003c/A\u003e\u003cB\u003ePart 13\u003c/B\u003e\n\n\u003cA NAME=\"744\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eKnowledge of the fact differs from knowledge of the reasoned fact. \n\u003cA NAME=\"745\"\u003e\u003c/A\u003eTo begin with, they differ within the same science and in two ways: (1) \n\u003cA NAME=\"746\"\u003e\u003c/A\u003ewhen the premisses of the syllogism are not immediate (for then the proximate \n\u003cA NAME=\"747\"\u003e\u003c/A\u003ecause is not contained in them-a necessary condition of knowledge of the \n\u003cA NAME=\"748\"\u003e\u003c/A\u003ereasoned fact): (2) when the premisses are immediate, but instead of the \n\u003cA NAME=\"749\"\u003e\u003c/A\u003ecause the better known of the two reciprocals is taken as the middle; for \n\u003cA NAME=\"750\"\u003e\u003c/A\u003eof two reciprocally predicable terms the one which is not the cause may \n\u003cA NAME=\"751\"\u003e\u003c/A\u003equite easily be the better known and so become the middle term of the demonstration. \n\u003cA NAME=\"752\"\u003e\u003c/A\u003eThus (2) (a) you might prove as follows that the planets are near because \n\u003cA NAME=\"753\"\u003e\u003c/A\u003ethey do not twinkle: let C be the planets, B not twinkling, A proximity. \n\u003cA NAME=\"754\"\u003e\u003c/A\u003eThen B is predicable of C; for the planets do not twinkle. But A is also \n\u003cA NAME=\"755\"\u003e\u003c/A\u003epredicable of B, since that which does not twinkle is near–we must take \n\u003cA NAME=\"756\"\u003e\u003c/A\u003ethis truth as having been reached by induction or sense-perception. Therefore \n\u003cA NAME=\"757\"\u003e\u003c/A\u003eA is a necessary predicate of C; so that we have demonstrated that the \n\u003cA NAME=\"758\"\u003e\u003c/A\u003eplanets are near. This syllogism, then, proves not the reasoned fact but \n\u003cA NAME=\"759\"\u003e\u003c/A\u003eonly the fact; since they are not near because they do not twinkle, but, \n\u003cA NAME=\"760\"\u003e\u003c/A\u003ebecause they are near, do not twinkle. The major and middle of the proof, \n\u003cA NAME=\"761\"\u003e\u003c/A\u003ehowever, may be reversed, and then the demonstration will be of the reasoned \n\u003cA NAME=\"762\"\u003e\u003c/A\u003efact. Thus: let C be the planets, B proximity, A not twinkling. Then B \n\u003cA NAME=\"763\"\u003e\u003c/A\u003eis an attribute of C, and A-not twinkling-of B. Consequently A is predicable \n\u003cA NAME=\"764\"\u003e\u003c/A\u003eof C, and the syllogism proves the reasoned fact, since its middle term \n\u003cA NAME=\"765\"\u003e\u003c/A\u003eis the proximate cause. Another example is the inference that the moon \n\u003cA NAME=\"766\"\u003e\u003c/A\u003eis spherical from its manner of waxing. Thus: since that which so waxes \n\u003cA NAME=\"767\"\u003e\u003c/A\u003eis spherical, and since the moon so waxes, clearly the moon is spherical. \n\u003cA NAME=\"768\"\u003e\u003c/A\u003ePut in this form, the syllogism turns out to be proof of the fact, but \n\u003cA NAME=\"769\"\u003e\u003c/A\u003eif the middle and major be reversed it is proof of the reasoned fact; since \n\u003cA NAME=\"770\"\u003e\u003c/A\u003ethe moon is not spherical because it waxes in a certain manner, but waxes \n\u003cA NAME=\"771\"\u003e\u003c/A\u003ein such a manner because it is spherical. (Let C be the moon, B spherical, \n\u003cA NAME=\"772\"\u003e\u003c/A\u003eand A waxing.) Again (b), in cases where the cause and the effect are not \n\u003cA NAME=\"773\"\u003e\u003c/A\u003ereciprocal and the effect is the better known, the fact is demonstrated \n\u003cA NAME=\"774\"\u003e\u003c/A\u003ebut not the reasoned fact. This also occurs (1) when the middle falls outside \n\u003cA NAME=\"775\"\u003e\u003c/A\u003ethe major and minor, for here too the strict cause is not given, and so \n\u003cA NAME=\"776\"\u003e\u003c/A\u003ethe demonstration is of the fact, not of the reasoned fact. For example, \n\u003cA NAME=\"777\"\u003e\u003c/A\u003ethe question \u0027Why does not a wall breathe?\u0027 might be answered, \u0027Because \n\u003cA NAME=\"778\"\u003e\u003c/A\u003eit is not an animal\u0027; but that answer would not give the strict cause, \n\u003cA NAME=\"779\"\u003e\u003c/A\u003ebecause if not being an animal causes the absence of respiration, then \n\u003cA NAME=\"780\"\u003e\u003c/A\u003ebeing an animal should be the cause of respiration, according to the rule \n\u003cA NAME=\"781\"\u003e\u003c/A\u003ethat if the negation of causes the non-inherence of y, the affirmation \n\u003cA NAME=\"782\"\u003e\u003c/A\u003eof x causes the inherence of y; e.g. if the disproportion of the hot and \n\u003cA NAME=\"783\"\u003e\u003c/A\u003ecold elements is the cause of ill health, their proportion is the cause \n\u003cA NAME=\"784\"\u003e\u003c/A\u003eof health; and conversely, if the assertion of x causes the inherence of \n\u003cA NAME=\"785\"\u003e\u003c/A\u003ey, the negation of x must cause y\u0027s non-inherence. But in the case given \n\u003cA NAME=\"786\"\u003e\u003c/A\u003ethis consequence does not result; for not every animal breathes. A syllogism \n\u003cA NAME=\"787\"\u003e\u003c/A\u003ewith this kind of cause takes place in the second figure. Thus: let A be \n\u003cA NAME=\"788\"\u003e\u003c/A\u003eanimal, B respiration, C wall. Then A is predicable of all B (for all that \n\u003cA NAME=\"789\"\u003e\u003c/A\u003ebreathes is animal), but of no C; and consequently B is predicable of no \n\u003cA NAME=\"790\"\u003e\u003c/A\u003eC; that is, the wall does not breathe. Such causes are like far-fetched \n\u003cA NAME=\"791\"\u003e\u003c/A\u003eexplanations, which precisely consist in making the cause too remote, as \n\u003cA NAME=\"792\"\u003e\u003c/A\u003ein Anacharsis\u0027 account of why the Scythians have no flute-players; namely \n\u003cA NAME=\"793\"\u003e\u003c/A\u003ebecause they have no vines.\n\u003cA NAME=\"794\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThus, then, do the syllogism of the fact and the syllogism of the \n\u003cA NAME=\"795\"\u003e\u003c/A\u003ereasoned fact differ within one science and according to the position of \n\u003cA NAME=\"796\"\u003e\u003c/A\u003ethe middle terms. But there is another way too in which the fact and the \n\u003cA NAME=\"797\"\u003e\u003c/A\u003ereasoned fact differ, and that is when they are investigated respectively \n\u003cA NAME=\"798\"\u003e\u003c/A\u003eby different sciences. This occurs in the case of problems related to one \n\u003cA NAME=\"799\"\u003e\u003c/A\u003eanother as subordinate and superior, as when optical problems are subordinated \n\u003cA NAME=\"800\"\u003e\u003c/A\u003eto geometry, mechanical problems to stereometry, harmonic problems to arithmetic, \n\u003cA NAME=\"801\"\u003e\u003c/A\u003ethe data of observation to astronomy. (Some of these sciences bear almost \n\u003cA NAME=\"802\"\u003e\u003c/A\u003ethe same name; e.g. mathematical and nautical astronomy, mathematical and \n\u003cA NAME=\"803\"\u003e\u003c/A\u003eacoustical harmonics.) Here it is the business of the empirical observers \n\u003cA NAME=\"804\"\u003e\u003c/A\u003eto know the fact, of the mathematicians to know the reasoned fact; for \n\u003cA NAME=\"805\"\u003e\u003c/A\u003ethe latter are in possession of the demonstrations giving the causes, and \n\u003cA NAME=\"806\"\u003e\u003c/A\u003eare often ignorant of the fact: just as we have often a clear insight into \n\u003cA NAME=\"807\"\u003e\u003c/A\u003ea universal, but through lack of observation are ignorant of some of its \n\u003cA NAME=\"808\"\u003e\u003c/A\u003eparticular instances. These connexions have a perceptible existence though \n\u003cA NAME=\"809\"\u003e\u003c/A\u003ethey are manifestations of forms. For the mathematical sciences concern \n\u003cA NAME=\"810\"\u003e\u003c/A\u003eforms: they do not demonstrate properties of a substratum, since, even \n\u003cA NAME=\"811\"\u003e\u003c/A\u003ethough the geometrical subjects are predicable as properties of a perceptible \n\u003cA NAME=\"812\"\u003e\u003c/A\u003esubstratum, it is not as thus predicable that the mathematician demonstrates \n\u003cA NAME=\"813\"\u003e\u003c/A\u003eproperties of them. As optics is related to geometry, so another science \n\u003cA NAME=\"814\"\u003e\u003c/A\u003eis related to optics, namely the theory of the rainbow. Here knowledge \n\u003cA NAME=\"815\"\u003e\u003c/A\u003eof the fact is within the province of the natural philosopher, knowledge \n\u003cA NAME=\"816\"\u003e\u003c/A\u003eof the reasoned fact within that of the optician, either qua optician or \n\u003cA NAME=\"817\"\u003e\u003c/A\u003equa mathematical optician. Many sciences not standing in this mutual relation \n\u003cA NAME=\"818\"\u003e\u003c/A\u003eenter into it at points; e.g. medicine and geometry: it is the physician\u0027s \n\u003cA NAME=\"819\"\u003e\u003c/A\u003ebusiness to know that circular wounds heal more slowly, the geometer\u0027s \n\u003cA NAME=\"820\"\u003e\u003c/A\u003eto know the reason why.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"821\"\u003e\u003c/A\u003e\u003cB\u003ePart 14\u003c/B\u003e\n\n\u003cA NAME=\"822\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eOf all the figures the most scientific is the first. Thus, it is \n\u003cA NAME=\"823\"\u003e\u003c/A\u003ethe vehicle of the demonstrations of all the mathematical sciences, such \n\u003cA NAME=\"824\"\u003e\u003c/A\u003eas arithmetic, geometry, and optics, and practically all of all sciences \n\u003cA NAME=\"825\"\u003e\u003c/A\u003ethat investigate causes: for the syllogism of the reasoned fact is either \n\u003cA NAME=\"826\"\u003e\u003c/A\u003eexclusively or generally speaking and in most cases in this figure-a second \n\u003cA NAME=\"827\"\u003e\u003c/A\u003eproof that this figure is the most scientific; for grasp of a reasoned \n\u003cA NAME=\"828\"\u003e\u003c/A\u003econclusion is the primary condition of knowledge. Thirdly, the first is \n\u003cA NAME=\"829\"\u003e\u003c/A\u003ethe only figure which enables us to pursue knowledge of the essence of \n\u003cA NAME=\"830\"\u003e\u003c/A\u003ea thing. In the second figure no affirmative conclusion is possible, and \n\u003cA NAME=\"831\"\u003e\u003c/A\u003eknowledge of a thing\u0027s essence must be affirmative; while in the third \n\u003cA NAME=\"832\"\u003e\u003c/A\u003efigure the conclusion can be affirmative, but cannot be universal, and \n\u003cA NAME=\"833\"\u003e\u003c/A\u003eessence must have a universal character: e.g. man is not two-footed animal \n\u003cA NAME=\"834\"\u003e\u003c/A\u003ein any qualified sense, but universally. Finally, the first figure has \n\u003cA NAME=\"835\"\u003e\u003c/A\u003eno need of the others, while it is by means of the first that the other \n\u003cA NAME=\"836\"\u003e\u003c/A\u003etwo figures are developed, and have their intervals closepacked until immediate \n\u003cA NAME=\"837\"\u003e\u003c/A\u003epremisses are reached.\n\u003cA NAME=\"838\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eClearly, therefore, the first figure is the primary condition of \n\u003cA NAME=\"839\"\u003e\u003c/A\u003eknowledge.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"840\"\u003e\u003c/A\u003e\u003cB\u003ePart 15\u003c/B\u003e\n\n\u003cA NAME=\"841\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eJust as an attribute A may (as we saw) be atomically connected \n\u003cA NAME=\"842\"\u003e\u003c/A\u003ewith a subject B, so its disconnexion may be atomic. I call \u0027atomic\u0027 connexions \n\u003cA NAME=\"843\"\u003e\u003c/A\u003eor disconnexions which involve no intermediate term; since in that case \n\u003cA NAME=\"844\"\u003e\u003c/A\u003ethe connexion or disconnexion will not be mediated by something other than \n\u003cA NAME=\"845\"\u003e\u003c/A\u003ethe terms themselves. It follows that if either A or B, or both A and B, \n\u003cA NAME=\"846\"\u003e\u003c/A\u003ehave a genus, their disconnexion cannot be primary. Thus: let C be the \n\u003cA NAME=\"847\"\u003e\u003c/A\u003egenus of A. Then, if C is not the genus of B-for A may well have a genus \n\u003cA NAME=\"848\"\u003e\u003c/A\u003ewhich is not the genus of B-there will be a syllogism proving A\u0027s disconnexion \n\u003cA NAME=\"849\"\u003e\u003c/A\u003efrom B thus:\n\u003cA NAME=\"850\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003e\u003cB\u003eall A is C,\u003c/B\u003e \u003cB\u003eno B is C,\u003c/B\u003e \u003cB\u003etherefore no B is A.\u003c/B\u003e \n\u003cA NAME=\"851\"\u003e\u003c/A\u003eOr if it is B which has a genus D, we have\n\u003cA NAME=\"852\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003e\u003cB\u003eall B is D,\u003c/B\u003e \u003cB\u003eno D is A,\u003c/B\u003e \u003cB\u003etherefore no B is A, by \n\u003cA NAME=\"853\"\u003e\u003c/A\u003esyllogism;\u003c/B\u003e and the proof will be similar if both A and B have a genus. \n\u003cA NAME=\"854\"\u003e\u003c/A\u003eThat the genus of A need not be the genus of B and vice versa, is shown \n\u003cA NAME=\"855\"\u003e\u003c/A\u003eby the existence of mutually exclusive coordinate series of predication. \n\u003cA NAME=\"856\"\u003e\u003c/A\u003eIf no term in the series ACD…is predicable of any term in the series \n\u003cA NAME=\"857\"\u003e\u003c/A\u003eBEF…,and if G-a term in the former series-is the genus of A, clearly \n\u003cA NAME=\"858\"\u003e\u003c/A\u003eG will not be the genus of B; since, if it were, the series would not be \n\u003cA NAME=\"859\"\u003e\u003c/A\u003emutually exclusive. So also if B has a genus, it will not be the genus \n\u003cA NAME=\"860\"\u003e\u003c/A\u003eof A. If, on the other hand, neither A nor B has a genus and A does not \n\u003cA NAME=\"861\"\u003e\u003c/A\u003einhere in B, this disconnexion must be atomic. If there be a middle term, \n\u003cA NAME=\"862\"\u003e\u003c/A\u003eone or other of them is bound to have a genus, for the syllogism will be \n\u003cA NAME=\"863\"\u003e\u003c/A\u003eeither in the first or the second figure. If it is in the first, B will \n\u003cA NAME=\"864\"\u003e\u003c/A\u003ehave a genus-for the premiss containing it must be affirmative: if in the \n\u003cA NAME=\"865\"\u003e\u003c/A\u003esecond, either A or B indifferently, since syllogism is possible if either \n\u003cA NAME=\"866\"\u003e\u003c/A\u003eis contained in a negative premiss, but not if both premisses are \n\u003cA NAME=\"867\"\u003e\u003c/A\u003enegative.\n\u003cA NAME=\"868\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eHence it is clear that one thing may be atomically disconnected \n\u003cA NAME=\"869\"\u003e\u003c/A\u003efrom another, and we have stated when and how this is \n\u003cA NAME=\"870\"\u003e\u003c/A\u003epossible.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"871\"\u003e\u003c/A\u003e\u003cB\u003ePart 16\u003c/B\u003e\n\n\u003cA NAME=\"872\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIgnorance-defined not as the negation of knowledge but as a positive \n\u003cA NAME=\"873\"\u003e\u003c/A\u003estate of mind-is error produced by inference.\n\u003cA NAME=\"874\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003e(1) Let us first consider propositions asserting a predicate\u0027s \n\u003cA NAME=\"875\"\u003e\u003c/A\u003eimmediate connexion with or disconnexion from a subject. Here, it is true, \n\u003cA NAME=\"876\"\u003e\u003c/A\u003epositive error may befall one in alternative ways; for it may arise where \n\u003cA NAME=\"877\"\u003e\u003c/A\u003eone directly believes a connexion or disconnexion as well as where one\u0027s \n\u003cA NAME=\"878\"\u003e\u003c/A\u003ebelief is acquired by inference. The error, however, that consists in a \n\u003cA NAME=\"879\"\u003e\u003c/A\u003edirect belief is without complication; but the error resulting from inference-which \n\u003cA NAME=\"880\"\u003e\u003c/A\u003ehere concerns us-takes many forms. Thus, let A be atomically disconnected \n\u003cA NAME=\"881\"\u003e\u003c/A\u003efrom all B: then the conclusion inferred through a middle term C, that \n\u003cA NAME=\"882\"\u003e\u003c/A\u003eall B is A, will be a case of error produced by syllogism. Now, two cases \n\u003cA NAME=\"883\"\u003e\u003c/A\u003eare possible. Either (a) both premisses, or (b) one premiss only, may be \n\u003cA NAME=\"884\"\u003e\u003c/A\u003efalse. (a) If neither A is an attribute of any C nor C of any B, whereas \n\u003cA NAME=\"885\"\u003e\u003c/A\u003ethe contrary was posited in both cases, both premisses will be false. (C \n\u003cA NAME=\"886\"\u003e\u003c/A\u003emay quite well be so related to A and B that C is neither subordinate to \n\u003cA NAME=\"887\"\u003e\u003c/A\u003eA nor a universal attribute of B: for B, since A was said to be primarily \n\u003cA NAME=\"888\"\u003e\u003c/A\u003edisconnected from B, cannot have a genus, and A need not necessarily be \n\u003cA NAME=\"889\"\u003e\u003c/A\u003ea universal attribute of all things. Consequently both premisses may be \n\u003cA NAME=\"890\"\u003e\u003c/A\u003efalse.) On the other hand, (b) one of the premisses may be true, though \n\u003cA NAME=\"891\"\u003e\u003c/A\u003enot either indifferently but only the major A-C since, B having no genus, \n\u003cA NAME=\"892\"\u003e\u003c/A\u003ethe premiss C-B will always be false, while A-C may be true. This is the \n\u003cA NAME=\"893\"\u003e\u003c/A\u003ecase if, for example, A is related atomically to both C and B; because \n\u003cA NAME=\"894\"\u003e\u003c/A\u003ewhen the same term is related atomically to more terms than one, neither \n\u003cA NAME=\"895\"\u003e\u003c/A\u003eof those terms will belong to the other. It is, of course, equally the \n\u003cA NAME=\"896\"\u003e\u003c/A\u003ecase if A-C is not atomic.\n\u003cA NAME=\"897\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eError of attribution, then, occurs through these causes and in \n\u003cA NAME=\"898\"\u003e\u003c/A\u003ethis form only-for we found that no syllogism of universal attribution \n\u003cA NAME=\"899\"\u003e\u003c/A\u003ewas possible in any figure but the first. On the other hand, an error of \n\u003cA NAME=\"900\"\u003e\u003c/A\u003enon-attribution may occur either in the first or in the second figure. \n\u003cA NAME=\"901\"\u003e\u003c/A\u003eLet us therefore first explain the various forms it takes in the first \n\u003cA NAME=\"902\"\u003e\u003c/A\u003efigure and the character of the premisses in each case.\n\u003cA NAME=\"903\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003e(c) It may occur when both premisses are false; e.g. supposing \n\u003cA NAME=\"904\"\u003e\u003c/A\u003eA atomically connected with both C and B, if it be then assumed that no \n\u003cA NAME=\"905\"\u003e\u003c/A\u003eC is and all B is C, both premisses are false.\n\u003cA NAME=\"906\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003e(d) It is also possible when one is false. This may be either premiss \n\u003cA NAME=\"907\"\u003e\u003c/A\u003eindifferently. A-C may be true, C-B false-A-C true because A is not an \n\u003cA NAME=\"908\"\u003e\u003c/A\u003eattribute of all things, C-B false because C, which never has the attribute \n\u003cA NAME=\"909\"\u003e\u003c/A\u003eA, cannot be an attribute of B; for if C-B were true, the premiss A-C would \n\u003cA NAME=\"910\"\u003e\u003c/A\u003eno longer be true, and besides if both premisses were true, the conclusion \n\u003cA NAME=\"911\"\u003e\u003c/A\u003ewould be true. Or again, C-B may be true and A-C false; e.g. if both C \n\u003cA NAME=\"912\"\u003e\u003c/A\u003eand A contain B as genera, one of them must be subordinate to the other, \n\u003cA NAME=\"913\"\u003e\u003c/A\u003eso that if the premiss takes the form No C is A, it will be false. This \n\u003cA NAME=\"914\"\u003e\u003c/A\u003emakes it clear that whether either or both premisses are false, the conclusion \n\u003cA NAME=\"915\"\u003e\u003c/A\u003ewill equally be false.\n\u003cA NAME=\"916\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIn the second figure the premisses cannot both be wholly false; \n\u003cA NAME=\"917\"\u003e\u003c/A\u003efor if all B is A, no middle term can be with truth universally affirmed \n\u003cA NAME=\"918\"\u003e\u003c/A\u003eof one extreme and universally denied of the other: but premisses in which \n\u003cA NAME=\"919\"\u003e\u003c/A\u003ethe middle is affirmed of one extreme and denied of the other are the necessary \n\u003cA NAME=\"920\"\u003e\u003c/A\u003econdition if one is to get a valid inference at all. Therefore if, taken \n\u003cA NAME=\"921\"\u003e\u003c/A\u003ein this way, they are wholly false, their contraries conversely should \n\u003cA NAME=\"922\"\u003e\u003c/A\u003ebe wholly true. But this is impossible. On the other hand, there is nothing \n\u003cA NAME=\"923\"\u003e\u003c/A\u003eto prevent both premisses being partially false; e.g. if actually some \n\u003cA NAME=\"924\"\u003e\u003c/A\u003eA is C and some B is C, then if it is premised that all A is C and no B \n\u003cA NAME=\"925\"\u003e\u003c/A\u003eis C, both premisses are false, yet partially, not wholly, false. The same \n\u003cA NAME=\"926\"\u003e\u003c/A\u003eis true if the major is made negative instead of the minor. Or one premiss \n\u003cA NAME=\"927\"\u003e\u003c/A\u003emay be wholly false, and it may be either of them. Thus, supposing that \n\u003cA NAME=\"928\"\u003e\u003c/A\u003eactually an attribute of all A must also be an attribute of all B, then \n\u003cA NAME=\"929\"\u003e\u003c/A\u003eif C is yet taken to be a universal attribute of all but universally non-attributable \n\u003cA NAME=\"930\"\u003e\u003c/A\u003eto B, C-A will be true but C-B false. Again, actually that which is an \n\u003cA NAME=\"931\"\u003e\u003c/A\u003eattribute of no B will not be an attribute of all A either; for if it be \n\u003cA NAME=\"932\"\u003e\u003c/A\u003ean attribute of all A, it will also be an attribute of all B, which is \n\u003cA NAME=\"933\"\u003e\u003c/A\u003econtrary to supposition; but if C be nevertheless assumed to be a universal \n\u003cA NAME=\"934\"\u003e\u003c/A\u003eattribute of A, but an attribute of no B, then the premiss C-B is true \n\u003cA NAME=\"935\"\u003e\u003c/A\u003ebut the major is false. The case is similar if the major is made the negative \n\u003cA NAME=\"936\"\u003e\u003c/A\u003epremiss. For in fact what is an attribute of no A will not be an attribute \n\u003cA NAME=\"937\"\u003e\u003c/A\u003eof any B either; and if it be yet assumed that C is universally non-attributable \n\u003cA NAME=\"938\"\u003e\u003c/A\u003eto A, but a universal attribute of B, the premiss C-A is true but the minor \n\u003cA NAME=\"939\"\u003e\u003c/A\u003ewholly false. Again, in fact it is false to assume that that which is an \n\u003cA NAME=\"940\"\u003e\u003c/A\u003eattribute of all B is an attribute of no A, for if it be an attribute of \n\u003cA NAME=\"941\"\u003e\u003c/A\u003eall B, it must be an attribute of some A. If then C is nevertheless assumed \n\u003cA NAME=\"942\"\u003e\u003c/A\u003eto be an attribute of all B but of no A, C-B will be true but C-A \n\u003cA NAME=\"943\"\u003e\u003c/A\u003efalse.\n\u003cA NAME=\"944\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is thus clear that in the case of atomic propositions erroneous \n\u003cA NAME=\"945\"\u003e\u003c/A\u003einference will be possible not only when both premisses are false but also \n\u003cA NAME=\"946\"\u003e\u003c/A\u003ewhen only one is false.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"947\"\u003e\u003c/A\u003e\u003cB\u003ePart 17\u003c/B\u003e\n\n\u003cA NAME=\"948\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIn the case of attributes not atomically connected with or disconnected \n\u003cA NAME=\"949\"\u003e\u003c/A\u003efrom their subjects, (a) (i) as long as the false conclusion is inferred \n\u003cA NAME=\"950\"\u003e\u003c/A\u003ethrough the \u0027appropriate\u0027 middle, only the major and not both premisses \n\u003cA NAME=\"951\"\u003e\u003c/A\u003ecan be false. By \u0027appropriate middle\u0027 I mean the middle term through which \n\u003cA NAME=\"952\"\u003e\u003c/A\u003ethe contradictory-i.e. the true-conclusion is inferrible. Thus, let A be \n\u003cA NAME=\"953\"\u003e\u003c/A\u003eattributable to B through a middle term C: then, since to produce a conclusion \n\u003cA NAME=\"954\"\u003e\u003c/A\u003ethe premiss C-B must be taken affirmatively, it is clear that this premiss \n\u003cA NAME=\"955\"\u003e\u003c/A\u003emust always be true, for its quality is not changed. But the major A-C \n\u003cA NAME=\"956\"\u003e\u003c/A\u003eis false, for it is by a change in the quality of A-C that the conclusion \n\u003cA NAME=\"957\"\u003e\u003c/A\u003ebecomes its contradictory-i.e. true. Similarly (ii) if the middle is taken \n\u003cA NAME=\"958\"\u003e\u003c/A\u003efrom another series of predication; e.g. suppose D to be not only contained \n\u003cA NAME=\"959\"\u003e\u003c/A\u003ewithin A as a part within its whole but also predicable of all B. Then \n\u003cA NAME=\"960\"\u003e\u003c/A\u003ethe premiss D-B must remain unchanged, but the quality of A-D must be changed; \n\u003cA NAME=\"961\"\u003e\u003c/A\u003eso that D-B is always true, A-D always false. Such error is practically \n\u003cA NAME=\"962\"\u003e\u003c/A\u003eidentical with that which is inferred through the \u0027appropriate\u0027 middle. \n\u003cA NAME=\"963\"\u003e\u003c/A\u003eOn the other hand, (b) if the conclusion is not inferred through the \u0027appropriate\u0027 \n\u003cA NAME=\"964\"\u003e\u003c/A\u003emiddle-(i) when the middle is subordinate to A but is predicable of no \n\u003cA NAME=\"965\"\u003e\u003c/A\u003eB, both premisses must be false, because if there is to be a conclusion \n\u003cA NAME=\"966\"\u003e\u003c/A\u003eboth must be posited as asserting the contrary of what is actually the \n\u003cA NAME=\"967\"\u003e\u003c/A\u003efact, and so posited both become false: e.g. suppose that actually all \n\u003cA NAME=\"968\"\u003e\u003c/A\u003eD is A but no B is D; then if these premisses are changed in quality, a \n\u003cA NAME=\"969\"\u003e\u003c/A\u003econclusion will follow and both of the new premisses will be false. When, \n\u003cA NAME=\"970\"\u003e\u003c/A\u003ehowever, (ii) the middle D is not subordinate to A, A-D will be true, D-B \n\u003cA NAME=\"971\"\u003e\u003c/A\u003efalse-A-D true because A was not subordinate to D, D-B false because if \n\u003cA NAME=\"972\"\u003e\u003c/A\u003eit had been true, the conclusion too would have been true; but it is ex \n\u003cA NAME=\"973\"\u003e\u003c/A\u003ehypothesi false.\n\u003cA NAME=\"974\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWhen the erroneous inference is in the second figure, both premisses \n\u003cA NAME=\"975\"\u003e\u003c/A\u003ecannot be entirely false; since if B is subordinate to A, there can be \n\u003cA NAME=\"976\"\u003e\u003c/A\u003eno middle predicable of all of one extreme and of none of the other, as \n\u003cA NAME=\"977\"\u003e\u003c/A\u003ewas stated before. One premiss, however, may be false, and it may be either \n\u003cA NAME=\"978\"\u003e\u003c/A\u003eof them. Thus, if C is actually an attribute of both A and B, but is assumed \n\u003cA NAME=\"979\"\u003e\u003c/A\u003eto be an attribute of A only and not of B, C-A will be true, C-B false: \n\u003cA NAME=\"980\"\u003e\u003c/A\u003eor again if C be assumed to be attributable to B but to no A, C-B will \n\u003cA NAME=\"981\"\u003e\u003c/A\u003ebe true, C-A false.\n\u003cA NAME=\"982\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWe have stated when and through what kinds of premisses error will \n\u003cA NAME=\"983\"\u003e\u003c/A\u003eresult in cases where the erroneous conclusion is negative. If the conclusion \n\u003cA NAME=\"984\"\u003e\u003c/A\u003eis affirmative, (a) (i) it may be inferred through the \u0027appropriate\u0027 middle \n\u003cA NAME=\"985\"\u003e\u003c/A\u003eterm. In this case both premisses cannot be false since, as we said before, \n\u003cA NAME=\"986\"\u003e\u003c/A\u003eC-B must remain unchanged if there is to be a conclusion, and consequently \n\u003cA NAME=\"987\"\u003e\u003c/A\u003eA-C, the quality of which is changed, will always be false. This is equally \n\u003cA NAME=\"988\"\u003e\u003c/A\u003etrue if (ii) the middle is taken from another series of predication, as \n\u003cA NAME=\"989\"\u003e\u003c/A\u003ewas stated to be the case also with regard to negative error; for D-B must \n\u003cA NAME=\"990\"\u003e\u003c/A\u003eremain unchanged, while the quality of A-D must be converted, and the type \n\u003cA NAME=\"991\"\u003e\u003c/A\u003eof error is the same as before.\n\u003cA NAME=\"992\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003e(b) The middle may be inappropriate. Then (i) if D is subordinate \n\u003cA NAME=\"993\"\u003e\u003c/A\u003eto A, A-D will be true, but D-B false; since A may quite well be predicable \n\u003cA NAME=\"994\"\u003e\u003c/A\u003eof several terms no one of which can be subordinated to another. If, however, \n\u003cA NAME=\"995\"\u003e\u003c/A\u003e(ii) D is not subordinate to A, obviously A-D, since it is affirmed, will \n\u003cA NAME=\"996\"\u003e\u003c/A\u003ealways be false, while D-B may be either true or false; for A may very \n\u003cA NAME=\"997\"\u003e\u003c/A\u003ewell be an attribute of no D, whereas all B is D, e.g. no science is animal, \n\u003cA NAME=\"998\"\u003e\u003c/A\u003eall music is science. Equally well A may be an attribute of no D, and D \n\u003cA NAME=\"999\"\u003e\u003c/A\u003eof no B. It emerges, then, that if the middle term is not subordinate to \n\u003cA NAME=\"1000\"\u003e\u003c/A\u003ethe major, not only both premisses but either singly may be \n\u003cA NAME=\"1001\"\u003e\u003c/A\u003efalse.\n\u003cA NAME=\"1002\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThus we have made it clear how many varieties of erroneous inference \n\u003cA NAME=\"1003\"\u003e\u003c/A\u003eare liable to happen and through what kinds of premisses they occur, in \n\u003cA NAME=\"1004\"\u003e\u003c/A\u003ethe case both of immediate and of demonstrable truths.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"1005\"\u003e\u003c/A\u003e\u003cB\u003ePart 18\u003c/B\u003e\n\n\u003cA NAME=\"1006\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is also clear that the loss of any one of the senses entails \n\u003cA NAME=\"1007\"\u003e\u003c/A\u003ethe loss of a corresponding portion of knowledge, and that, since we learn \n\u003cA NAME=\"1008\"\u003e\u003c/A\u003eeither by induction or by demonstration, this knowledge cannot be acquired. \n\u003cA NAME=\"1009\"\u003e\u003c/A\u003eThus demonstration develops from universals, induction from particulars; \n\u003cA NAME=\"1010\"\u003e\u003c/A\u003ebut since it is possible to familiarize the pupil with even the so-called \n\u003cA NAME=\"1011\"\u003e\u003c/A\u003emathematical abstractions only through induction-i.e. only because each \n\u003cA NAME=\"1012\"\u003e\u003c/A\u003esubject genus possesses, in virtue of a determinate mathematical character, \n\u003cA NAME=\"1013\"\u003e\u003c/A\u003ecertain properties which can be treated as separate even though they do \n\u003cA NAME=\"1014\"\u003e\u003c/A\u003enot exist in isolation-it is consequently impossible to come to grasp universals \n\u003cA NAME=\"1015\"\u003e\u003c/A\u003eexcept through induction. But induction is impossible for those who have \n\u003cA NAME=\"1016\"\u003e\u003c/A\u003enot sense-perception. For it is sense-perception alone which is adequate \n\u003cA NAME=\"1017\"\u003e\u003c/A\u003efor grasping the particulars: they cannot be objects of scientific knowledge, \n\u003cA NAME=\"1018\"\u003e\u003c/A\u003ebecause neither can universals give us knowledge of them without induction, \n\u003cA NAME=\"1019\"\u003e\u003c/A\u003enor can we get it through induction without sense-perception.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"1020\"\u003e\u003c/A\u003e\u003cB\u003ePart 19\u003c/B\u003e\n\n\u003cA NAME=\"1021\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eEvery syllogism is effected by means of three terms. One kind of \n\u003cA NAME=\"1022\"\u003e\u003c/A\u003esyllogism serves to prove that A inheres in C by showing that A inheres \n\u003cA NAME=\"1023\"\u003e\u003c/A\u003ein B and B in C; the other is negative and one of its premisses asserts \n\u003cA NAME=\"1024\"\u003e\u003c/A\u003eone term of another, while the other denies one term of another. It is \n\u003cA NAME=\"1025\"\u003e\u003c/A\u003eclear, then, that these are the fundamentals and so-called hypotheses of \n\u003cA NAME=\"1026\"\u003e\u003c/A\u003esyllogism. Assume them as they have been stated, and proof is bound to \n\u003cA NAME=\"1027\"\u003e\u003c/A\u003efollow-proof that A inheres in C through B, and again that A inheres in \n\u003cA NAME=\"1028\"\u003e\u003c/A\u003eB through some other middle term, and similarly that B inheres in C. If \n\u003cA NAME=\"1029\"\u003e\u003c/A\u003eour reasoning aims at gaining credence and so is merely dialectical, it \n\u003cA NAME=\"1030\"\u003e\u003c/A\u003eis obvious that we have only to see that our inference is based on premisses \n\u003cA NAME=\"1031\"\u003e\u003c/A\u003eas credible as possible: so that if a middle term between A and B is credible \n\u003cA NAME=\"1032\"\u003e\u003c/A\u003ethough not real, one can reason through it and complete a dialectical syllogism. \n\u003cA NAME=\"1033\"\u003e\u003c/A\u003eIf, however, one is aiming at truth, one must be guided by the real connexions \n\u003cA NAME=\"1034\"\u003e\u003c/A\u003eof subjects and attributes. Thus: since there are attributes which are \n\u003cA NAME=\"1035\"\u003e\u003c/A\u003epredicated of a subject essentially or naturally and not coincidentally-not, \n\u003cA NAME=\"1036\"\u003e\u003c/A\u003ethat is, in the sense in which we say \u0027That white (thing) is a man\u0027, which \n\u003cA NAME=\"1037\"\u003e\u003c/A\u003eis not the same mode of predication as when we say \u0027The man is white\u0027: \n\u003cA NAME=\"1038\"\u003e\u003c/A\u003ethe man is white not because he is something else but because he is man, \n\u003cA NAME=\"1039\"\u003e\u003c/A\u003ebut the white is man because \u0027being white\u0027 coincides with \u0027humanity\u0027 within \n\u003cA NAME=\"1040\"\u003e\u003c/A\u003eone substratum-therefore there are terms such as are naturally subjects \n\u003cA NAME=\"1041\"\u003e\u003c/A\u003eof predicates. Suppose, then, C such a term not itself attributable to \n\u003cA NAME=\"1042\"\u003e\u003c/A\u003eanything else as to a subject, but the proximate subject of the attribute \n\u003cA NAME=\"1043\"\u003e\u003c/A\u003eB–i.e. so that B-C is immediate; suppose further E related immediately \n\u003cA NAME=\"1044\"\u003e\u003c/A\u003eto F, and F to B. The first question is, must this series terminate, or \n\u003cA NAME=\"1045\"\u003e\u003c/A\u003ecan it proceed to infinity? The second question is as follows: Suppose \n\u003cA NAME=\"1046\"\u003e\u003c/A\u003enothing is essentially predicated of A, but A is predicated primarily of \n\u003cA NAME=\"1047\"\u003e\u003c/A\u003eH and of no intermediate prior term, and suppose H similarly related to \n\u003cA NAME=\"1048\"\u003e\u003c/A\u003eG and G to B; then must this series also terminate, or can it too proceed \n\u003cA NAME=\"1049\"\u003e\u003c/A\u003eto infinity? There is this much difference between the questions: the first \n\u003cA NAME=\"1050\"\u003e\u003c/A\u003eis, is it possible to start from that which is not itself attributable \n\u003cA NAME=\"1051\"\u003e\u003c/A\u003eto anything else but is the subject of attributes, and ascend to infinity? \n\u003cA NAME=\"1052\"\u003e\u003c/A\u003eThe second is the problem whether one can start from that which is a predicate \n\u003cA NAME=\"1053\"\u003e\u003c/A\u003ebut not itself a subject of predicates, and descend to infinity? A third \n\u003cA NAME=\"1054\"\u003e\u003c/A\u003equestion is, if the extreme terms are fixed, can there be an infinity of \n\u003cA NAME=\"1055\"\u003e\u003c/A\u003emiddles? I mean this: suppose for example that A inheres in C and B is \n\u003cA NAME=\"1056\"\u003e\u003c/A\u003eintermediate between them, but between B and A there are other middles, \n\u003cA NAME=\"1057\"\u003e\u003c/A\u003eand between these again fresh middles; can these proceed to infinity or \n\u003cA NAME=\"1058\"\u003e\u003c/A\u003ecan they not? This is the equivalent of inquiring, do demonstrations proceed \n\u003cA NAME=\"1059\"\u003e\u003c/A\u003eto infinity, i.e. is everything demonstrable? Or do ultimate subject and \n\u003cA NAME=\"1060\"\u003e\u003c/A\u003eprimary attribute limit one another?\n\u003cA NAME=\"1061\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eI hold that the same questions arise with regard to negative conclusions \n\u003cA NAME=\"1062\"\u003e\u003c/A\u003eand premisses: viz. if A is attributable to no B, then either this predication \n\u003cA NAME=\"1063\"\u003e\u003c/A\u003ewill be primary, or there will be an intermediate term prior to B to which \n\u003cA NAME=\"1064\"\u003e\u003c/A\u003ea is not attributable-G, let us say, which is attributable to all B-and \n\u003cA NAME=\"1065\"\u003e\u003c/A\u003ethere may still be another term H prior to G, which is attributable to \n\u003cA NAME=\"1066\"\u003e\u003c/A\u003eall G. The same questions arise, I say, because in these cases too either \n\u003cA NAME=\"1067\"\u003e\u003c/A\u003ethe series of prior terms to which a is not attributable is infinite or \n\u003cA NAME=\"1068\"\u003e\u003c/A\u003eit terminates.\n\u003cA NAME=\"1069\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eOne cannot ask the same questions in the case of reciprocating \n\u003cA NAME=\"1070\"\u003e\u003c/A\u003eterms, since when subject and predicate are convertible there is neither \n\u003cA NAME=\"1071\"\u003e\u003c/A\u003eprimary nor ultimate subject, seeing that all the reciprocals qua subjects \n\u003cA NAME=\"1072\"\u003e\u003c/A\u003estand in the same relation to one another, whether we say that the subject \n\u003cA NAME=\"1073\"\u003e\u003c/A\u003ehas an infinity of attributes or that both subjects and attributes-and \n\u003cA NAME=\"1074\"\u003e\u003c/A\u003ewe raised the question in both cases-are infinite in number. These questions \n\u003cA NAME=\"1075\"\u003e\u003c/A\u003ethen cannot be asked-unless, indeed, the terms can reciprocate by two different \n\u003cA NAME=\"1076\"\u003e\u003c/A\u003emodes, by accidental predication in one relation and natural predication \n\u003cA NAME=\"1077\"\u003e\u003c/A\u003ein the other.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"1078\"\u003e\u003c/A\u003e\u003cB\u003ePart 20\u003c/B\u003e\n\n\u003cA NAME=\"1079\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eNow, it is clear that if the predications terminate in both the \n\u003cA NAME=\"1080\"\u003e\u003c/A\u003eupward and the downward direction (by \u0027upward\u0027 I mean the ascent to the \n\u003cA NAME=\"1081\"\u003e\u003c/A\u003emore universal, by \u0027downward\u0027 the descent to the more particular), the \n\u003cA NAME=\"1082\"\u003e\u003c/A\u003emiddle terms cannot be infinite in number. For suppose that A is predicated \n\u003cA NAME=\"1083\"\u003e\u003c/A\u003eof F, and that the intermediates-call them BB\u0027B\"…-are infinite, then \n\u003cA NAME=\"1084\"\u003e\u003c/A\u003eclearly you might descend from and find one term predicated of another \n\u003cA NAME=\"1085\"\u003e\u003c/A\u003ead infinitum, since you have an infinity of terms between you and F; and \n\u003cA NAME=\"1086\"\u003e\u003c/A\u003eequally, if you ascend from F, there are infinite terms between you and \n\u003cA NAME=\"1087\"\u003e\u003c/A\u003eA. It follows that if these processes are impossible there cannot be an \n\u003cA NAME=\"1088\"\u003e\u003c/A\u003einfinity of intermediates between A and F. Nor is it of any effect to urge \n\u003cA NAME=\"1089\"\u003e\u003c/A\u003ethat some terms of the series AB…F are contiguous so as to exclude intermediates, \n\u003cA NAME=\"1090\"\u003e\u003c/A\u003ewhile others cannot be taken into the argument at all: whichever terms \n\u003cA NAME=\"1091\"\u003e\u003c/A\u003eof the series B…I take, the number of intermediates in the direction \n\u003cA NAME=\"1092\"\u003e\u003c/A\u003eeither of A or of F must be finite or infinite: where the infinite series \n\u003cA NAME=\"1093\"\u003e\u003c/A\u003estarts, whether from the first term or from a lat\r\n\u003chr\u003e\r\n\u003cTABLE BORDER=\"0\" CELLSPACING=\"15\"\u003e\n\u003cTR ALIGN=\"CENTER\" VALIGN=\"CENTER\"\u003e\n\u003cTD ALIGN=\"CENTER\" VALIGN=\"BOTTOM\" NOWRAP\u003e\u003ca href=\"/index.html\"Go to home page\u0027; return true;\" TARGET=\"_top\"\u003e \u003c/A\u003e\n\u003cFONT SIZE=\"-1\"\u003e\u003cBR\u003e\u003ca href=\"/index.html\"Go to home page\u0027; return true;\" TARGET=\"_top\"\u003eHome\u003c/A\u003e\u003cBR\u003e\u0026nbsp;\u003c/FONT\u003e\u003c/TD\u003e\n\n\u003cTD ALIGN=\"CENTER\" VALIGN=\"BOTTOM\" NOWRAP\u003e\u003ca href=\"/Browse/index-Aristotle.html\"Browse a list of titles\u0027; return true;\" TARGET=\"_top\"\u003e \u003c/A\u003e\n\u003cFONT SIZE=\"-1\"\u003e\u003cBR\u003e\u003ca href=\"/Browse/index-Aristotle.html\"Browse a list of titles\u0027; return true;\" TARGET=\"_top\"\u003eBrowse and\u003cBR\u003eComment\u003c/A\u003e\u003c/FONT\u003e\u003c/TD\u003e\n\n\u003cTD ALIGN=\"CENTER\" VALIGN=\"BOTTOM\" NOWRAP\u003e\u003ca href=\"/Search/index.html\"Search texts\u0027; return true;\" TARGET=\"_top\"\u003e \u003c/A\u003e\n\u003cFONT SIZE=\"-1\"\u003e\u003cBR\u003e\u003ca href=\"/Search/index.html\"Search texts\u0027; return true;\" TARGET=\"_top\"\u003eSearch\u003c/A\u003e\u003cBR\u003e\u0026nbsp;\u003c/FONT\u003e\u003c/TD\u003e\n\n\u003cTD ALIGN=\"CENTER\" VALIGN=\"BOTTOM\" NOWRAP\u003e\u003ca href=\"/Buy/Aristotle.html\"Buy books and CD-ROMs\u0027; return true;\" TARGET=\"_top\"\u003e \u003c/A\u003e\n\u003cFONT SIZE=\"-1\"\u003e\u003cBR\u003e\u003ca href=\"/Buy/Aristotle.html\"Buy books and CD-ROMs\u0027; return true;\" TARGET=\"_top\"\u003eBuy Books and\u003cBR\u003eCD-ROMs\u003c/A\u003e\u003c/FONT\u003e\u003c/TD\u003e\n\n\u003cTD ALIGN=\"CENTER\" VALIGN=\"BOTTOM\" NOWRAP\u003e\u003ca href=\"/Help/general.html\"Get help\u0027; return true;\" TARGET=\"_top\"\u003e \u003c/A\u003e\n\u003cFONT SIZE=\"-1\"\u003e\u003cBR\u003e\u003ca href=\"/Help/general.html\"Get help\u0027; return true;\" TARGET=\"_top\"\u003eHelp\u003c/A\u003e\u003cBR\u003e\u0026nbsp;\u003c/FONT\u003e\u003c/TD\u003e\n\n\u003c/TR\u003e\n\u003c/TABLE\u003e\n\n\u003cHR SIZE=\"1\" COLOR=\"990033\" NOSHADE WIDTH=\"30%\"\u003e\n\u003cBR\u003e\n\u003cFONT SIZE=\"+2\"\u003e\u003cB\u003ePosterior Analytics\u003c/B\u003e\u003c/FONT\u003e\n\u003cFONT SIZE=\"+1\"\u003e\u003cBR\u003e\u003cBR\u003eBy Aristotle\u003c/FONT\u003e\n\n\u003cBLOCKQUOTE\u003e\u003cB\u003eCommentary:\u003c/B\u003e A few comments have been posted about\n\u003cU\u003ePosterior Analytics\u003c/U\u003e.\n\n\u003cBR\u003e\u003cBR\u003e\u003cB\u003eDownload:\u003c/B\u003e A \ntext-only version is \u003cA HREF=\"posterior.mb.txt\"Download text-only version\u0027; return true;\"\u003eavailable for download\u003c/A\u003e.\n\n\u003cBR\u003e\u003cHR SIZE=\"1\" COLOR=\"990033\" NOSHADE\u003e\u003cBR\u003e\n\n\u003cA NAME=\"1\"\u003e\u003c/A\u003e\u003cFONT SIZE=\"+1\"\u003e\u003cB\u003ePosterior Analytics\u003c/B\u003e\u003c/FONT\u003e\n\u003cA NAME=\"2\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eBy Aristotle\n\u003cA NAME=\"3\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWritten 350 B.C.E\n\u003cBR\u003e\u003cBR\u003eTranslated by G. R. G. Mure\n\n\u003cBR\u003e\u003cTABLE WIDTH=\"60%\" BORDER=\"0\"\u003e\n\u003cTR VALIGN=\"TOP\"\u003e\n\u003cTD ALIGN=\"LEFT\" WIDTH=\"30%\" NOWRAP\u003e\u003cA HREF=\"posterior.1.i.html\"Book I\u0027; return true;\"\u003e \u003c/A\u003e\n\n\u0026nbsp;\u0026nbsp;\u0026nbsp;\u003c/TD\u003e\n\u003cTD ALIGN=\"CENTER\" NOWRAP\u003e\u003cA HREF=\"posterior.html\"Go to table of contents\u0027; return true;\"\u003eTable of Contents\u003c/A\u003e\n\u003cBR\u003e\u003cBR\u003e\u003cFONT SIZE=\"+1\"\u003e\u003cB\u003eBook II\u003c/B\u003e\u003c/FONT\u003e\u003c/TD\u003e\n\u003cTD ALIGN=\"RIGHT\" WIDTH=\"30%\" NOWRAP\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u003c/TD\u003e\n\u003c/TR\u003e\n\u003c/TABLE\u003e\n\u003cBR\u003e\n\u003cA NAME=\"start\"\u003e\u003c/A\u003e\n\n\u003cA NAME=\"10\"\u003e\u003c/A\u003e\u003cB\u003ePart 1\u003c/B\u003e\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"11\"\u003e\u003c/A\u003eThe kinds of question we ask are as many as the kinds of things which we \n\u003cA NAME=\"12\"\u003e\u003c/A\u003eknow. They are in fact four:-(1) whether the connexion of an attribute \n\u003cA NAME=\"13\"\u003e\u003c/A\u003ewith a thing is a fact, (2) what is the reason of the connexion, (3) whether \n\u003cA NAME=\"14\"\u003e\u003c/A\u003ea thing exists, (4) What is the nature of the thing. Thus, when our question \n\u003cA NAME=\"15\"\u003e\u003c/A\u003econcerns a complex of thing and attribute and we ask whether the thing \n\u003cA NAME=\"16\"\u003e\u003c/A\u003eis thus or otherwise qualified-whether, e.g. the sun suffers eclipse or \n\u003cA NAME=\"17\"\u003e\u003c/A\u003enot-then we are asking as to the fact of a connexion. That our inquiry \n\u003cA NAME=\"18\"\u003e\u003c/A\u003eceases with the discovery that the sun does suffer eclipse is an indication \n\u003cA NAME=\"19\"\u003e\u003c/A\u003eof this; and if we know from the start that the sun suffers eclipse, we \n\u003cA NAME=\"20\"\u003e\u003c/A\u003edo not inquire whether it does so or not. On the other hand, when we know \n\u003cA NAME=\"21\"\u003e\u003c/A\u003ethe fact we ask the reason; as, for example, when we know that the sun \n\u003cA NAME=\"22\"\u003e\u003c/A\u003eis being eclipsed and that an earthquake is in progress, it is the reason \n\u003cA NAME=\"23\"\u003e\u003c/A\u003eof eclipse or earthquake into which we inquire.\n\u003cA NAME=\"24\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWhere a complex is concerned, then, those are the two questions \n\u003cA NAME=\"25\"\u003e\u003c/A\u003ewe ask; but for some objects of inquiry we have a different kind of question \n\u003cA NAME=\"26\"\u003e\u003c/A\u003eto ask, such as whether there is or is not a centaur or a God. (By \u0027is \n\u003cA NAME=\"27\"\u003e\u003c/A\u003eor is not\u0027 I mean \u0027is or is not, without further qualification\u0027; as opposed \n\u003cA NAME=\"28\"\u003e\u003c/A\u003eto \u0027is or is not [e.g.] white\u0027.) On the other hand, when we have ascertained \n\u003cA NAME=\"29\"\u003e\u003c/A\u003ethe thing\u0027s existence, we inquire as to its nature, asking, for instance, \n\u003cA NAME=\"30\"\u003e\u003c/A\u003e\u0027what, then, is God?\u0027 or \u0027what is man?\u0027.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"31\"\u003e\u003c/A\u003e\u003cB\u003ePart 2\u003c/B\u003e\n\n\u003cA NAME=\"32\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThese, then, are the four kinds of question we ask, and it is in \n\u003cA NAME=\"33\"\u003e\u003c/A\u003ethe answers to these questions that our knowledge consists.\n\u003cA NAME=\"34\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eNow when we ask whether a connexion is a fact, or whether a thing \n\u003cA NAME=\"35\"\u003e\u003c/A\u003ewithout qualification is, we are really asking whether the connexion or \n\u003cA NAME=\"36\"\u003e\u003c/A\u003ethe thing has a \u0027middle\u0027; and when we have ascertained either that the \n\u003cA NAME=\"37\"\u003e\u003c/A\u003econnexion is a fact or that the thing is-i.e. ascertained either the partial \n\u003cA NAME=\"38\"\u003e\u003c/A\u003eor the unqualified being of the thing-and are proceeding to ask the reason \n\u003cA NAME=\"39\"\u003e\u003c/A\u003eof the connexion or the nature of the thing, then we are asking what the \n\u003cA NAME=\"40\"\u003e\u003c/A\u003e\u0027middle\u0027 is.\n\u003cA NAME=\"41\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003e(By distinguishing the fact of the connexion and the existence \n\u003cA NAME=\"42\"\u003e\u003c/A\u003eof the thing as respectively the partial and the unqualified being of the \n\u003cA NAME=\"43\"\u003e\u003c/A\u003ething, I mean that if we ask \u0027does the moon suffer eclipse?\u0027, or \u0027does \n\u003cA NAME=\"44\"\u003e\u003c/A\u003ethe moon wax?\u0027, the question concerns a part of the thing\u0027s being; for \n\u003cA NAME=\"45\"\u003e\u003c/A\u003ewhat we are asking in such questions is whether a thing is this or that, \n\u003cA NAME=\"46\"\u003e\u003c/A\u003ei.e. has or has not this or that attribute: whereas, if we ask whether \n\u003cA NAME=\"47\"\u003e\u003c/A\u003ethe moon or night exists, the question concerns the unqualified being of \n\u003cA NAME=\"48\"\u003e\u003c/A\u003ea thing.)\n\u003cA NAME=\"49\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWe conclude that in all our inquiries we are asking either whether \n\u003cA NAME=\"50\"\u003e\u003c/A\u003ethere is a \u0027middle\u0027 or what the \u0027middle\u0027 is: for the \u0027middle\u0027 here is precisely \n\u003cA NAME=\"51\"\u003e\u003c/A\u003ethe cause, and it is the cause that we seek in all our inquiries. Thus, \n\u003cA NAME=\"52\"\u003e\u003c/A\u003e\u0027Does the moon suffer eclipse?\u0027 means \u0027Is there or is there not a cause \n\u003cA NAME=\"53\"\u003e\u003c/A\u003eproducing eclipse of the moon?\u0027, and when we have learnt that there is, \n\u003cA NAME=\"54\"\u003e\u003c/A\u003eour next question is, \u0027What, then, is this cause? for the cause through \n\u003cA NAME=\"55\"\u003e\u003c/A\u003ewhich a thing is-not is this or that, i.e. has this or that attribute, \n\u003cA NAME=\"56\"\u003e\u003c/A\u003ebut without qualification is-and the cause through which it is-not is without \n\u003cA NAME=\"57\"\u003e\u003c/A\u003equalification, but is this or that as having some essential attribute or \n\u003cA NAME=\"58\"\u003e\u003c/A\u003esome accident-are both alike the middle\u0027. By that which is without qualification \n\u003cA NAME=\"59\"\u003e\u003c/A\u003eI mean the subject, e.g. moon or earth or sun or triangle; by that which \n\u003cA NAME=\"60\"\u003e\u003c/A\u003ea subject is (in the partial sense) I mean a property, e.g. eclipse, equality \n\u003cA NAME=\"61\"\u003e\u003c/A\u003eor inequality, interposition or non-interposition. For in all these examples \n\u003cA NAME=\"62\"\u003e\u003c/A\u003eit is clear that the nature of the thing and the reason of the fact are \n\u003cA NAME=\"63\"\u003e\u003c/A\u003eidentical: the question \u0027What is eclipse?\u0027 and its answer \u0027The privation \n\u003cA NAME=\"64\"\u003e\u003c/A\u003eof the moon\u0027s light by the interposition of the earth\u0027 are identical with \n\u003cA NAME=\"65\"\u003e\u003c/A\u003ethe question \u0027What is the reason of eclipse?\u0027 or \u0027Why does the moon suffer \n\u003cA NAME=\"66\"\u003e\u003c/A\u003eeclipse?\u0027 and the reply \u0027Because of the failure of light through the earth\u0027s \n\u003cA NAME=\"67\"\u003e\u003c/A\u003eshutting it out\u0027. Again, for \u0027What is a concord? A commensurate numerical \n\u003cA NAME=\"68\"\u003e\u003c/A\u003eratio of a high and a low note\u0027, we may substitute \u0027What ratio makes a \n\u003cA NAME=\"69\"\u003e\u003c/A\u003ehigh and a low note concordant? Their relation according to a commensurate \n\u003cA NAME=\"70\"\u003e\u003c/A\u003enumerical ratio.\u0027 \u0027Are the high and the low note concordant?\u0027 is equivalent \n\u003cA NAME=\"71\"\u003e\u003c/A\u003eto \u0027Is their ratio commensurate?\u0027; and when we find that it is commensurate, \n\u003cA NAME=\"72\"\u003e\u003c/A\u003ewe ask \u0027What, then, is their ratio?\u0027.\n\u003cA NAME=\"73\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eCases in which the \u0027middle\u0027 is sensible show that the object of \n\u003cA NAME=\"74\"\u003e\u003c/A\u003eour inquiry is always the \u0027middle\u0027: we inquire, because we have not perceived \n\u003cA NAME=\"75\"\u003e\u003c/A\u003eit, whether there is or is not a \u0027middle\u0027 causing, e.g. an eclipse. On \n\u003cA NAME=\"76\"\u003e\u003c/A\u003ethe other hand, if we were on the moon we should not be inquiring either \n\u003cA NAME=\"77\"\u003e\u003c/A\u003eas to the fact or the reason, but both fact and reason would be obvious \n\u003cA NAME=\"78\"\u003e\u003c/A\u003esimultaneously. For the act of perception would have enabled us to know \n\u003cA NAME=\"79\"\u003e\u003c/A\u003ethe universal too; since, the present fact of an eclipse being evident, \n\u003cA NAME=\"80\"\u003e\u003c/A\u003eperception would then at the same time give us the present fact of the \n\u003cA NAME=\"81\"\u003e\u003c/A\u003eearth\u0027s screening the sun\u0027s light, and from this would arise the \n\u003cA NAME=\"82\"\u003e\u003c/A\u003euniversal.\n\u003cA NAME=\"83\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThus, as we maintain, to know a thing\u0027s nature is to know the reason \n\u003cA NAME=\"84\"\u003e\u003c/A\u003ewhy it is; and this is equally true of things in so far as they are said \n\u003cA NAME=\"85\"\u003e\u003c/A\u003ewithout qualification to he as opposed to being possessed of some attribute, \n\u003cA NAME=\"86\"\u003e\u003c/A\u003eand in so far as they are said to be possessed of some attribute such as \n\u003cA NAME=\"87\"\u003e\u003c/A\u003eequal to right angles, or greater or less.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"88\"\u003e\u003c/A\u003e\u003cB\u003ePart 3\u003c/B\u003e\n\n\u003cA NAME=\"89\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is clear, then, that all questions are a search for a \u0027middle\u0027. \n\u003cA NAME=\"90\"\u003e\u003c/A\u003eLet us now state how essential nature is revealed and in what way it can \n\u003cA NAME=\"91\"\u003e\u003c/A\u003ebe reduced to demonstration; what definition is, and what things are definable. \n\u003cA NAME=\"92\"\u003e\u003c/A\u003eAnd let us first discuss certain difficulties which these questions raise, \n\u003cA NAME=\"93\"\u003e\u003c/A\u003ebeginning what we have to say with a point most intimately connected with \n\u003cA NAME=\"94\"\u003e\u003c/A\u003eour immediately preceding remarks, namely the doubt that might be felt \n\u003cA NAME=\"95\"\u003e\u003c/A\u003eas to whether or not it is possible to know the same thing in the same \n\u003cA NAME=\"96\"\u003e\u003c/A\u003erelation, both by definition and by demonstration. It might, I mean, be \n\u003cA NAME=\"97\"\u003e\u003c/A\u003eurged that definition is held to concern essential nature and is in every \n\u003cA NAME=\"98\"\u003e\u003c/A\u003ecase universal and affirmative; whereas, on the other hand, some conclusions \n\u003cA NAME=\"99\"\u003e\u003c/A\u003eare negative and some are not universal; e.g. all in the second figure \n\u003cA NAME=\"100\"\u003e\u003c/A\u003eare negative, none in the third are universal. And again, not even all \n\u003cA NAME=\"101\"\u003e\u003c/A\u003eaffirmative conclusions in the first figure are definable, e.g. \u0027every \n\u003cA NAME=\"102\"\u003e\u003c/A\u003etriangle has its angles equal to two right angles\u0027. An argument proving \n\u003cA NAME=\"103\"\u003e\u003c/A\u003ethis difference between demonstration and definition is that to have scientific \n\u003cA NAME=\"104\"\u003e\u003c/A\u003eknowledge of the demonstrable is identical with possessing a demonstration \n\u003cA NAME=\"105\"\u003e\u003c/A\u003eof it: hence if demonstration of such conclusions as these is possible, \n\u003cA NAME=\"106\"\u003e\u003c/A\u003ethere clearly cannot also be definition of them. If there could, one might \n\u003cA NAME=\"107\"\u003e\u003c/A\u003eknow such a conclusion also in virtue of its definition without possessing \n\u003cA NAME=\"108\"\u003e\u003c/A\u003ethe demonstration of it; for there is nothing to stop our having the one \n\u003cA NAME=\"109\"\u003e\u003c/A\u003ewithout the other.\n\u003cA NAME=\"110\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eInduction too will sufficiently convince us of this difference; \n\u003cA NAME=\"111\"\u003e\u003c/A\u003efor never yet by defining anything-essential attribute or accident-did \n\u003cA NAME=\"112\"\u003e\u003c/A\u003ewe get knowledge of it. Again, if to define is to acquire knowledge of \n\u003cA NAME=\"113\"\u003e\u003c/A\u003ea substance, at any rate such attributes are not substances.\n\u003cA NAME=\"114\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is evident, then, that not everything demonstrable can be defined. \n\u003cA NAME=\"115\"\u003e\u003c/A\u003eWhat then? Can everything definable be demonstrated, or not? There is one \n\u003cA NAME=\"116\"\u003e\u003c/A\u003eof our previous arguments which covers this too. Of a single thing qua \n\u003cA NAME=\"117\"\u003e\u003c/A\u003esingle there is a single scientific knowledge. Hence, since to know the \n\u003cA NAME=\"118\"\u003e\u003c/A\u003edemonstrable scientifically is to possess the demonstration of it, an impossible \n\u003cA NAME=\"119\"\u003e\u003c/A\u003econsequence will follow:-possession of its definition without its demonstration \n\u003cA NAME=\"120\"\u003e\u003c/A\u003ewill give knowledge of the demonstrable.\n\u003cA NAME=\"121\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eMoreover, the basic premisses of demonstrations are definitions, \n\u003cA NAME=\"122\"\u003e\u003c/A\u003eand it has already been shown that these will be found indemonstrable; \n\u003cA NAME=\"123\"\u003e\u003c/A\u003eeither the basic premisses will be demonstrable and will depend on prior \n\u003cA NAME=\"124\"\u003e\u003c/A\u003epremisses, and the regress will be endless; or the primary truths will \n\u003cA NAME=\"125\"\u003e\u003c/A\u003ebe indemonstrable definitions.\n\u003cA NAME=\"126\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eBut if the definable and the demonstrable are not wholly the same, \n\u003cA NAME=\"127\"\u003e\u003c/A\u003emay they yet be partially the same? Or is that impossible, because there \n\u003cA NAME=\"128\"\u003e\u003c/A\u003ecan be no demonstration of the definable? There can be none, because definition \n\u003cA NAME=\"129\"\u003e\u003c/A\u003eis of the essential nature or being of something, and all demonstrations \n\u003cA NAME=\"130\"\u003e\u003c/A\u003eevidently posit and assume the essential nature-mathematical demonstrations, \n\u003cA NAME=\"131\"\u003e\u003c/A\u003efor example, the nature of unity and the odd, and all the other sciences \n\u003cA NAME=\"132\"\u003e\u003c/A\u003elikewise. Moreover, every demonstration proves a predicate of a subject \n\u003cA NAME=\"133\"\u003e\u003c/A\u003eas attaching or as not attaching to it, but in definition one thing is \n\u003cA NAME=\"134\"\u003e\u003c/A\u003enot predicated of another; we do not, e.g. predicate animal of biped nor \n\u003cA NAME=\"135\"\u003e\u003c/A\u003ebiped of animal, nor yet figure of plane-plane not being figure nor figure \n\u003cA NAME=\"136\"\u003e\u003c/A\u003eplane. Again, to prove essential nature is not the same as to prove the \n\u003cA NAME=\"137\"\u003e\u003c/A\u003efact of a connexion. Now definition reveals essential nature, demonstration \n\u003cA NAME=\"138\"\u003e\u003c/A\u003ereveals that a given attribute attaches or does not attach to a given subject; \n\u003cA NAME=\"139\"\u003e\u003c/A\u003ebut different things require different demonstrations-unless the one demonstration \n\u003cA NAME=\"140\"\u003e\u003c/A\u003eis related to the other as part to whole. I add this because if all triangles \n\u003cA NAME=\"141\"\u003e\u003c/A\u003ehave been proved to possess angles equal to two right angles, then this \n\u003cA NAME=\"142\"\u003e\u003c/A\u003eattribute has been proved to attach to isosceles; for isosceles is a part \n\u003cA NAME=\"143\"\u003e\u003c/A\u003eof which all triangles constitute the whole. But in the case before us \n\u003cA NAME=\"144\"\u003e\u003c/A\u003ethe fact and the essential nature are not so related to one another, since \n\u003cA NAME=\"145\"\u003e\u003c/A\u003ethe one is not a part of the other.\n\u003cA NAME=\"146\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eSo it emerges that not all the definable is demonstrable nor all \n\u003cA NAME=\"147\"\u003e\u003c/A\u003ethe demonstrable definable; and we may draw the general conclusion that \n\u003cA NAME=\"148\"\u003e\u003c/A\u003ethere is no identical object of which it is possible to possess both a \n\u003cA NAME=\"149\"\u003e\u003c/A\u003edefinition and a demonstration. It follows obviously that definition and \n\u003cA NAME=\"150\"\u003e\u003c/A\u003edemonstration are neither identical nor contained either within the other: \n\u003cA NAME=\"151\"\u003e\u003c/A\u003eif they were, their objects would be related either as identical or as \n\u003cA NAME=\"152\"\u003e\u003c/A\u003ewhole and part.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"153\"\u003e\u003c/A\u003e\u003cB\u003ePart 4\u003c/B\u003e\n\n\u003cA NAME=\"154\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eSo much, then, for the first stage of our problem. The next step \n\u003cA NAME=\"155\"\u003e\u003c/A\u003eis to raise the question whether syllogism-i.e. demonstration-of the definable \n\u003cA NAME=\"156\"\u003e\u003c/A\u003enature is possible or, as our recent argument assumed, \n\u003cA NAME=\"157\"\u003e\u003c/A\u003eimpossible.\n\u003cA NAME=\"158\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWe might argue it impossible on the following grounds:-(a) syllogism \n\u003cA NAME=\"159\"\u003e\u003c/A\u003eproves an attribute of a subject through the middle term; on the other \n\u003cA NAME=\"160\"\u003e\u003c/A\u003ehand (b) its definable nature is both \u0027peculiar\u0027 to a subject and predicated \n\u003cA NAME=\"161\"\u003e\u003c/A\u003eof it as belonging to its essence. But in that case (1) the subject, its \n\u003cA NAME=\"162\"\u003e\u003c/A\u003edefinition, and the middle term connecting them must be reciprocally predicable \n\u003cA NAME=\"163\"\u003e\u003c/A\u003eof one another; for if A is to C, obviously A is \u0027peculiar\u0027 to B and B \n\u003cA NAME=\"164\"\u003e\u003c/A\u003eto C-in fact all three terms are \u0027peculiar\u0027 to one another: and further \n\u003cA NAME=\"165\"\u003e\u003c/A\u003e(2) if A inheres in the essence of all B and B is predicated universally \n\u003cA NAME=\"166\"\u003e\u003c/A\u003eof all C as belonging to C\u0027s essence, A also must be predicated of C as \n\u003cA NAME=\"167\"\u003e\u003c/A\u003ebelonging to its essence.\n\u003cA NAME=\"168\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIf one does not take this relation as thus duplicated-if, that \n\u003cA NAME=\"169\"\u003e\u003c/A\u003eis, A is predicated as being of the essence of B, but B is not of the essence \n\u003cA NAME=\"170\"\u003e\u003c/A\u003eof the subjects of which it is predicated-A will not necessarily be predicated \n\u003cA NAME=\"171\"\u003e\u003c/A\u003eof C as belonging to its essence. So both premisses will predicate essence, \n\u003cA NAME=\"172\"\u003e\u003c/A\u003eand consequently B also will be predicated of C as its essence. Since, \n\u003cA NAME=\"173\"\u003e\u003c/A\u003etherefore, both premisses do predicate essence-i.e. definable form-C\u0027s \n\u003cA NAME=\"174\"\u003e\u003c/A\u003edefinable form will appear in the middle term before the conclusion is \n\u003cA NAME=\"175\"\u003e\u003c/A\u003edrawn.\n\u003cA NAME=\"176\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWe may generalize by supposing that it is possible to prove the \n\u003cA NAME=\"177\"\u003e\u003c/A\u003eessential nature of man. Let C be man, A man\u0027s essential nature–two-footed \n\u003cA NAME=\"178\"\u003e\u003c/A\u003eanimal, or aught else it may be. Then, if we are to syllogize, A must be \n\u003cA NAME=\"179\"\u003e\u003c/A\u003epredicated of all B. But this premiss will be mediated by a fresh definition, \n\u003cA NAME=\"180\"\u003e\u003c/A\u003ewhich consequently will also be the essential nature of man. Therefore \n\u003cA NAME=\"181\"\u003e\u003c/A\u003ethe argument assumes what it has to prove, since B too is the essential \n\u003cA NAME=\"182\"\u003e\u003c/A\u003enature of man. It is, however, the case in which there are only the two \n\u003cA NAME=\"183\"\u003e\u003c/A\u003epremisses-i.e. in which the premisses are primary and immediate-which we \n\u003cA NAME=\"184\"\u003e\u003c/A\u003eought to investigate, because it best illustrates the point under \n\u003cA NAME=\"185\"\u003e\u003c/A\u003ediscussion.\n\u003cA NAME=\"186\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThus they who prove the essential nature of soul or man or anything \n\u003cA NAME=\"187\"\u003e\u003c/A\u003eelse through reciprocating terms beg the question. It would be begging \n\u003cA NAME=\"188\"\u003e\u003c/A\u003ethe question, for example, to contend that the soul is that which causes \n\u003cA NAME=\"189\"\u003e\u003c/A\u003eits own life, and that what causes its own life is a self-moving number; \n\u003cA NAME=\"190\"\u003e\u003c/A\u003efor one would have to postulate that the soul is a self-moving number in \n\u003cA NAME=\"191\"\u003e\u003c/A\u003ethe sense of being identical with it. For if A is predicable as a mere \n\u003cA NAME=\"192\"\u003e\u003c/A\u003econsequent of B and B of C, A will not on that account be the definable \n\u003cA NAME=\"193\"\u003e\u003c/A\u003eform of C: A will merely be what it was true to say of C. Even if A is \n\u003cA NAME=\"194\"\u003e\u003c/A\u003epredicated of all B inasmuch as B is identical with a species of A, still \n\u003cA NAME=\"195\"\u003e\u003c/A\u003eit will not follow: being an animal is predicated of being a man-since \n\u003cA NAME=\"196\"\u003e\u003c/A\u003eit is true that in all instances to be human is to be animal, just as it \n\u003cA NAME=\"197\"\u003e\u003c/A\u003eis also true that every man is an animal-but not as identical with being \n\u003cA NAME=\"198\"\u003e\u003c/A\u003eman.\n\u003cA NAME=\"199\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWe conclude, then, that unless one takes both the premisses as \n\u003cA NAME=\"200\"\u003e\u003c/A\u003epredicating essence, one cannot infer that A is the definable form and \n\u003cA NAME=\"201\"\u003e\u003c/A\u003eessence of C: but if one does so take them, in assuming B one will have \n\u003cA NAME=\"202\"\u003e\u003c/A\u003eassumed, before drawing the conclusion, what the definable form of C is; \n\u003cA NAME=\"203\"\u003e\u003c/A\u003eso that there has been no inference, for one has begged the \n\u003cA NAME=\"204\"\u003e\u003c/A\u003equestion.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"205\"\u003e\u003c/A\u003e\u003cB\u003ePart 5\u003c/B\u003e\n\n\u003cA NAME=\"206\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eNor, as was said in my formal logic, is the method of division \n\u003cA NAME=\"207\"\u003e\u003c/A\u003ea process of inference at all, since at no point does the characterization \n\u003cA NAME=\"208\"\u003e\u003c/A\u003eof the subject follow necessarily from the premising of certain other facts: \n\u003cA NAME=\"209\"\u003e\u003c/A\u003edivision demonstrates as little as does induction. For in a genuine demonstration \n\u003cA NAME=\"210\"\u003e\u003c/A\u003ethe conclusion must not be put as a question nor depend on a concession, \n\u003cA NAME=\"211\"\u003e\u003c/A\u003ebut must follow necessarily from its premisses, even if the respondent \n\u003cA NAME=\"212\"\u003e\u003c/A\u003edeny it. The definer asks \u0027Is man animal or inanimate?\u0027 and then assumes-he \n\u003cA NAME=\"213\"\u003e\u003c/A\u003ehas not inferred-that man is animal. Next, when presented with an exhaustive \n\u003cA NAME=\"214\"\u003e\u003c/A\u003edivision of animal into terrestrial and aquatic, he assumes that man is \n\u003cA NAME=\"215\"\u003e\u003c/A\u003eterrestrial. Moreover, that man is the complete formula, terrestrial-animal, \n\u003cA NAME=\"216\"\u003e\u003c/A\u003edoes not follow necessarily from the premisses: this too is an assumption, \n\u003cA NAME=\"217\"\u003e\u003c/A\u003eand equally an assumption whether the division comprises many differentiae \n\u003cA NAME=\"218\"\u003e\u003c/A\u003eor few. (Indeed as this method of division is used by those who proceed \n\u003cA NAME=\"219\"\u003e\u003c/A\u003eby it, even truths that can be inferred actually fail to appear as such.) \n\u003cA NAME=\"220\"\u003e\u003c/A\u003eFor why should not the whole of this formula be true of man, and yet not \n\u003cA NAME=\"221\"\u003e\u003c/A\u003eexhibit his essential nature or definable form? Again, what guarantee is \n\u003cA NAME=\"222\"\u003e\u003c/A\u003ethere against an unessential addition, or against the omission of the final \n\u003cA NAME=\"223\"\u003e\u003c/A\u003eor of an intermediate determinant of the substantial \n\u003cA NAME=\"224\"\u003e\u003c/A\u003ebeing?\n\u003cA NAME=\"225\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThe champion of division might here urge that though these lapses \n\u003cA NAME=\"226\"\u003e\u003c/A\u003edo occur, yet we can solve that difficulty if all the attributes we assume \n\u003cA NAME=\"227\"\u003e\u003c/A\u003eare constituents of the definable form, and if, postulating the genus, \n\u003cA NAME=\"228\"\u003e\u003c/A\u003ewe produce by division the requisite uninterrupted sequence of terms, and \n\u003cA NAME=\"229\"\u003e\u003c/A\u003eomit nothing; and that indeed we cannot fail to fulfil these conditions \n\u003cA NAME=\"230\"\u003e\u003c/A\u003eif what is to be divided falls whole into the division at each stage, and \n\u003cA NAME=\"231\"\u003e\u003c/A\u003enone of it is omitted; and that this-the dividendum-must without further \n\u003cA NAME=\"232\"\u003e\u003c/A\u003equestion be (ultimately) incapable of fresh specific division. Nevertheless, \n\u003cA NAME=\"233\"\u003e\u003c/A\u003ewe reply, division does not involve inference; if it gives knowledge, it \n\u003cA NAME=\"234\"\u003e\u003c/A\u003egives it in another way. Nor is there any absurdity in this: induction, \n\u003cA NAME=\"235\"\u003e\u003c/A\u003eperhaps, is not demonstration any more than is division, et it does make \n\u003cA NAME=\"236\"\u003e\u003c/A\u003eevident some truth. Yet to state a definition reached by division is not \n\u003cA NAME=\"237\"\u003e\u003c/A\u003eto state a conclusion: as, when conclusions are drawn without their appropriate \n\u003cA NAME=\"238\"\u003e\u003c/A\u003emiddles, the alleged necessity by which the inference follows from the \n\u003cA NAME=\"239\"\u003e\u003c/A\u003epremisses is open to a question as to the reason for it, so definitions \n\u003cA NAME=\"240\"\u003e\u003c/A\u003ereached by division invite the same question.\n\u003cA NAME=\"241\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThus to the question \u0027What is the essential nature of man?\u0027 the \n\u003cA NAME=\"242\"\u003e\u003c/A\u003edivider replies \u0027Animal, mortal, footed, biped, wingless\u0027; and when at \n\u003cA NAME=\"243\"\u003e\u003c/A\u003eeach step he is asked \u0027Why?\u0027, he will say, and, as he thinks, proves by \n\u003cA NAME=\"244\"\u003e\u003c/A\u003edivision, that all animal is mortal or immortal: but such a formula taken \n\u003cA NAME=\"245\"\u003e\u003c/A\u003ein its entirety is not definition; so that even if division does demonstrate \n\u003cA NAME=\"246\"\u003e\u003c/A\u003eits formula, definition at any rate does not turn out to be a conclusion \n\u003cA NAME=\"247\"\u003e\u003c/A\u003eof inference.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"248\"\u003e\u003c/A\u003e\u003cB\u003ePart 6\u003c/B\u003e\n\n\u003cA NAME=\"249\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eCan we nevertheless actually demonstrate what a thing essentially \n\u003cA NAME=\"250\"\u003e\u003c/A\u003eand substantially is, but hypothetically, i.e. by premising (1) that its \n\u003cA NAME=\"251\"\u003e\u003c/A\u003edefinable form is constituted by the \u0027peculiar\u0027 attributes of its essential \n\u003cA NAME=\"252\"\u003e\u003c/A\u003enature; (2) that such and such are the only attributes of its essential \n\u003cA NAME=\"253\"\u003e\u003c/A\u003enature, and that the complete synthesis of them is peculiar to the thing; \n\u003cA NAME=\"254\"\u003e\u003c/A\u003eand thus-since in this synthesis consists the being of the thing-obtaining \n\u003cA NAME=\"255\"\u003e\u003c/A\u003eour conclusion? Or is the truth that, since proof must be through the middle \n\u003cA NAME=\"256\"\u003e\u003c/A\u003eterm, the definable form is once more assumed in this minor premiss \n\u003cA NAME=\"257\"\u003e\u003c/A\u003etoo?\n\u003cA NAME=\"258\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eFurther, just as in syllogizing we do not premise what syllogistic \n\u003cA NAME=\"259\"\u003e\u003c/A\u003einference is (since the premisses from which we conclude must be related \n\u003cA NAME=\"260\"\u003e\u003c/A\u003eas whole and part), so the definable form must not fall within the syllogism \n\u003cA NAME=\"261\"\u003e\u003c/A\u003ebut remain outside the premisses posited. It is only against a doubt as \n\u003cA NAME=\"262\"\u003e\u003c/A\u003eto its having been a syllogistic inference at all that we have to defend \n\u003cA NAME=\"263\"\u003e\u003c/A\u003eour argument as conforming to the definition of syllogism. It is only when \n\u003cA NAME=\"264\"\u003e\u003c/A\u003esome one doubts whether the conclusion proved is the definable form that \n\u003cA NAME=\"265\"\u003e\u003c/A\u003ewe have to defend it as conforming to the definition of definable form \n\u003cA NAME=\"266\"\u003e\u003c/A\u003ewhich we assumed. Hence syllogistic inference must be possible even without \n\u003cA NAME=\"267\"\u003e\u003c/A\u003ethe express statement of what syllogism is or what definable form \n\u003cA NAME=\"268\"\u003e\u003c/A\u003eis.\n\u003cA NAME=\"269\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThe following type of hypothetical proof also begs the question. \n\u003cA NAME=\"270\"\u003e\u003c/A\u003eIf evil is definable as the divisible, and the definition of a thing\u0027s \n\u003cA NAME=\"271\"\u003e\u003c/A\u003econtrary-if it has one the contrary of the thing\u0027s definition; then, if \n\u003cA NAME=\"272\"\u003e\u003c/A\u003egood is the contrary of evil and the indivisible of the divisible, we conclude \n\u003cA NAME=\"273\"\u003e\u003c/A\u003ethat to be good is essentially to be indivisible. The question is begged \n\u003cA NAME=\"274\"\u003e\u003c/A\u003ebecause definable form is assumed as a premiss, and as a premiss which \n\u003cA NAME=\"275\"\u003e\u003c/A\u003eis to prove definable form. \u0027But not the same definable form\u0027, you may \n\u003cA NAME=\"276\"\u003e\u003c/A\u003eobject. That I admit, for in demonstrations also we premise that \u0027this\u0027 \n\u003cA NAME=\"277\"\u003e\u003c/A\u003eis predicable of \u0027that\u0027; but in this premiss the term we assert of the \n\u003cA NAME=\"278\"\u003e\u003c/A\u003eminor is neither the major itself nor a term identical in definition, or \n\u003cA NAME=\"279\"\u003e\u003c/A\u003econvertible, with the major.\n\u003cA NAME=\"280\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eAgain, both proof by division and the syllogism just described \n\u003cA NAME=\"281\"\u003e\u003c/A\u003eare open to the question why man should be animal-biped-terrestrial and \n\u003cA NAME=\"282\"\u003e\u003c/A\u003enot merely animal and terrestrial, since what they premise does not ensure \n\u003cA NAME=\"283\"\u003e\u003c/A\u003ethat the predicates shall constitute a genuine unity and not merely belong \n\u003cA NAME=\"284\"\u003e\u003c/A\u003eto a single subject as do musical and grammatical when predicated of the \n\u003cA NAME=\"285\"\u003e\u003c/A\u003esame man.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"286\"\u003e\u003c/A\u003e\u003cB\u003ePart 7\u003c/B\u003e\n\n\u003cA NAME=\"287\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eHow then by definition shall we prove substance or essential nature? \n\u003cA NAME=\"288\"\u003e\u003c/A\u003eWe cannot show it as a fresh fact necessarily following from the assumption \n\u003cA NAME=\"289\"\u003e\u003c/A\u003eof premisses admitted to be facts-the method of demonstration: we may not \n\u003cA NAME=\"290\"\u003e\u003c/A\u003eproceed as by induction to establish a universal on the evidence of groups \n\u003cA NAME=\"291\"\u003e\u003c/A\u003eof particulars which offer no exception, because induction proves not what \n\u003cA NAME=\"292\"\u003e\u003c/A\u003ethe essential nature of a thing is but that it has or has not some attribute. \n\u003cA NAME=\"293\"\u003e\u003c/A\u003eTherefore, since presumably one cannot prove essential nature by an appeal \n\u003cA NAME=\"294\"\u003e\u003c/A\u003eto sense perception or by pointing with the finger, what other method \n\u003cA NAME=\"295\"\u003e\u003c/A\u003eremains?\n\u003cA NAME=\"296\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eTo put it another way: how shall we by definition prove essential \n\u003cA NAME=\"297\"\u003e\u003c/A\u003enature? He who knows what human-or any other-nature is, must know also \n\u003cA NAME=\"298\"\u003e\u003c/A\u003ethat man exists; for no one knows the nature of what does not exist-one \n\u003cA NAME=\"299\"\u003e\u003c/A\u003ecan know the meaning of the phrase or name \u0027goat-stag\u0027 but not what the \n\u003cA NAME=\"300\"\u003e\u003c/A\u003eessential nature of a goat-stag is. But further, if definition can prove \n\u003cA NAME=\"301\"\u003e\u003c/A\u003ewhat is the essential nature of a thing, can it also prove that it exists? \n\u003cA NAME=\"302\"\u003e\u003c/A\u003eAnd how will it prove them both by the same process, since definition exhibits \n\u003cA NAME=\"303\"\u003e\u003c/A\u003eone single thing and demonstration another single thing, and what human \n\u003cA NAME=\"304\"\u003e\u003c/A\u003enature is and the fact that man exists are not the same thing? Then too \n\u003cA NAME=\"305\"\u003e\u003c/A\u003ewe hold that it is by demonstration that the being of everything must be \n\u003cA NAME=\"306\"\u003e\u003c/A\u003eproved-unless indeed to be were its essence; and, since being is not a \n\u003cA NAME=\"307\"\u003e\u003c/A\u003egenus, it is not the essence of anything. Hence the being of anything as \n\u003cA NAME=\"308\"\u003e\u003c/A\u003efact is matter for demonstration; and this is the actual procedure of the \n\u003cA NAME=\"309\"\u003e\u003c/A\u003esciences, for the geometer assumes the meaning of the word triangle, but \n\u003cA NAME=\"310\"\u003e\u003c/A\u003ethat it is possessed of some attribute he proves. What is it, then, that \n\u003cA NAME=\"311\"\u003e\u003c/A\u003ewe shall prove in defining essential nature? Triangle? In that case a man \n\u003cA NAME=\"312\"\u003e\u003c/A\u003ewill know by definition what a thing\u0027s nature is without knowing whether \n\u003cA NAME=\"313\"\u003e\u003c/A\u003eit exists. But that is impossible.\n\u003cA NAME=\"314\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eMoreover it is clear, if we consider the methods of defining actually \n\u003cA NAME=\"315\"\u003e\u003c/A\u003ein use, that definition does not prove that the thing defined exists: since \n\u003cA NAME=\"316\"\u003e\u003c/A\u003eeven if there does actually exist something which is equidistant from a \n\u003cA NAME=\"317\"\u003e\u003c/A\u003ecentre, yet why should the thing named in the definition exist? Why, in \n\u003cA NAME=\"318\"\u003e\u003c/A\u003eother words, should this be the formula defining circle? One might equally \n\u003cA NAME=\"319\"\u003e\u003c/A\u003ewell call it the definition of mountain copper. For definitions do not \n\u003cA NAME=\"320\"\u003e\u003c/A\u003ecarry a further guarantee that the thing defined can exist or that it is \n\u003cA NAME=\"321\"\u003e\u003c/A\u003ewhat they claim to define: one can always ask why.\n\u003cA NAME=\"322\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eSince, therefore, to define is to prove either a thing\u0027s essential \n\u003cA NAME=\"323\"\u003e\u003c/A\u003enature or the meaning of its name, we may conclude that definition, if \n\u003cA NAME=\"324\"\u003e\u003c/A\u003eit in no sense proves essential nature, is a set of words signifying precisely \n\u003cA NAME=\"325\"\u003e\u003c/A\u003ewhat a name signifies. But that were a strange consequence; for (1) both \n\u003cA NAME=\"326\"\u003e\u003c/A\u003ewhat is not substance and what does not exist at all would be definable, \n\u003cA NAME=\"327\"\u003e\u003c/A\u003esince even non-existents can be signified by a name: (2) all sets of words \n\u003cA NAME=\"328\"\u003e\u003c/A\u003eor sentences would be definitions, since any kind of sentence could be \n\u003cA NAME=\"329\"\u003e\u003c/A\u003egiven a name; so that we should all be talking in definitions, and even \n\u003cA NAME=\"330\"\u003e\u003c/A\u003ethe Iliad would be a definition: (3) no demonstration can prove that any \n\u003cA NAME=\"331\"\u003e\u003c/A\u003eparticular name means any particular thing: neither, therefore, do definitions, \n\u003cA NAME=\"332\"\u003e\u003c/A\u003ein addition to revealing the meaning of a name, also reveal that the name \n\u003cA NAME=\"333\"\u003e\u003c/A\u003ehas this meaning. It appears then from these considerations that neither \n\u003cA NAME=\"334\"\u003e\u003c/A\u003edefinition and syllogism nor their objects are identical, and further that \n\u003cA NAME=\"335\"\u003e\u003c/A\u003edefinition neither demonstrates nor proves anything, and that knowledge \n\u003cA NAME=\"336\"\u003e\u003c/A\u003eof essential nature is not to be obtained either by definition or by \n\u003cA NAME=\"337\"\u003e\u003c/A\u003edemonstration.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"338\"\u003e\u003c/A\u003e\u003cB\u003ePart 8\u003c/B\u003e\n\n\u003cA NAME=\"339\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWe must now start afresh and consider which of these conclusions \n\u003cA NAME=\"340\"\u003e\u003c/A\u003eare sound and which are not, and what is the nature of definition, and \n\u003cA NAME=\"341\"\u003e\u003c/A\u003ewhether essential nature is in any sense demonstrable and definable or \n\u003cA NAME=\"342\"\u003e\u003c/A\u003ein none.\n\u003cA NAME=\"343\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eNow to know its essential nature is, as we said, the same as to \n\u003cA NAME=\"344\"\u003e\u003c/A\u003eknow the cause of a thing\u0027s existence, and the proof of this depends on \n\u003cA NAME=\"345\"\u003e\u003c/A\u003ethe fact that a thing must have a cause. Moreover, this cause is either \n\u003cA NAME=\"346\"\u003e\u003c/A\u003eidentical with the essential nature of the thing or distinct from it; and \n\u003cA NAME=\"347\"\u003e\u003c/A\u003eif its cause is distinct from it, the essential nature of the thing is \n\u003cA NAME=\"348\"\u003e\u003c/A\u003eeither demonstrable or indemonstrable. Consequently, if the cause is distinct \n\u003cA NAME=\"349\"\u003e\u003c/A\u003efrom the thing\u0027s essential nature and demonstration is possible, the cause \n\u003cA NAME=\"350\"\u003e\u003c/A\u003emust be the middle term, and, the conclusion proved being universal and \n\u003cA NAME=\"351\"\u003e\u003c/A\u003eaffirmative, the proof is in the first figure. So the method just examined \n\u003cA NAME=\"352\"\u003e\u003c/A\u003eof proving it through another essential nature would be one way of proving \n\u003cA NAME=\"353\"\u003e\u003c/A\u003eessential nature, because a conclusion containing essential nature must \n\u003cA NAME=\"354\"\u003e\u003c/A\u003ebe inferred through a middle which is an essential nature just as a \u0027peculiar\u0027 \n\u003cA NAME=\"355\"\u003e\u003c/A\u003eproperty must be inferred through a middle which is a \u0027peculiar\u0027 property; \n\u003cA NAME=\"356\"\u003e\u003c/A\u003eso that of the two definable natures of a single thing this method will \n\u003cA NAME=\"357\"\u003e\u003c/A\u003eprove one and not the other.\n\u003cA NAME=\"358\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eNow it was said before that this method could not amount to demonstration \n\u003cA NAME=\"359\"\u003e\u003c/A\u003eof essential nature-it is actually a dialectical proof of it-so let us \n\u003cA NAME=\"360\"\u003e\u003c/A\u003ebegin again and explain by what method it can be demonstrated. When we \n\u003cA NAME=\"361\"\u003e\u003c/A\u003eare aware of a fact we seek its reason, and though sometimes the fact and \n\u003cA NAME=\"362\"\u003e\u003c/A\u003ethe reason dawn on us simultaneously, yet we cannot apprehend the reason \n\u003cA NAME=\"363\"\u003e\u003c/A\u003ea moment sooner than the fact; and clearly in just the same way we cannot \n\u003cA NAME=\"364\"\u003e\u003c/A\u003eapprehend a thing\u0027s definable form without apprehending that it exists, \n\u003cA NAME=\"365\"\u003e\u003c/A\u003esince while we are ignorant whether it exists we cannot know its essential \n\u003cA NAME=\"366\"\u003e\u003c/A\u003enature. Moreover we are aware whether a thing exists or not sometimes through \n\u003cA NAME=\"367\"\u003e\u003c/A\u003eapprehending an element in its character, and sometimes accidentally, as, \n\u003cA NAME=\"368\"\u003e\u003c/A\u003efor example, when we are aware of thunder as a noise in the clouds, of \n\u003cA NAME=\"369\"\u003e\u003c/A\u003eeclipse as a privation of light, or of man as some species of animal, or \n\u003cA NAME=\"370\"\u003e\u003c/A\u003eof the soul as a self-moving thing. As often as we have accidental knowledge \n\u003cA NAME=\"371\"\u003e\u003c/A\u003ethat the thing exists, we must be in a wholly negative state as regards \n\u003cA NAME=\"372\"\u003e\u003c/A\u003eawareness of its essential nature; for we have not got genuine knowledge \n\u003cA NAME=\"373\"\u003e\u003c/A\u003eeven of its existence, and to search for a thing\u0027s essential nature when \n\u003cA NAME=\"374\"\u003e\u003c/A\u003ewe are unaware that it exists is to search for nothing. On the other hand, \n\u003cA NAME=\"375\"\u003e\u003c/A\u003ewhenever we apprehend an element in the thing\u0027s character there is less \n\u003cA NAME=\"376\"\u003e\u003c/A\u003edifficulty. Thus it follows that the degree of our knowledge of a thing\u0027s \n\u003cA NAME=\"377\"\u003e\u003c/A\u003eessential nature is determined by the sense in which we are aware that \n\u003cA NAME=\"378\"\u003e\u003c/A\u003eit exists. Let us then take the following as our first instance of being \n\u003cA NAME=\"379\"\u003e\u003c/A\u003eaware of an element in the essential nature. Let A be eclipse, C the moon, \n\u003cA NAME=\"380\"\u003e\u003c/A\u003eB the earth\u0027s acting as a screen. Now to ask whether the moon is eclipsed \n\u003cA NAME=\"381\"\u003e\u003c/A\u003eor not is to ask whether or not B has occurred. But that is precisely the \n\u003cA NAME=\"382\"\u003e\u003c/A\u003esame as asking whether A has a defining condition; and if this condition \n\u003cA NAME=\"383\"\u003e\u003c/A\u003eactually exists, we assert that A also actually exists. Or again we may \n\u003cA NAME=\"384\"\u003e\u003c/A\u003eask which side of a contradiction the defining condition necessitates: \n\u003cA NAME=\"385\"\u003e\u003c/A\u003edoes it make the angles of a triangle equal or not equal to two right angles? \n\u003cA NAME=\"386\"\u003e\u003c/A\u003eWhen we have found the answer, if the premisses are immediate, we know \n\u003cA NAME=\"387\"\u003e\u003c/A\u003efact and reason together; if they are not immediate, we know the fact without \n\u003cA NAME=\"388\"\u003e\u003c/A\u003ethe reason, as in the following example: let C be the moon, A eclipse, \n\u003cA NAME=\"389\"\u003e\u003c/A\u003eB the fact that the moon fails to produce shadows though she is full and \n\u003cA NAME=\"390\"\u003e\u003c/A\u003ethough no visible body intervenes between us and her. Then if B, failure \n\u003cA NAME=\"391\"\u003e\u003c/A\u003eto produce shadows in spite of the absence of an intervening body, is attributable \n\u003cA NAME=\"392\"\u003e\u003c/A\u003eA to C, and eclipse, is attributable to B, it is clear that the moon is \n\u003cA NAME=\"393\"\u003e\u003c/A\u003eeclipsed, but the reason why is not yet clear, and we know that eclipse \n\u003cA NAME=\"394\"\u003e\u003c/A\u003eexists, but we do not know what its essential nature is. But when it is \n\u003cA NAME=\"395\"\u003e\u003c/A\u003eclear that A is attributable to C and we proceed to ask the reason of this \n\u003cA NAME=\"396\"\u003e\u003c/A\u003efact, we are inquiring what is the nature of B: is it the earth\u0027s acting \n\u003cA NAME=\"397\"\u003e\u003c/A\u003eas a screen, or the moon\u0027s rotation or her extinction? But B is the definition \n\u003cA NAME=\"398\"\u003e\u003c/A\u003eof the other term, viz. in these examples, of the major term A; for eclipse \n\u003cA NAME=\"399\"\u003e\u003c/A\u003eis constituted by the earth acting as a screen. Thus, (1) \u0027What is thunder?\u0027 \n\u003cA NAME=\"400\"\u003e\u003c/A\u003e\u0027The quenching of fire in cloud\u0027, and (2) \u0027Why does it thunder?\u0027 \u0027Because \n\u003cA NAME=\"401\"\u003e\u003c/A\u003efire is quenched in the cloud\u0027, are equivalent. Let C be cloud, A thunder, \n\u003cA NAME=\"402\"\u003e\u003c/A\u003eB the quenching of fire. Then B is attributable to C, cloud, since fire \n\u003cA NAME=\"403\"\u003e\u003c/A\u003eis quenched in it; and A, noise, is attributable to B; and B is assuredly \n\u003cA NAME=\"404\"\u003e\u003c/A\u003ethe definition of the major term A. If there be a further mediating cause \n\u003cA NAME=\"405\"\u003e\u003c/A\u003eof B, it will be one of the remaining partial definitions of \n\u003cA NAME=\"406\"\u003e\u003c/A\u003eA.\n\u003cA NAME=\"407\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWe have stated then how essential nature is discovered and becomes \n\u003cA NAME=\"408\"\u003e\u003c/A\u003eknown, and we see that, while there is no syllogism-i.e. no demonstrative \n\u003cA NAME=\"409\"\u003e\u003c/A\u003esyllogism-of essential nature, yet it is through syllogism, viz. demonstrative \n\u003cA NAME=\"410\"\u003e\u003c/A\u003esyllogism, that essential nature is exhibited. So we conclude that neither \n\u003cA NAME=\"411\"\u003e\u003c/A\u003ecan the essential nature of anything which has a cause distinct from itself \n\u003cA NAME=\"412\"\u003e\u003c/A\u003ebe known without demonstration, nor can it be demonstrated; and this is \n\u003cA NAME=\"413\"\u003e\u003c/A\u003ewhat we contended in our preliminary discussions.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"414\"\u003e\u003c/A\u003e\u003cB\u003ePart 9\u003c/B\u003e\n\n\u003cA NAME=\"415\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eNow while some things have a cause distinct from themselves, others \n\u003cA NAME=\"416\"\u003e\u003c/A\u003ehave not. Hence it is evident that there are essential natures which are \n\u003cA NAME=\"417\"\u003e\u003c/A\u003eimmediate, that is are basic premisses; and of these not only that they \n\u003cA NAME=\"418\"\u003e\u003c/A\u003eare but also what they are must be assumed or revealed in some other way. \n\u003cA NAME=\"419\"\u003e\u003c/A\u003eThis too is the actual procedure of the arithmetician, who assumes both \n\u003cA NAME=\"420\"\u003e\u003c/A\u003ethe nature and the existence of unit. On the other hand, it is possible \n\u003cA NAME=\"421\"\u003e\u003c/A\u003e(in the manner explained) to exhibit through demonstration the essential \n\u003cA NAME=\"422\"\u003e\u003c/A\u003enature of things which have a \u0027middle\u0027, i.e. a cause of their substantial \n\u003cA NAME=\"423\"\u003e\u003c/A\u003ebeing other than that being itself; but we do not thereby demonstrate \n\u003cA NAME=\"424\"\u003e\u003c/A\u003eit.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"425\"\u003e\u003c/A\u003e\u003cB\u003ePart 10\u003c/B\u003e\n\n\u003cA NAME=\"426\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eSince definition is said to be the statement of a thing\u0027s nature, \n\u003cA NAME=\"427\"\u003e\u003c/A\u003eobviously one kind of definition will be a statement of the meaning of \n\u003cA NAME=\"428\"\u003e\u003c/A\u003ethe name, or of an equivalent nominal formula. A definition in this sense \n\u003cA NAME=\"429\"\u003e\u003c/A\u003etells you, e.g. the meaning of the phrase \u0027triangular character\u0027. When \n\u003cA NAME=\"430\"\u003e\u003c/A\u003ewe are aware that triangle exists, we inquire the reason why it exists. \n\u003cA NAME=\"431\"\u003e\u003c/A\u003eBut it is difficult thus to learn the definition of things the existence \n\u003cA NAME=\"432\"\u003e\u003c/A\u003eof which we do not genuinely know-the cause of this difficulty being, as \n\u003cA NAME=\"433\"\u003e\u003c/A\u003ewe said before, that we only know accidentally whether or not the thing \n\u003cA NAME=\"434\"\u003e\u003c/A\u003eexists. Moreover, a statement may be a unity in either of two ways, by \n\u003cA NAME=\"435\"\u003e\u003c/A\u003econjunction, like the Iliad, or because it exhibits a single predicate \n\u003cA NAME=\"436\"\u003e\u003c/A\u003eas inhering not accidentally in a single subject.\n\u003cA NAME=\"437\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThat then is one way of defining definition. Another kind of definition \n\u003cA NAME=\"438\"\u003e\u003c/A\u003eis a formula exhibiting the cause of a thing\u0027s existence. Thus the former \n\u003cA NAME=\"439\"\u003e\u003c/A\u003esignifies without proving, but the latter will clearly be a quasi-demonstration \n\u003cA NAME=\"440\"\u003e\u003c/A\u003eof essential nature, differing from demonstration in the arrangement of \n\u003cA NAME=\"441\"\u003e\u003c/A\u003eits terms. For there is a difference between stating why it thunders, and \n\u003cA NAME=\"442\"\u003e\u003c/A\u003estating what is the essential nature of thunder; since the first statement \n\u003cA NAME=\"443\"\u003e\u003c/A\u003ewill be \u0027Because fire is quenched in the clouds\u0027, while the statement of \n\u003cA NAME=\"444\"\u003e\u003c/A\u003ewhat the nature of thunder is will be \u0027The noise of fire being quenched \n\u003cA NAME=\"445\"\u003e\u003c/A\u003ein the clouds\u0027. Thus the same statement takes a different form: in one \n\u003cA NAME=\"446\"\u003e\u003c/A\u003eform it is continuous demonstration, in the other definition. Again, thunder \n\u003cA NAME=\"447\"\u003e\u003c/A\u003ecan be defined as noise in the clouds, which is the conclusion of the demonstration \n\u003cA NAME=\"448\"\u003e\u003c/A\u003eembodying essential nature. On the other hand the definition of immediates \n\u003cA NAME=\"449\"\u003e\u003c/A\u003eis an indemonstrable positing of essential nature.\n\u003cA NAME=\"450\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWe conclude then that definition is (a) an indemonstrable statement \n\u003cA NAME=\"451\"\u003e\u003c/A\u003eof essential nature, or (b) a syllogism of essential nature differing from \n\u003cA NAME=\"452\"\u003e\u003c/A\u003edemonstration in grammatical form, or (c) the conclusion of a demonstration \n\u003cA NAME=\"453\"\u003e\u003c/A\u003egiving essential nature.\n\u003cA NAME=\"454\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eOur discussion has therefore made plain (1) in what sense and of \n\u003cA NAME=\"455\"\u003e\u003c/A\u003ewhat things the essential nature is demonstrable, and in what sense and \n\u003cA NAME=\"456\"\u003e\u003c/A\u003eof what things it is not; (2) what are the various meanings of the term \n\u003cA NAME=\"457\"\u003e\u003c/A\u003edefinition, and in what sense and of what things it proves the essential \n\u003cA NAME=\"458\"\u003e\u003c/A\u003enature, and in what sense and of what things it does not; (3) what is the \n\u003cA NAME=\"459\"\u003e\u003c/A\u003erelation of definition to demonstration, and how far the same thing is \n\u003cA NAME=\"460\"\u003e\u003c/A\u003eboth definable and demonstrable and how far it is not.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"461\"\u003e\u003c/A\u003e\u003cB\u003ePart 11\u003c/B\u003e\n\n\u003cA NAME=\"462\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWe think we have scientific knowledge when we know the cause, and \n\u003cA NAME=\"463\"\u003e\u003c/A\u003ethere are four causes: (1) the definable form, (2) an antecedent which \n\u003cA NAME=\"464\"\u003e\u003c/A\u003enecessitates a consequent, (3) the efficient cause, (4) the final cause. \n\u003cA NAME=\"465\"\u003e\u003c/A\u003eHence each of these can be the middle term of a proof, for (a) though the \n\u003cA NAME=\"466\"\u003e\u003c/A\u003einference from antecedent to necessary consequent does not hold if only \n\u003cA NAME=\"467\"\u003e\u003c/A\u003eone premiss is assumed-two is the minimum-still when there are two it holds \n\u003cA NAME=\"468\"\u003e\u003c/A\u003eon condition that they have a single common middle term. So it is from \n\u003cA NAME=\"469\"\u003e\u003c/A\u003ethe assumption of this single middle term that the conclusion follows necessarily. \n\u003cA NAME=\"470\"\u003e\u003c/A\u003eThe following example will also show this. Why is the angle in a semicircle \n\u003cA NAME=\"471\"\u003e\u003c/A\u003ea right angle?-or from what assumption does it follow that it is a right \n\u003cA NAME=\"472\"\u003e\u003c/A\u003eangle? Thus, let A be right angle, B the half of two right angles, C the \n\u003cA NAME=\"473\"\u003e\u003c/A\u003eangle in a semicircle. Then B is the cause in virtue of which A, right \n\u003cA NAME=\"474\"\u003e\u003c/A\u003eangle, is attributable to C, the angle in a semicircle, since B=A and the \n\u003cA NAME=\"475\"\u003e\u003c/A\u003eother, viz. C,=B, for C is half of two right angles. Therefore it is the \n\u003cA NAME=\"476\"\u003e\u003c/A\u003eassumption of B, the half of two right angles, from which it follows that \n\u003cA NAME=\"477\"\u003e\u003c/A\u003eA is attributable to C, i.e. that the angle in a semicircle is a right \n\u003cA NAME=\"478\"\u003e\u003c/A\u003eangle. Moreover, B is identical with (b) the defining form of A, since \n\u003cA NAME=\"479\"\u003e\u003c/A\u003eit is what A\u0027s definition signifies. Moreover, the formal cause has already \n\u003cA NAME=\"480\"\u003e\u003c/A\u003ebeen shown to be the middle. (c) \u0027Why did the Athenians become involved \n\u003cA NAME=\"481\"\u003e\u003c/A\u003ein the Persian war?\u0027 means \u0027What cause originated the waging of war against \n\u003cA NAME=\"482\"\u003e\u003c/A\u003ethe Athenians?\u0027 and the answer is, \u0027Because they raided Sardis with the \n\u003cA NAME=\"483\"\u003e\u003c/A\u003eEretrians\u0027, since this originated the war. Let A be war, B unprovoked raiding, \n\u003cA NAME=\"484\"\u003e\u003c/A\u003eC the Athenians. Then B, unprovoked raiding, is true of C, the Athenians, \n\u003cA NAME=\"485\"\u003e\u003c/A\u003eand A is true of B, since men make war on the unjust aggressor. So A, having \n\u003cA NAME=\"486\"\u003e\u003c/A\u003ewar waged upon them, is true of B, the initial aggressors, and B is true \n\u003cA NAME=\"487\"\u003e\u003c/A\u003eof C, the Athenians, who were the aggressors. Hence here too the cause-in \n\u003cA NAME=\"488\"\u003e\u003c/A\u003ethis case the efficient cause-is the middle term. (d) This is no less true \n\u003cA NAME=\"489\"\u003e\u003c/A\u003ewhere the cause is the final cause. E.g. why does one take a walk after \n\u003cA NAME=\"490\"\u003e\u003c/A\u003esupper? For the sake of one\u0027s health. Why does a house exist? For the preservation \n\u003cA NAME=\"491\"\u003e\u003c/A\u003eof one\u0027s goods. The end in view is in the one case health, in the other \n\u003cA NAME=\"492\"\u003e\u003c/A\u003epreservation. To ask the reason why one must walk after supper is precisely \n\u003cA NAME=\"493\"\u003e\u003c/A\u003eto ask to what end one must do it. Let C be walking after supper, B the \n\u003cA NAME=\"494\"\u003e\u003c/A\u003enon-regurgitation of food, A health. Then let walking after supper possess \n\u003cA NAME=\"495\"\u003e\u003c/A\u003ethe property of preventing food from rising to the orifice of the stomach, \n\u003cA NAME=\"496\"\u003e\u003c/A\u003eand let this condition be healthy; since it seems that B, the non-regurgitation \n\u003cA NAME=\"497\"\u003e\u003c/A\u003eof food, is attributable to C, taking a walk, and that A, health, is attributable \n\u003cA NAME=\"498\"\u003e\u003c/A\u003eto B. What, then, is the cause through which A, the final cause, inheres \n\u003cA NAME=\"499\"\u003e\u003c/A\u003ein C? It is B, the non-regurgitation of food; but B is a kind of definition \n\u003cA NAME=\"500\"\u003e\u003c/A\u003eof A, for A will be explained by it. Why is B the cause of A\u0027s belonging \n\u003cA NAME=\"501\"\u003e\u003c/A\u003eto C? Because to be in a condition such as B is to be in health. The definitions \n\u003cA NAME=\"502\"\u003e\u003c/A\u003emust be transposed, and then the detail will become clearer. Incidentally, \n\u003cA NAME=\"503\"\u003e\u003c/A\u003ehere the order of coming to be is the reverse of what it is in proof through \n\u003cA NAME=\"504\"\u003e\u003c/A\u003ethe efficient cause: in the efficient order the middle term must come to \n\u003cA NAME=\"505\"\u003e\u003c/A\u003ebe first, whereas in the teleological order the minor, C, must first take \n\u003cA NAME=\"506\"\u003e\u003c/A\u003eplace, and the end in view comes last in time.\n\u003cA NAME=\"507\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThe same thing may exist for an end and be necessitated as well. \n\u003cA NAME=\"508\"\u003e\u003c/A\u003eFor example, light shines through a lantern (1) because that which consists \n\u003cA NAME=\"509\"\u003e\u003c/A\u003eof relatively small particles necessarily passes through pores larger than \n\u003cA NAME=\"510\"\u003e\u003c/A\u003ethose particles-assuming that light does issue by penetration- and (2) \n\u003cA NAME=\"511\"\u003e\u003c/A\u003efor an end, namely to save us from stumbling. If then, a thing can exist \n\u003cA NAME=\"512\"\u003e\u003c/A\u003ethrough two causes, can it come to be through two causes-as for instance \n\u003cA NAME=\"513\"\u003e\u003c/A\u003eif thunder be a hiss and a roar necessarily produced by the quenching of \n\u003cA NAME=\"514\"\u003e\u003c/A\u003efire, and also designed, as the Pythagoreans say, for a threat to terrify \n\u003cA NAME=\"515\"\u003e\u003c/A\u003ethose that lie in Tartarus? Indeed, there are very many such cases, mostly \n\u003cA NAME=\"516\"\u003e\u003c/A\u003eamong the processes and products of the natural world; for nature, in different \n\u003cA NAME=\"517\"\u003e\u003c/A\u003esenses of the term \u0027nature\u0027, produces now for an end, now by \n\u003cA NAME=\"518\"\u003e\u003c/A\u003enecessity.\n\u003cA NAME=\"519\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eNecessity too is of two kinds. It may work in accordance with a \n\u003cA NAME=\"520\"\u003e\u003c/A\u003ething\u0027s natural tendency, or by constraint and in opposition to it; as, \n\u003cA NAME=\"521\"\u003e\u003c/A\u003efor instance, by necessity a stone is borne both upwards and downwards, \n\u003cA NAME=\"522\"\u003e\u003c/A\u003ebut not by the same necessity.\n\u003cA NAME=\"523\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eOf the products of man\u0027s intelligence some are never due to chance \n\u003cA NAME=\"524\"\u003e\u003c/A\u003eor necessity but always to an end, as for example a house or a statue; \n\u003cA NAME=\"525\"\u003e\u003c/A\u003eothers, such as health or safety, may result from chance as \n\u003cA NAME=\"526\"\u003e\u003c/A\u003ewell.\n\u003cA NAME=\"527\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is mostly in cases where the issue is indeterminate (though \n\u003cA NAME=\"528\"\u003e\u003c/A\u003eonly where the production does not originate in chance, and the end is \n\u003cA NAME=\"529\"\u003e\u003c/A\u003econsequently good), that a result is due to an end, and this is true alike \n\u003cA NAME=\"530\"\u003e\u003c/A\u003ein nature or in art. By chance, on the other hand, nothing comes to be \n\u003cA NAME=\"531\"\u003e\u003c/A\u003efor an end.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"532\"\u003e\u003c/A\u003e\u003cB\u003ePart 12\u003c/B\u003e\n\u003cA NAME=\"533\"\u003e\u003c/A\u003eThe effect may be still coming to be, or its occurrence may be past or \n\u003cA NAME=\"534\"\u003e\u003c/A\u003efuture, yet the cause will be the same as when it is actually existent-for \n\u003cA NAME=\"535\"\u003e\u003c/A\u003eit is the middle which is the cause-except that if the effect actually \n\u003cA NAME=\"536\"\u003e\u003c/A\u003eexists the cause is actually existent, if it is coming to be so is the \n\u003cA NAME=\"537\"\u003e\u003c/A\u003ecause, if its occurrence is past the cause is past, if future the cause \n\u003cA NAME=\"538\"\u003e\u003c/A\u003eis future. For example, the moon was eclipsed because the earth intervened, \n\u003cA NAME=\"539\"\u003e\u003c/A\u003eis becoming eclipsed because the earth is in process of intervening, will \n\u003cA NAME=\"540\"\u003e\u003c/A\u003ebe eclipsed because the earth will intervene, is eclipsed because the earth \n\u003cA NAME=\"541\"\u003e\u003c/A\u003eintervenes.\n\u003cA NAME=\"542\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eTo take a second example: assuming that the definition of ice is \n\u003cA NAME=\"543\"\u003e\u003c/A\u003esolidified water, let C be water, A solidified, B the middle, which is \n\u003cA NAME=\"544\"\u003e\u003c/A\u003ethe cause, namely total failure of heat. Then B is attributed to C, and \n\u003cA NAME=\"545\"\u003e\u003c/A\u003eA, solidification, to B: ice when B is occurring, has formed when B has \n\u003cA NAME=\"546\"\u003e\u003c/A\u003eoccurred, and will form when B shall occur.\n\u003cA NAME=\"547\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThis sort of cause, then, and its effect come to be simultaneously \n\u003cA NAME=\"548\"\u003e\u003c/A\u003ewhen they are in process of becoming, and exist simultaneously when they \n\u003cA NAME=\"549\"\u003e\u003c/A\u003eactually exist; and the same holds good when they are past and when they \n\u003cA NAME=\"550\"\u003e\u003c/A\u003eare future. But what of cases where they are not simultaneous? Can causes \n\u003cA NAME=\"551\"\u003e\u003c/A\u003eand effects different from one another form, as they seem to us to form, \n\u003cA NAME=\"552\"\u003e\u003c/A\u003ea continuous succession, a past effect resulting from a past cause different \n\u003cA NAME=\"553\"\u003e\u003c/A\u003efrom itself, a future effect from a future cause different from it, and \n\u003cA NAME=\"554\"\u003e\u003c/A\u003ean effect which is coming-to-be from a cause different from and prior to \n\u003cA NAME=\"555\"\u003e\u003c/A\u003eit? Now on this theory it is from the posterior event that we reason (and \n\u003cA NAME=\"556\"\u003e\u003c/A\u003ethis though these later events actually have their source of origin in \n\u003cA NAME=\"557\"\u003e\u003c/A\u003eprevious events–a fact which shows that also when the effect is coming-to-be \n\u003cA NAME=\"558\"\u003e\u003c/A\u003ewe still reason from the posterior event), and from the event we cannot \n\u003cA NAME=\"559\"\u003e\u003c/A\u003ereason (we cannot argue that because an event A has occurred, therefore \n\u003cA NAME=\"560\"\u003e\u003c/A\u003ean event B has occurred subsequently to A but still in the past-and the \n\u003cA NAME=\"561\"\u003e\u003c/A\u003esame holds good if the occurrence is future)-cannot reason because, be \n\u003cA NAME=\"562\"\u003e\u003c/A\u003ethe time interval definite or indefinite, it will never be possible to \n\u003cA NAME=\"563\"\u003e\u003c/A\u003einfer that because it is true to say that A occurred, therefore it is true \n\u003cA NAME=\"564\"\u003e\u003c/A\u003eto say that B, the subsequent event, occurred; for in the interval between \n\u003cA NAME=\"565\"\u003e\u003c/A\u003ethe events, though A has already occurred, the latter statement will be \n\u003cA NAME=\"566\"\u003e\u003c/A\u003efalse. And the same argument applies also to future events; i.e. one cannot \n\u003cA NAME=\"567\"\u003e\u003c/A\u003einfer from an event which occurred in the past that a future event will \n\u003cA NAME=\"568\"\u003e\u003c/A\u003eoccur. The reason of this is that the middle must be homogeneous, past \n\u003cA NAME=\"569\"\u003e\u003c/A\u003ewhen the extremes are past, future when they are future, coming to be when \n\u003cA NAME=\"570\"\u003e\u003c/A\u003ethey are coming-to-be, actually existent when they are actually existent; \n\u003cA NAME=\"571\"\u003e\u003c/A\u003eand there cannot be a middle term homogeneous with extremes respectively \n\u003cA NAME=\"572\"\u003e\u003c/A\u003epast and future. And it is a further difficulty in this theory that the \n\u003cA NAME=\"573\"\u003e\u003c/A\u003etime interval can be neither indefinite nor definite, since during it the \n\u003cA NAME=\"574\"\u003e\u003c/A\u003einference will be false. We have also to inquire what it is that holds \n\u003cA NAME=\"575\"\u003e\u003c/A\u003eevents together so that the coming-to-be now occurring in actual things \n\u003cA NAME=\"576\"\u003e\u003c/A\u003efollows upon a past event. It is evident, we may suggest, that a past event \n\u003cA NAME=\"577\"\u003e\u003c/A\u003eand a present process cannot be \u0027contiguous\u0027, for not even two past events \n\u003cA NAME=\"578\"\u003e\u003c/A\u003ecan be \u0027contiguous\u0027. For past events are limits and atomic; so just as \n\u003cA NAME=\"579\"\u003e\u003c/A\u003epoints are not \u0027contiguous\u0027 neither are past events, since both are indivisible. \n\u003cA NAME=\"580\"\u003e\u003c/A\u003eFor the same reason a past event and a present process cannot be \u0027contiguous\u0027, \n\u003cA NAME=\"581\"\u003e\u003c/A\u003efor the process is divisible, the event indivisible. Thus the relation \n\u003cA NAME=\"582\"\u003e\u003c/A\u003eof present process to past event is analogous to that of line to point, \n\u003cA NAME=\"583\"\u003e\u003c/A\u003esince a process contains an infinity of past events. These questions, however, \n\u003cA NAME=\"584\"\u003e\u003c/A\u003emust receive a more explicit treatment in our general theory of \n\u003cA NAME=\"585\"\u003e\u003c/A\u003echange.\n\u003cA NAME=\"586\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThe following must suffice as an account of the manner in which \n\u003cA NAME=\"587\"\u003e\u003c/A\u003ethe middle would be identical with the cause on the supposition that coming-to-be \n\u003cA NAME=\"588\"\u003e\u003c/A\u003eis a series of consecutive events: for in the terms of such a series too \n\u003cA NAME=\"589\"\u003e\u003c/A\u003ethe middle and major terms must form an immediate premiss; e.g. we argue \n\u003cA NAME=\"590\"\u003e\u003c/A\u003ethat, since C has occurred, therefore A occurred: and C\u0027s occurrence was \n\u003cA NAME=\"591\"\u003e\u003c/A\u003eposterior, A\u0027s prior; but C is the source of the inference because it is \n\u003cA NAME=\"592\"\u003e\u003c/A\u003enearer to the present moment, and the starting-point of time is the present. \n\u003cA NAME=\"593\"\u003e\u003c/A\u003eWe next argue that, since D has occurred, therefore C occurred. Then we \n\u003cA NAME=\"594\"\u003e\u003c/A\u003econclude that, since D has occurred, therefore A must have occurred; and \n\u003cA NAME=\"595\"\u003e\u003c/A\u003ethe cause is C, for since D has occurred C must have occurred, and since \n\u003cA NAME=\"596\"\u003e\u003c/A\u003eC has occurred A must previously have occurred.\n\u003cA NAME=\"597\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIf we get our middle term in this way, will the series terminate \n\u003cA NAME=\"598\"\u003e\u003c/A\u003ein an immediate premiss, or since, as we said, no two events are \u0027contiguous\u0027, \n\u003cA NAME=\"599\"\u003e\u003c/A\u003ewill a fresh middle term always intervene because there is an infinity \n\u003cA NAME=\"600\"\u003e\u003c/A\u003eof middles? No: though no two events are \u0027contiguous\u0027, yet we must start \n\u003cA NAME=\"601\"\u003e\u003c/A\u003efrom a premiss consisting of a middle and the present event as major. The \n\u003cA NAME=\"602\"\u003e\u003c/A\u003elike is true of future events too, since if it is true to say that D will \n\u003cA NAME=\"603\"\u003e\u003c/A\u003eexist, it must be a prior truth to say that A will exist, and the cause \n\u003cA NAME=\"604\"\u003e\u003c/A\u003eof this conclusion is C; for if D will exist, C will exist prior to D, \n\u003cA NAME=\"605\"\u003e\u003c/A\u003eand if C will exist, A will exist prior to it. And here too the same infinite \n\u003cA NAME=\"606\"\u003e\u003c/A\u003edivisibility might be urged, since future events are not \u0027contiguous\u0027. \n\u003cA NAME=\"607\"\u003e\u003c/A\u003eBut here too an immediate basic premiss must be assumed. And in the world \n\u003cA NAME=\"608\"\u003e\u003c/A\u003eof fact this is so: if a house has been built, then blocks must have been \n\u003cA NAME=\"609\"\u003e\u003c/A\u003equarried and shaped. The reason is that a house having been built necessitates \n\u003cA NAME=\"610\"\u003e\u003c/A\u003ea foundation having been laid, and if a foundation has been laid blocks \n\u003cA NAME=\"611\"\u003e\u003c/A\u003emust have been shaped beforehand. Again, if a house will be built, blocks \n\u003cA NAME=\"612\"\u003e\u003c/A\u003ewill similarly be shaped beforehand; and proof is through the middle in \n\u003cA NAME=\"613\"\u003e\u003c/A\u003ethe same way, for the foundation will exist before the \n\u003cA NAME=\"614\"\u003e\u003c/A\u003ehouse.\n\u003cA NAME=\"615\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eNow we observe in Nature a certain kind of circular process of \n\u003cA NAME=\"616\"\u003e\u003c/A\u003ecoming-to-be; and this is possible only if the middle and extreme terms \n\u003cA NAME=\"617\"\u003e\u003c/A\u003eare reciprocal, since conversion is conditioned by reciprocity in the terms \n\u003cA NAME=\"618\"\u003e\u003c/A\u003eof the proof. This-the convertibility of conclusions and premisses-has \n\u003cA NAME=\"619\"\u003e\u003c/A\u003ebeen proved in our early chapters, and the circular process is an instance \n\u003cA NAME=\"620\"\u003e\u003c/A\u003eof this. In actual fact it is exemplified thus: when the earth had been \n\u003cA NAME=\"621\"\u003e\u003c/A\u003emoistened an exhalation was bound to rise, and when an exhalation had risen \n\u003cA NAME=\"622\"\u003e\u003c/A\u003ecloud was bound to form, and from the formation of cloud rain necessarily \n\u003cA NAME=\"623\"\u003e\u003c/A\u003eresulted and by the fall of rain the earth was necessarily moistened: but \n\u003cA NAME=\"624\"\u003e\u003c/A\u003ethis was the starting-point, so that a circle is completed; for posit any \n\u003cA NAME=\"625\"\u003e\u003c/A\u003eone of the terms and another follows from it, and from that another, and \n\u003cA NAME=\"626\"\u003e\u003c/A\u003efrom that again the first.\n\u003cA NAME=\"627\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eSome occurrences are universal (for they are, or come-to-be what \n\u003cA NAME=\"628\"\u003e\u003c/A\u003ethey are, always and in ever case); others again are not always what they \n\u003cA NAME=\"629\"\u003e\u003c/A\u003eare but only as a general rule: for instance, not every man can grow a \n\u003cA NAME=\"630\"\u003e\u003c/A\u003ebeard, but it is the general rule. In the case of such connexions the middle \n\u003cA NAME=\"631\"\u003e\u003c/A\u003eterm too must be a general rule. For if A is predicated universally of \n\u003cA NAME=\"632\"\u003e\u003c/A\u003eB and B of C, A too must be predicated always and in every instance of \n\u003cA NAME=\"633\"\u003e\u003c/A\u003eC, since to hold in every instance and always is of the nature of the universal. \n\u003cA NAME=\"634\"\u003e\u003c/A\u003eBut we have assumed a connexion which is a general rule; consequently the \n\u003cA NAME=\"635\"\u003e\u003c/A\u003emiddle term B must also be a general rule. So connexions which embody a \n\u003cA NAME=\"636\"\u003e\u003c/A\u003egeneral rule-i.e. which exist or come to be as a general rule-will also \n\u003cA NAME=\"637\"\u003e\u003c/A\u003ederive from immediate basic premisses.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"638\"\u003e\u003c/A\u003e\u003cB\u003ePart 13\u003c/B\u003e\n\n\u003cA NAME=\"639\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWe have already explained how essential nature is set out in the \n\u003cA NAME=\"640\"\u003e\u003c/A\u003eterms of a demonstration, and the sense in which it is or is not demonstrable \n\u003cA NAME=\"641\"\u003e\u003c/A\u003eor definable; so let us now discuss the method to be adopted in tracing \n\u003cA NAME=\"642\"\u003e\u003c/A\u003ethe elements predicated as constituting the definable \n\u003cA NAME=\"643\"\u003e\u003c/A\u003eform.\n\u003cA NAME=\"644\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eNow of the attributes which inhere always in each several thing \n\u003cA NAME=\"645\"\u003e\u003c/A\u003ethere are some which are wider in extent than it but not wider than its \n\u003cA NAME=\"646\"\u003e\u003c/A\u003egenus (by attributes of wider extent mean all such as are universal attributes \n\u003cA NAME=\"647\"\u003e\u003c/A\u003eof each several subject, but in their application are not confined to that \n\u003cA NAME=\"648\"\u003e\u003c/A\u003esubject). while an attribute may inhere in every triad, yet also in a subject \n\u003cA NAME=\"649\"\u003e\u003c/A\u003enot a triad-as being inheres in triad but also in subjects not numbers \n\u003cA NAME=\"650\"\u003e\u003c/A\u003eat all-odd on the other hand is an attribute inhering in every triad and \n\u003cA NAME=\"651\"\u003e\u003c/A\u003eof wider application (inhering as it does also in pentad), but which does \n\u003cA NAME=\"652\"\u003e\u003c/A\u003enot extend beyond the genus of triad; for pentad is a number, but nothing \n\u003cA NAME=\"653\"\u003e\u003c/A\u003eoutside number is odd. It is such attributes which we have to select, up \n\u003cA NAME=\"654\"\u003e\u003c/A\u003eto the exact point at which they are severally of wider extent than the \n\u003cA NAME=\"655\"\u003e\u003c/A\u003esubject but collectively coextensive with it; for this synthesis must be \n\u003cA NAME=\"656\"\u003e\u003c/A\u003ethe substance of the thing. For example every triad possesses the attributes \n\u003cA NAME=\"657\"\u003e\u003c/A\u003enumber, odd, and prime in both senses, i.e. not only as possessing no divisors, \n\u003cA NAME=\"658\"\u003e\u003c/A\u003ebut also as not being a sum of numbers. This, then, is precisely what triad \n\u003cA NAME=\"659\"\u003e\u003c/A\u003eis, viz. a number, odd, and prime in the former and also the latter sense \n\u003cA NAME=\"660\"\u003e\u003c/A\u003eof the term: for these attributes taken severally apply, the first two \n\u003cA NAME=\"661\"\u003e\u003c/A\u003eto all odd numbers, the last to the dyad also as well as to the triad, \n\u003cA NAME=\"662\"\u003e\u003c/A\u003ebut, taken collectively, to no other subject. Now since we have shown above\u0027 \n\u003cA NAME=\"663\"\u003e\u003c/A\u003ethat attributes predicated as belonging to the essential nature are necessary \n\u003cA NAME=\"664\"\u003e\u003c/A\u003eand that universals are necessary, and since the attributes which we select \n\u003cA NAME=\"665\"\u003e\u003c/A\u003eas inhering in triad, or in any other subject whose attributes we select \n\u003cA NAME=\"666\"\u003e\u003c/A\u003ein this way, are predicated as belonging to its essential nature, triad \n\u003cA NAME=\"667\"\u003e\u003c/A\u003ewill thus possess these attributes necessarily. Further, that the synthesis \n\u003cA NAME=\"668\"\u003e\u003c/A\u003eof them constitutes the substance of triad is shown by the following argument. \n\u003cA NAME=\"669\"\u003e\u003c/A\u003eIf it is not identical with the being of triad, it must be related to triad \n\u003cA NAME=\"670\"\u003e\u003c/A\u003eas a genus named or nameless. It will then be of wider extent than triad-assuming \n\u003cA NAME=\"671\"\u003e\u003c/A\u003ethat wider potential extent is the character of a genus. If on the other \n\u003cA NAME=\"672\"\u003e\u003c/A\u003ehand this synthesis is applicable to no subject other than the individual \n\u003cA NAME=\"673\"\u003e\u003c/A\u003etriads, it will be identical with the being of triad, because we make the \n\u003cA NAME=\"674\"\u003e\u003c/A\u003efurther assumption that the substance of each subject is the predication \n\u003cA NAME=\"675\"\u003e\u003c/A\u003eof elements in its essential nature down to the last differentia characterizing \n\u003cA NAME=\"676\"\u003e\u003c/A\u003ethe individuals. It follows that any other synthesis thus exhibited will \n\u003cA NAME=\"677\"\u003e\u003c/A\u003elikewise be identical with the being of the subject.\n\u003cA NAME=\"678\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThe author of a hand-book on a subject that is a generic whole \n\u003cA NAME=\"679\"\u003e\u003c/A\u003eshould divide the genus into its first infimae species-number e.g. into \n\u003cA NAME=\"680\"\u003e\u003c/A\u003etriad and dyad-and then endeavour to seize their definitions by the method \n\u003cA NAME=\"681\"\u003e\u003c/A\u003ewe have described-the definition, for example, of straight line or circle \n\u003cA NAME=\"682\"\u003e\u003c/A\u003eor right angle. After that, having established what the category is to \n\u003cA NAME=\"683\"\u003e\u003c/A\u003ewhich the subaltern genus belongs-quantity or quality, for instance-he \n\u003cA NAME=\"684\"\u003e\u003c/A\u003eshould examine the properties \u0027peculiar\u0027 to the species, working through \n\u003cA NAME=\"685\"\u003e\u003c/A\u003ethe proximate common differentiae. He should proceed thus because the attributes \n\u003cA NAME=\"686\"\u003e\u003c/A\u003eof the genera compounded of the infimae species will be clearly given by \n\u003cA NAME=\"687\"\u003e\u003c/A\u003ethe definitions of the species; since the basic element of them all is \n\u003cA NAME=\"688\"\u003e\u003c/A\u003ethe definition, i.e. the simple infirma species, and the attributes inhere \n\u003cA NAME=\"689\"\u003e\u003c/A\u003eessentially in the simple infimae species, in the genera only in virtue \n\u003cA NAME=\"690\"\u003e\u003c/A\u003eof these.\n\u003cA NAME=\"691\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eDivisions according to differentiae are a useful accessory to this \n\u003cA NAME=\"692\"\u003e\u003c/A\u003emethod. What force they have as proofs we did, indeed, explain above, but \n\u003cA NAME=\"693\"\u003e\u003c/A\u003ethat merely towards collecting the essential nature they may be of use \n\u003cA NAME=\"694\"\u003e\u003c/A\u003ewe will proceed to show. They might, indeed, seem to be of no use at all, \n\u003cA NAME=\"695\"\u003e\u003c/A\u003ebut rather to assume everything at the start and to be no better than an \n\u003cA NAME=\"696\"\u003e\u003c/A\u003einitial assumption made without division. But, in fact, the order in which \n\u003cA NAME=\"697\"\u003e\u003c/A\u003ethe attributes are predicated does make a difference–it matters whether \n\u003cA NAME=\"698\"\u003e\u003c/A\u003ewe say animal-tame-biped, or biped-animal-tame. For if every definable \n\u003cA NAME=\"699\"\u003e\u003c/A\u003ething consists of two elements and \u0027animal-tame\u0027 forms a unity, and again \n\u003cA NAME=\"700\"\u003e\u003c/A\u003eout of this and the further differentia man (or whatever else is the unity \n\u003cA NAME=\"701\"\u003e\u003c/A\u003eunder construction) is constituted, then the elements we assume have necessarily \n\u003cA NAME=\"702\"\u003e\u003c/A\u003ebeen reached by division. Again, division is the only possible method of \n\u003cA NAME=\"703\"\u003e\u003c/A\u003eavoiding the omission of any element of the essential nature. Thus, if \n\u003cA NAME=\"704\"\u003e\u003c/A\u003ethe primary genus is assumed and we then take one of the lower divisions, \n\u003cA NAME=\"705\"\u003e\u003c/A\u003ethe dividendum will not fall whole into this division: e.g. it is not all \n\u003cA NAME=\"706\"\u003e\u003c/A\u003eanimal which is either whole-winged or split-winged but all winged animal, \n\u003cA NAME=\"707\"\u003e\u003c/A\u003efor it is winged animal to which this differentiation belongs. The primary \n\u003cA NAME=\"708\"\u003e\u003c/A\u003edifferentiation of animal is that within which all animal falls. The like \n\u003cA NAME=\"709\"\u003e\u003c/A\u003eis true of every other genus, whether outside animal or a subaltern genus \n\u003cA NAME=\"710\"\u003e\u003c/A\u003eof animal; e.g. the primary differentiation of bird is that within which \n\u003cA NAME=\"711\"\u003e\u003c/A\u003efalls every bird, of fish that within which falls every fish. So, if we \n\u003cA NAME=\"712\"\u003e\u003c/A\u003eproceed in this way, we can be sure that nothing has been omitted: by any \n\u003cA NAME=\"713\"\u003e\u003c/A\u003eother method one is bound to omit something without knowing \n\u003cA NAME=\"714\"\u003e\u003c/A\u003eit.\n\u003cA NAME=\"715\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eTo define and divide one need not know the whole of existence. \n\u003cA NAME=\"716\"\u003e\u003c/A\u003eYet some hold it impossible to know the differentiae distinguishing each \n\u003cA NAME=\"717\"\u003e\u003c/A\u003ething from every single other thing without knowing every single other \n\u003cA NAME=\"718\"\u003e\u003c/A\u003ething; and one cannot, they say, know each thing without knowing its differentiae, \n\u003cA NAME=\"719\"\u003e\u003c/A\u003esince everything is identical with that from which it does not differ, \n\u003cA NAME=\"720\"\u003e\u003c/A\u003eand other than that from which it differs. Now first of all this is a fallacy: \n\u003cA NAME=\"721\"\u003e\u003c/A\u003enot every differentia precludes identity, since many differentiae inhere \n\u003cA NAME=\"722\"\u003e\u003c/A\u003ein things specifically identical, though not in the substance of these \n\u003cA NAME=\"723\"\u003e\u003c/A\u003enor essentially. Secondly, when one has taken one\u0027s differing pair of opposites \n\u003cA NAME=\"724\"\u003e\u003c/A\u003eand assumed that the two sides exhaust the genus, and that the subject \n\u003cA NAME=\"725\"\u003e\u003c/A\u003eone seeks to define is present in one or other of them, and one has further \n\u003cA NAME=\"726\"\u003e\u003c/A\u003everified its presence in one of them; then it does not matter whether or \n\u003cA NAME=\"727\"\u003e\u003c/A\u003enot one knows all the other subjects of which the differentiae are also \n\u003cA NAME=\"728\"\u003e\u003c/A\u003epredicated. For it is obvious that when by this process one reaches subjects \n\u003cA NAME=\"729\"\u003e\u003c/A\u003eincapable of further differentiation one will possess the formula defining \n\u003cA NAME=\"730\"\u003e\u003c/A\u003ethe substance. Moreover, to postulate that the division exhausts the genus \n\u003cA NAME=\"731\"\u003e\u003c/A\u003eis not illegitimate if the opposites exclude a middle; since if it is the \n\u003cA NAME=\"732\"\u003e\u003c/A\u003edifferentia of that genus, anything contained in the genus must lie on \n\u003cA NAME=\"733\"\u003e\u003c/A\u003eone of the two sides.\n\u003cA NAME=\"734\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIn establishing a definition by division one should keep three \n\u003cA NAME=\"735\"\u003e\u003c/A\u003eobjects in view: (1) the admission only of elements in the definable form, \n\u003cA NAME=\"736\"\u003e\u003c/A\u003e(2) the arrangement of these in the right order, (3) the omission of no \n\u003cA NAME=\"737\"\u003e\u003c/A\u003esuch elements. The first is feasible because one can establish genus and \n\u003cA NAME=\"738\"\u003e\u003c/A\u003edifferentia through the topic of the genus, just as one can conclude the \n\u003cA NAME=\"739\"\u003e\u003c/A\u003einherence of an accident through the topic of the accident. The right order \n\u003cA NAME=\"740\"\u003e\u003c/A\u003ewill be achieved if the right term is assumed as primary, and this will \n\u003cA NAME=\"741\"\u003e\u003c/A\u003ebe ensured if the term selected is predicable of all the others but not \n\u003cA NAME=\"742\"\u003e\u003c/A\u003eall they of it; since there must be one such term. Having assumed this \n\u003cA NAME=\"743\"\u003e\u003c/A\u003ewe at once proceed in the same way with the lower terms; for our second \n\u003cA NAME=\"744\"\u003e\u003c/A\u003eterm will be the first of the remainder, our third the first of those which \n\u003cA NAME=\"745\"\u003e\u003c/A\u003efollow the second in a \u0027contiguous\u0027 series, since when the higher term \n\u003cA NAME=\"746\"\u003e\u003c/A\u003eis excluded, that term of the remainder which is \u0027contiguous\u0027 to it will \n\u003cA NAME=\"747\"\u003e\u003c/A\u003ebe primary, and so on. Our procedure makes it clear that no elements in \n\u003cA NAME=\"748\"\u003e\u003c/A\u003ethe definable form have been omitted: we have taken the differentia that \n\u003cA NAME=\"749\"\u003e\u003c/A\u003ecomes first in the order of division, pointing out that animal, e.g. is \n\u003cA NAME=\"750\"\u003e\u003c/A\u003edivisible exhaustively into A and B, and that the subject accepts one of \n\u003cA NAME=\"751\"\u003e\u003c/A\u003ethe two as its predicate. Next we have taken the differentia of the whole \n\u003cA NAME=\"752\"\u003e\u003c/A\u003ethus reached, and shown that the whole we finally reach is not further \n\u003cA NAME=\"753\"\u003e\u003c/A\u003edivisible-i.e. that as soon as we have taken the last differentia to form \n\u003cA NAME=\"754\"\u003e\u003c/A\u003ethe concrete totality, this totality admits of no division into species. \n\u003cA NAME=\"755\"\u003e\u003c/A\u003eFor it is clear that there is no superfluous addition, since all these \n\u003cA NAME=\"756\"\u003e\u003c/A\u003eterms we have selected are elements in the definable form; and nothing \n\u003cA NAME=\"757\"\u003e\u003c/A\u003elacking, since any omission would have to be a genus or a differentia. \n\u003cA NAME=\"758\"\u003e\u003c/A\u003eNow the primary term is a genus, and this term taken in conjunction with \n\u003cA NAME=\"759\"\u003e\u003c/A\u003eits differentiae is a genus: moreover the differentiae are all included, \n\u003cA NAME=\"760\"\u003e\u003c/A\u003ebecause there is now no further differentia; if there were, the final concrete \n\u003cA NAME=\"761\"\u003e\u003c/A\u003ewould admit of division into species, which, we said, is not the \n\u003cA NAME=\"762\"\u003e\u003c/A\u003ecase.\n\u003cA NAME=\"763\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eTo resume our account of the right method of investigation: We \n\u003cA NAME=\"764\"\u003e\u003c/A\u003emust start by observing a set of similar-i.e. specifically identical-individuals, \n\u003cA NAME=\"765\"\u003e\u003c/A\u003eand consider what element they have in common. We must then apply the same \n\u003cA NAME=\"766\"\u003e\u003c/A\u003eprocess to another set of individuals which belong to one species and are \n\u003cA NAME=\"767\"\u003e\u003c/A\u003egenerically but not specifically identical with the former set. When we \n\u003cA NAME=\"768\"\u003e\u003c/A\u003ehave established what the common element is in all members of this second \n\u003cA NAME=\"769\"\u003e\u003c/A\u003especies, and likewise in members of further species, we should again consider \n\u003cA NAME=\"770\"\u003e\u003c/A\u003ewhether the results established possess any identity, and persevere until \n\u003cA NAME=\"771\"\u003e\u003c/A\u003ewe reach a single formula, since this will be the definition of the thing. \n\u003cA NAME=\"772\"\u003e\u003c/A\u003eBut if we reach not one formula but two or more, evidently the definiendum \n\u003cA NAME=\"773\"\u003e\u003c/A\u003ecannot be one thing but must be more than one. I may illustrate my meaning \n\u003cA NAME=\"774\"\u003e\u003c/A\u003eas follows. If we were inquiring what the essential nature of pride is, \n\u003cA NAME=\"775\"\u003e\u003c/A\u003ewe should examine instances of proud men we know of to see what, as such, \n\u003cA NAME=\"776\"\u003e\u003c/A\u003ethey have in common; e.g. if Alcibiades was proud, or Achilles and Ajax \n\u003cA NAME=\"777\"\u003e\u003c/A\u003ewere proud, we should find on inquiring what they all had in common, that \n\u003cA NAME=\"778\"\u003e\u003c/A\u003eit was intolerance of insult; it was this which drove Alcibiades to war, \n\u003cA NAME=\"779\"\u003e\u003c/A\u003eAchilles wrath, and Ajax to suicide. We should next examine other cases, \n\u003cA NAME=\"780\"\u003e\u003c/A\u003eLysander, for example, or Socrates, and then if these have in common indifference \n\u003cA NAME=\"781\"\u003e\u003c/A\u003ealike to good and ill fortune, I take these two results and inquire what \n\u003cA NAME=\"782\"\u003e\u003c/A\u003ecommon element have equanimity amid the vicissitudes of life and impatience \n\u003cA NAME=\"783\"\u003e\u003c/A\u003eof dishonour. If they have none, there will be two genera of pride. Besides, \n\u003cA NAME=\"784\"\u003e\u003c/A\u003eevery definition is always universal and commensurate: the physician does \n\u003cA NAME=\"785\"\u003e\u003c/A\u003enot prescribe what is healthy for a single eye, but for all eyes or for \n\u003cA NAME=\"786\"\u003e\u003c/A\u003ea determinate species of eye. It is also easier by this method to define \n\u003cA NAME=\"787\"\u003e\u003c/A\u003ethe single species than the universal, and that is why our procedure should \n\u003cA NAME=\"788\"\u003e\u003c/A\u003ebe from the several species to the universal genera-this for the further \n\u003cA NAME=\"789\"\u003e\u003c/A\u003ereason too that equivocation is less readily detected in genera than in \n\u003cA NAME=\"790\"\u003e\u003c/A\u003einfimae species. Indeed, perspicuity is essential in definitions, just \n\u003cA NAME=\"791\"\u003e\u003c/A\u003eas inferential movement is the minimum required in demonstrations; and \n\u003cA NAME=\"792\"\u003e\u003c/A\u003ewe shall attain perspicuity if we can collect separately the definition \n\u003cA NAME=\"793\"\u003e\u003c/A\u003eof each species through the group of singulars which we have established \n\u003cA NAME=\"794\"\u003e\u003c/A\u003ee.g. the definition of similarity not unqualified but restricted to colours \n\u003cA NAME=\"795\"\u003e\u003c/A\u003eand to figures; the definition of acuteness, but only of sound-and so proceed \n\u003cA NAME=\"796\"\u003e\u003c/A\u003eto the common universal with a careful avoidance of equivocation. We may \n\u003cA NAME=\"797\"\u003e\u003c/A\u003eadd that if dialectical disputation must not employ metaphors, clearly \n\u003cA NAME=\"798\"\u003e\u003c/A\u003emetaphors and metaphorical expressions are precluded in definition: otherwise \n\u003cA NAME=\"799\"\u003e\u003c/A\u003edialectic would involve metaphors.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"800\"\u003e\u003c/A\u003e\u003cB\u003ePart 14\u003c/B\u003e\n\n\u003cA NAME=\"801\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIn order to formulate the connexions we wish to prove we have to \n\u003cA NAME=\"802\"\u003e\u003c/A\u003eselect our analyses and divisions. The method of selection consists in \n\u003cA NAME=\"803\"\u003e\u003c/A\u003elaying down the common genus of all our subjects of investigation-if e.g. \n\u003cA NAME=\"804\"\u003e\u003c/A\u003ethey are animals, we lay down what the properties are which inhere in every \n\u003cA NAME=\"805\"\u003e\u003c/A\u003eanimal. These established, we next lay down the properties essentially \n\u003cA NAME=\"806\"\u003e\u003c/A\u003econnected with the first of the remaining classes-e.g. if this first subgenus \n\u003cA NAME=\"807\"\u003e\u003c/A\u003eis bird, the essential properties of every bird-and so on, always characterizing \n\u003cA NAME=\"808\"\u003e\u003c/A\u003ethe proximate subgenus. This will clearly at once enable us to say in virtue \n\u003cA NAME=\"809\"\u003e\u003c/A\u003eof what character the subgenera-man, e.g. or horse-possess their properties. \n\u003cA NAME=\"810\"\u003e\u003c/A\u003eLet A be animal, B the properties of every animal, C D E various species \n\u003cA NAME=\"811\"\u003e\u003c/A\u003eof animal. Then it is clear in virtue of what character B inheres in D-namely \n\u003cA NAME=\"812\"\u003e\u003c/A\u003eA-and that it inheres in C and E for the same reason: and throughout the \n\u003cA NAME=\"813\"\u003e\u003c/A\u003eremaining subgenera always the same rule applies.\n\u003cA NAME=\"814\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWe are now taking our examples from the traditional class-names, \n\u003cA NAME=\"815\"\u003e\u003c/A\u003ebut we must not confine ourselves to considering these. We must collect \n\u003cA NAME=\"816\"\u003e\u003c/A\u003eany other common character which we observe, and then consider with what \n\u003cA NAME=\"817\"\u003e\u003c/A\u003especies it is connected and what.properties belong to it. For example, \n\u003cA NAME=\"818\"\u003e\u003c/A\u003eas the common properties of horned animals we collect the possession of \n\u003cA NAME=\"819\"\u003e\u003c/A\u003ea third stomach and only one row of teeth. Then since it is clear in virtue \n\u003cA NAME=\"820\"\u003e\u003c/A\u003eof what character they possess these attributes-namely their horned character-the \n\u003cA NAME=\"821\"\u003e\u003c/A\u003enext question is, to what species does the possession of horns \n\u003cA NAME=\"822\"\u003e\u003c/A\u003eattach?\n\u003cA NAME=\"823\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eYet a further method of selection is by analogy: for we cannot \n\u003cA NAME=\"824\"\u003e\u003c/A\u003efind a single identical name to give to a squid\u0027s pounce, a fish\u0027s spine, \n\u003cA NAME=\"825\"\u003e\u003c/A\u003eand an animal\u0027s bone, although these too possess common properties as if \n\u003cA NAME=\"826\"\u003e\u003c/A\u003ethere were a single osseous nature.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"827\"\u003e\u003c/A\u003e\u003cB\u003ePart 15\u003c/B\u003e\n\n\u003cA NAME=\"828\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eSome connexions that require proof are identical in that they possess \n\u003cA NAME=\"829\"\u003e\u003c/A\u003ean identical \u0027middle\u0027 e.g. a whole group might be proved through \u0027reciprocal \n\u003cA NAME=\"830\"\u003e\u003c/A\u003ereplacement\u0027-and of these one class are identical in genus, namely all \n\u003cA NAME=\"831\"\u003e\u003c/A\u003ethose whose difference consists in their concerning different subjects \n\u003cA NAME=\"832\"\u003e\u003c/A\u003eor in their mode of manifestation. This latter class may be exemplified \n\u003cA NAME=\"833\"\u003e\u003c/A\u003eby the questions as to the causes respectively of echo, of reflection, \n\u003cA NAME=\"834\"\u003e\u003c/A\u003eand of the rainbow: the connexions to be proved which these questions embody \n\u003cA NAME=\"835\"\u003e\u003c/A\u003eare identical generically, because all three are forms of repercussion; \n\u003cA NAME=\"836\"\u003e\u003c/A\u003ebut specifically they are different.\n\u003cA NAME=\"837\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eOther connexions that require proof only differ in that the \u0027middle\u0027 \n\u003cA NAME=\"838\"\u003e\u003c/A\u003eof the one is subordinate to the \u0027middle\u0027 of the other. For example: Why \n\u003cA NAME=\"839\"\u003e\u003c/A\u003edoes the Nile rise towards the end of the month? Because towards its close \n\u003cA NAME=\"840\"\u003e\u003c/A\u003ethe month is more stormy. Why is the month more stormy towards its close? \n\u003cA NAME=\"841\"\u003e\u003c/A\u003eBecause the moon is waning. Here the one cause is subordinate to the \n\u003cA NAME=\"842\"\u003e\u003c/A\u003eother.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"843\"\u003e\u003c/A\u003e\u003cB\u003ePart 16\u003c/B\u003e\n\n\u003cA NAME=\"844\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThe question might be raised with regard to cause and effect whether \n\u003cA NAME=\"845\"\u003e\u003c/A\u003ewhen the effect is present the cause also is present; whether, for instance, \n\u003cA NAME=\"846\"\u003e\u003c/A\u003eif a plant sheds its leaves or the moon is eclipsed, there is present also \n\u003cA NAME=\"847\"\u003e\u003c/A\u003ethe cause of the eclipse or of the fall of the leaves-the possession of \n\u003cA NAME=\"848\"\u003e\u003c/A\u003ebroad leaves, let us say, in the latter case, in the former the earth\u0027s \n\u003cA NAME=\"849\"\u003e\u003c/A\u003einterposition. For, one might argue, if this cause is not present, these \n\u003cA NAME=\"850\"\u003e\u003c/A\u003ephenomena will have some other cause: if it is present, its effect will \n\u003cA NAME=\"851\"\u003e\u003c/A\u003ebe at once implied by it-the eclipse by the earth\u0027s interposition, the \n\u003cA NAME=\"852\"\u003e\u003c/A\u003efall of the leaves by the possession of broad leaves; but if so, they will \n\u003cA NAME=\"853\"\u003e\u003c/A\u003ebe logically coincident and each capable of proof through the other. Let \n\u003cA NAME=\"854\"\u003e\u003c/A\u003eme illustrate: Let A be deciduous character, B the possession of broad \n\u003cA NAME=\"855\"\u003e\u003c/A\u003eleaves, C vine. Now if A inheres in B (for every broad-leaved plant is \n\u003cA NAME=\"856\"\u003e\u003c/A\u003edeciduous), and B in C (every vine possessing broad leaves); then A inheres \n\u003cA NAME=\"857\"\u003e\u003c/A\u003ein C (every vine is deciduous), and the middle term B is the cause. But \n\u003cA NAME=\"858\"\u003e\u003c/A\u003ewe can also demonstrate that the vine has broad leaves because it is deciduous. \n\u003cA NAME=\"859\"\u003e\u003c/A\u003eThus, let D be broad-leaved, E deciduous, F vine. Then E inheres in F (since \n\u003cA NAME=\"860\"\u003e\u003c/A\u003eevery vine is deciduous), and D in E (for every deciduous plant has broad \n\u003cA NAME=\"861\"\u003e\u003c/A\u003eleaves): therefore every vine has broad leaves, and the cause is its deciduous \n\u003cA NAME=\"862\"\u003e\u003c/A\u003echaracter. If, however, they cannot each be the cause of the other (for \n\u003cA NAME=\"863\"\u003e\u003c/A\u003ecause is prior to effect, and the earth\u0027s interposition is the cause of \n\u003cA NAME=\"864\"\u003e\u003c/A\u003ethe moon\u0027s eclipse and not the eclipse of the interposition)-if, then, \n\u003cA NAME=\"865\"\u003e\u003c/A\u003edemonstration through the cause is of the reasoned fact and demonstration \n\u003cA NAME=\"866\"\u003e\u003c/A\u003enot through the cause is of the bare fact, one who knows it through the \n\u003cA NAME=\"867\"\u003e\u003c/A\u003eeclipse knows the fact of the earth\u0027s interposition but not the reasoned \n\u003cA NAME=\"868\"\u003e\u003c/A\u003efact. Moreover, that the eclipse is not the cause of the interposition, \n\u003cA NAME=\"869\"\u003e\u003c/A\u003ebut the interposition of the eclipse, is obvious because the interposition \n\u003cA NAME=\"870\"\u003e\u003c/A\u003eis an element in the definition of eclipse, which shows that the eclipse \n\u003cA NAME=\"871\"\u003e\u003c/A\u003eis known through the interposition and not vice versa.\n\u003cA NAME=\"872\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eOn the other hand, can a single effect have more than one cause? \n\u003cA NAME=\"873\"\u003e\u003c/A\u003eOne might argue as follows: if the same attribute is predicable of more \n\u003cA NAME=\"874\"\u003e\u003c/A\u003ethan one thing as its primary subject, let B be a primary subject in which \n\u003cA NAME=\"875\"\u003e\u003c/A\u003eA inheres, and C another primary subject of A, and D and E primary subjects \n\u003cA NAME=\"876\"\u003e\u003c/A\u003eof B and C respectively. A will then inhere in D and E, and B will be the \n\u003cA NAME=\"877\"\u003e\u003c/A\u003ecause of A\u0027s inherence in D, C of A\u0027s inherence in E. The presence of the \n\u003cA NAME=\"878\"\u003e\u003c/A\u003ecause thus necessitates that of the effect, but the presence of the effect \n\u003cA NAME=\"879\"\u003e\u003c/A\u003enecessitates the presence not of all that may cause it but only of a cause \n\u003cA NAME=\"880\"\u003e\u003c/A\u003ewhich yet need not be the whole cause. We may, however, suggest that if \n\u003cA NAME=\"881\"\u003e\u003c/A\u003ethe connexion to be proved is always universal and commensurate, not only \n\u003cA NAME=\"882\"\u003e\u003c/A\u003ewill the cause be a whole but also the effect will be universal and commensurate. \n\u003cA NAME=\"883\"\u003e\u003c/A\u003eFor instance, deciduous character will belong exclusively to a subject \n\u003cA NAME=\"884\"\u003e\u003c/A\u003ewhich is a whole, and, if this whole has species, universally and commensurately \n\u003cA NAME=\"885\"\u003e\u003c/A\u003eto those species-i.e. either to all species of plant or to a single species. \n\u003cA NAME=\"886\"\u003e\u003c/A\u003eSo in these universal and commensurate connexions the \u0027middle\u0027 and its \n\u003cA NAME=\"887\"\u003e\u003c/A\u003eeffect must reciprocate, i.e. be convertible. Supposing, for example, that \n\u003cA NAME=\"888\"\u003e\u003c/A\u003ethe reason why trees are deciduous is the coagulation of sap, then if a \n\u003cA NAME=\"889\"\u003e\u003c/A\u003etree is deciduous, coagulation must be present, and if coagulation is present-not \n\u003cA NAME=\"890\"\u003e\u003c/A\u003ein any subject but in a tree-then that tree must be \n\u003cA NAME=\"891\"\u003e\u003c/A\u003edeciduous.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"892\"\u003e\u003c/A\u003e\u003cB\u003ePart 17\u003c/B\u003e\n\n\u003cA NAME=\"893\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eCan the cause of an identical effect be not identical in every \n\u003cA NAME=\"894\"\u003e\u003c/A\u003einstance of the effect but different? Or is that impossible? Perhaps it \n\u003cA NAME=\"895\"\u003e\u003c/A\u003eis impossible if the effect is demonstrated as essential and not as inhering \n\u003cA NAME=\"896\"\u003e\u003c/A\u003ein virtue of a symptom or an accident-because the middle is then the definition \n\u003cA NAME=\"897\"\u003e\u003c/A\u003eof the major term-though possible if the demonstration is not essential. \n\u003cA NAME=\"898\"\u003e\u003c/A\u003eNow it is possible to consider the effect and its subject as an accidental \n\u003cA NAME=\"899\"\u003e\u003c/A\u003econjunction, though such conjunctions would not be regarded as connexions \n\u003cA NAME=\"900\"\u003e\u003c/A\u003edemanding scientific proof. But if they are accepted as such, the middle \n\u003cA NAME=\"901\"\u003e\u003c/A\u003ewill correspond to the extremes, and be equivocal if they are equivocal, \n\u003cA NAME=\"902\"\u003e\u003c/A\u003egenerically one if they are generically one. Take the question why proportionals \n\u003cA NAME=\"903\"\u003e\u003c/A\u003ealternate. The cause when they are lines, and when they are numbers, is \n\u003cA NAME=\"904\"\u003e\u003c/A\u003eboth different and identical; different in so far as lines are lines and \n\u003cA NAME=\"905\"\u003e\u003c/A\u003enot numbers, identical as involving a given determinate increment. In all \n\u003cA NAME=\"906\"\u003e\u003c/A\u003eproportionals this is so. Again, the cause of likeness between colour and \n\u003cA NAME=\"907\"\u003e\u003c/A\u003ecolour is other than that between figure and figure; for likeness here \n\u003cA NAME=\"908\"\u003e\u003c/A\u003eis equivocal, meaning perhaps in the latter case equality of the ratios \n\u003cA NAME=\"909\"\u003e\u003c/A\u003eof the sides and equality of the angles, in the case of colours identity \n\u003cA NAME=\"910\"\u003e\u003c/A\u003eof the act of perceiving them, or something else of the sort. Again, connexions \n\u003cA NAME=\"911\"\u003e\u003c/A\u003erequiring proof which are identical by analogy middles also \n\u003cA NAME=\"912\"\u003e\u003c/A\u003eanalogous.\n\u003cA NAME=\"913\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThe truth is that cause, effect, and subject are reciprocally predicable \n\u003cA NAME=\"914\"\u003e\u003c/A\u003ein the following way. If the species are taken severally, the effect is \n\u003cA NAME=\"915\"\u003e\u003c/A\u003ewider than the subject (e.g. the possession of external angles equal to \n\u003cA NAME=\"916\"\u003e\u003c/A\u003efour right angles is an attribute wider than triangle or are), but it is \n\u003cA NAME=\"917\"\u003e\u003c/A\u003ecoextensive with the species taken collectively (in this instance with \n\u003cA NAME=\"918\"\u003e\u003c/A\u003eall figures whose external angles are equal to four right angles). And \n\u003cA NAME=\"919\"\u003e\u003c/A\u003ethe middle likewise reciprocates, for the middle is a definition of the \n\u003cA NAME=\"920\"\u003e\u003c/A\u003emajor; which is incidentally the reason why all the sciences are built \n\u003cA NAME=\"921\"\u003e\u003c/A\u003eup through definition.\n\u003cA NAME=\"922\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWe may illustrate as follows. Deciduous is a universal attribute \n\u003cA NAME=\"923\"\u003e\u003c/A\u003eof vine, and is at the same time of wider extent than vine; and of fig, \n\u003cA NAME=\"924\"\u003e\u003c/A\u003eand is of wider extent than fig: but it is not wider than but coextensive \n\u003cA NAME=\"925\"\u003e\u003c/A\u003ewith the totality of the species. Then if you take the middle which is \n\u003cA NAME=\"926\"\u003e\u003c/A\u003eproximate, it is a definition of deciduous. I say that, because you will \n\u003cA NAME=\"927\"\u003e\u003c/A\u003efirst reach a middle next the subject, and a premiss asserting it of the \n\u003cA NAME=\"928\"\u003e\u003c/A\u003ewhole subject, and after that a middle-the coagulation of sap or something \n\u003cA NAME=\"929\"\u003e\u003c/A\u003eof the sort-proving the connexion of the first middle with the major: but \n\u003cA NAME=\"930\"\u003e\u003c/A\u003eit is the coagulation of sap at the junction of leaf-stalk and stem which \n\u003cA NAME=\"931\"\u003e\u003c/A\u003edefines deciduous.\n\u003cA NAME=\"932\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIf an explanation in formal terms of the inter-relation of cause \n\u003cA NAME=\"933\"\u003e\u003c/A\u003eand effect is demanded, we shall offer the following. Let A be an attribute \n\u003cA NAME=\"934\"\u003e\u003c/A\u003eof all B, and B of every species of D, but so that both A and B are wider \n\u003cA NAME=\"935\"\u003e\u003c/A\u003ethan their respective subjects. Then B will be a universal attribute of \n\u003cA NAME=\"936\"\u003e\u003c/A\u003eeach species of D (since I call such an attribute universal even if it \n\u003cA NAME=\"937\"\u003e\u003c/A\u003eis not commensurate, and I call an attribute primary universal if it is \n\u003cA NAME=\"938\"\u003e\u003c/A\u003ecommensurate, not with each species severally but with their totality), \n\u003cA NAME=\"939\"\u003e\u003c/A\u003eand it extends beyond each of them taken separately.\n\u003cA NAME=\"940\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThus, B is the cause of A\u0027s inherence in the species of D: consequently \n\u003cA NAME=\"941\"\u003e\u003c/A\u003eA must be of wider extent than B; otherwise why should B be the cause of \n\u003cA NAME=\"942\"\u003e\u003c/A\u003eA\u0027s inherence in D any more than A the cause of B\u0027s inherence in D? Now \n\u003cA NAME=\"943\"\u003e\u003c/A\u003eif A is an attribute of all the species of E, all the species of E will \n\u003cA NAME=\"944\"\u003e\u003c/A\u003ebe united by possessing some common cause other than B: otherwise how shall \n\u003cA NAME=\"945\"\u003e\u003c/A\u003ewe be able to say that A is predicable of all of which E is predicable, \n\u003cA NAME=\"946\"\u003e\u003c/A\u003ewhile E is not predicable of all of which A can be predicated? I mean how \n\u003cA NAME=\"947\"\u003e\u003c/A\u003ecan there fail to be some special cause of A\u0027s inherence in E, as there \n\u003cA NAME=\"948\"\u003e\u003c/A\u003ewas of A\u0027s inherence in all the species of D? Then are the species of E, \n\u003cA NAME=\"949\"\u003e\u003c/A\u003etoo, united by possessing some common cause? This cause we must look for. \n\u003cA NAME=\"950\"\u003e\u003c/A\u003eLet us call it C.\n\u003cA NAME=\"951\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWe conclude, then, that the same effect may have more than one \n\u003cA NAME=\"952\"\u003e\u003c/A\u003ecause, but not in subjects specifically identical. For instance, the cause \n\u003cA NAME=\"953\"\u003e\u003c/A\u003eof longevity in quadrupeds is lack of bile, in birds a dry constitution-or \n\u003cA NAME=\"954\"\u003e\u003c/A\u003ecertainly something different.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"955\"\u003e\u003c/A\u003e\u003cB\u003ePart 18\u003c/B\u003e\n\n\u003cA NAME=\"956\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIf immediate premisses are not reached at once, and there is not \n\u003cA NAME=\"957\"\u003e\u003c/A\u003emerely one middle but several middles, i.e. several causes; is the cause \n\u003cA NAME=\"958\"\u003e\u003c/A\u003eof the property\u0027s inherence in the several species the middle which is \n\u003cA NAME=\"959\"\u003e\u003c/A\u003eproximate to the primary universal, or the middle which is proximate to \n\u003cA NAME=\"960\"\u003e\u003c/A\u003ethe species? Clearly the cause is that nearest to each species severally \n\u003cA NAME=\"961\"\u003e\u003c/A\u003ein which it is manifested, for that is the cause of the subject\u0027s falling \n\u003cA NAME=\"962\"\u003e\u003c/A\u003eunder the universal. To illustrate formally: C is the cause of B\u0027s inherence \n\u003cA NAME=\"963\"\u003e\u003c/A\u003ein D; hence C is the cause of A\u0027s inherence in D, B of A\u0027s inherence in \n\u003cA NAME=\"964\"\u003e\u003c/A\u003eC, while the cause of A\u0027s inherence in B is B itself.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"965\"\u003e\u003c/A\u003e\u003cB\u003ePart 19\u003c/B\u003e\n\n\u003cA NAME=\"966\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eAs regards syllogism and demonstration, the definition of, and \n\u003cA NAME=\"967\"\u003e\u003c/A\u003ethe conditions required to produce each of them, are now clear, and with \n\u003cA NAME=\"968\"\u003e\u003c/A\u003ethat also the definition of, and the conditions required to produce, demonstrative \n\u003cA NAME=\"969\"\u003e\u003c/A\u003eknowledge, since it is the same as demonstration. As to the basic premisses, \n\u003cA NAME=\"970\"\u003e\u003c/A\u003ehow they become known and what is the developed state of knowledge of them \n\u003cA NAME=\"971\"\u003e\u003c/A\u003eis made clear by raising some preliminary problems.\n\u003cA NAME=\"972\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWe have already said that scientific knowledge through demonstration \n\u003cA NAME=\"973\"\u003e\u003c/A\u003eis impossible unless a man knows the primary immediate premisses. But there \n\u003cA NAME=\"974\"\u003e\u003c/A\u003eare questions which might be raised in respect of the apprehension of these \n\u003cA NAME=\"975\"\u003e\u003c/A\u003eimmediate premisses: one might not only ask whether it is of the same kind \n\u003cA NAME=\"976\"\u003e\u003c/A\u003eas the apprehension of the conclusions, but also whether there is or is \n\u003cA NAME=\"977\"\u003e\u003c/A\u003enot scientific knowledge of both; or scientific knowledge of the latter, \n\u003cA NAME=\"978\"\u003e\u003c/A\u003eand of the former a different kind of knowledge; and, further, whether \n\u003cA NAME=\"979\"\u003e\u003c/A\u003ethe developed states of knowledge are not innate but come to be in us, \n\u003cA NAME=\"980\"\u003e\u003c/A\u003eor are innate but at first unnoticed. Now it is strange if we possess them \n\u003cA NAME=\"981\"\u003e\u003c/A\u003efrom birth; for it means that we possess apprehensions more accurate than \n\u003cA NAME=\"982\"\u003e\u003c/A\u003edemonstration and fail to notice them. If on the other hand we acquire \n\u003cA NAME=\"983\"\u003e\u003c/A\u003ethem and do not previously possess them, how could we apprehend and learn \n\u003cA NAME=\"984\"\u003e\u003c/A\u003ewithout a basis of pre-existent knowledge? For that is impossible, as we \n\u003cA NAME=\"985\"\u003e\u003c/A\u003eused to find in the case of demonstration. So it emerges that neither can \n\u003cA NAME=\"986\"\u003e\u003c/A\u003ewe possess them from birth, nor can they come to be in us if we are without \n\u003cA NAME=\"987\"\u003e\u003c/A\u003eknowledge of them to the extent of having no such developed state at all. \n\u003cA NAME=\"988\"\u003e\u003c/A\u003eTherefore we must possess a capacity of some sort, but not such as to rank \n\u003cA NAME=\"989\"\u003e\u003c/A\u003ehigher in accuracy than these developed states. And this at least is an \n\u003cA NAME=\"990\"\u003e\u003c/A\u003eobvious characteristic of all animals, for they possess a congenital discriminative \n\u003cA NAME=\"991\"\u003e\u003c/A\u003ecapacity which is called sense-perception. But though sense-perception \n\u003cA NAME=\"992\"\u003e\u003c/A\u003eis innate in all animals, in some the sense-impression comes to persist, \n\u003cA NAME=\"993\"\u003e\u003c/A\u003ein others it does not. So animals in which this persistence does not come \n\u003cA NAME=\"994\"\u003e\u003c/A\u003eto be have either no knowledge at all outside the act of perceiving, or \n\u003cA NAME=\"995\"\u003e\u003c/A\u003eno knowledge of objects of which no impression persists; animals in which \n\u003cA NAME=\"996\"\u003e\u003c/A\u003eit does come into being have perception and can continue to retain the \n\u003cA NAME=\"997\"\u003e\u003c/A\u003esense-impression in the soul: and when such persistence is frequently repeated \n\u003cA NAME=\"998\"\u003e\u003c/A\u003ea further distinction at once arises between those which out of the persistence \n\u003cA NAME=\"999\"\u003e\u003c/A\u003eof such sense-impressions develop a power of systematizing them and those \n\u003cA NAME=\"1000\"\u003e\u003c/A\u003ewhich do not. So out of sense-perception comes to be what we call memory, \n\u003cA NAME=\"1001\"\u003e\u003c/A\u003eand out of frequently repeated memories of the same thing develops experience; \n\u003cA NAME=\"1002\"\u003e\u003c/A\u003efor a number of memories constitute a single experience. From experience \n\u003cA NAME=\"1003\"\u003e\u003c/A\u003eagain-i.e. from the universal now stabilized in its entirety within the \n\u003cA NAME=\"1004\"\u003e\u003c/A\u003esoul, the one beside the many which is a single identity within them all-originate \n\u003cA NAME=\"1005\"\u003e\u003c/A\u003ethe skill of the craftsman and the knowledge of the man of science, skill \n\u003cA NAME=\"1006\"\u003e\u003c/A\u003ein the sphere of coming to be and science in the sphere of \n\u003cA NAME=\"1007\"\u003e\u003c/A\u003ebeing.\n\u003cA NAME=\"1008\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWe conclude that these states of knowledge are neither innate in \n\u003cA NAME=\"1009\"\u003e\u003c/A\u003ea determinate form, nor developed from other higher states of knowledge, \n\u003cA NAME=\"1010\"\u003e\u003c/A\u003ebut from sense-perception. It is like a rout in battle stopped by first \n\u003cA NAME=\"1011\"\u003e\u003c/A\u003eone man making a stand and then another, until the original formation has \n\u003cA NAME=\"1012\"\u003e\u003c/A\u003ebeen restored. The soul is so constituted as to be capable of this \n\u003cA NAME=\"1013\"\u003e\u003c/A\u003eprocess.\n\u003cA NAME=\"1014\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eLet us now restate the account given already, though with insufficient \n\u003cA NAME=\"1015\"\u003e\u003c/A\u003eclearness. When one of a number of logically indiscriminable particulars \n\u003cA NAME=\"1016\"\u003e\u003c/A\u003ehas made a stand, the earliest universal is present in the soul: for though \n\u003cA NAME=\"1017\"\u003e\u003c/A\u003ethe act of sense-perception is of the particular, its content is universal-is \n\u003cA NAME=\"1018\"\u003e\u003c/A\u003eman, for example, not the man Callias. A fresh stand is made among these \n\u003cA NAME=\"1019\"\u003e\u003c/A\u003erudimentary universals, and the process does not cease until the indivisible \n\u003cA NAME=\"1020\"\u003e\u003c/A\u003econcepts, the true universals, are established: e.g. such and such a species \n\u003cA NAME=\"1021\"\u003e\u003c/A\u003eof animal is a step towards the genus animal, which by the same process \n\u003cA NAME=\"1022\"\u003e\u003c/A\u003eis a step towards a further generalization.\n\u003cA NAME=\"1023\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThus it is clear that we must get to know the primary premisses \n\u003cA NAME=\"1024\"\u003e\u003c/A\u003eby induction; for the method by which even sense-perception implants the \n\u003cA NAME=\"1025\"\u003e\u003c/A\u003euniversal is inductive. Now of the thinking states by which we grasp truth, \n\u003cA NAME=\"1026\"\u003e\u003c/A\u003esome are unfailingly true, others admit of error-opinion, for instance, \n\u003cA NAME=\"1027\"\u003e\u003c/A\u003eand calculation, whereas scientific knowing and intuition are always true: \n\u003cA NAME=\"1028\"\u003e\u003c/A\u003efurther, no other kind of thought except intuition is more accurate than \n\u003cA NAME=\"1029\"\u003e\u003c/A\u003escientific knowledge, whereas primary premisses are more knowable than \n\u003cA NAME=\"1030\"\u003e\u003c/A\u003edemonstrations, and all scientific knowledge is discursive. From these \n\u003cA NAME=\"1031\"\u003e\u003c/A\u003econsiderations it follows that there will be no scientific knowledge of \n\u003cA NAME=\"1032\"\u003e\u003c/A\u003ethe primary premisses, and since except intuition nothing can be truer \n\u003cA NAME=\"1033\"\u003e\u003c/A\u003ethan scientific knowledge, it will be intuition that apprehends the primary \n\u003cA NAME=\"1034\"\u003e\u003c/A\u003epremisses-a result which also follows from the fact that demonstration \n\u003cA NAME=\"1035\"\u003e\u003c/A\u003ecannot be the originative source of demonstration, nor, consequently, scientific \n\u003cA NAME=\"1036\"\u003e\u003c/A\u003eknowledge of scientific knowledge.If, therefore, it is the only other kind \n\u003cA NAME=\"1037\"\u003e\u003c/A\u003eof true thinking except scientific knowing, intuition will be the originative \n\u003cA NAME=\"1038\"\u003e\u003c/A\u003esource of scientific knowledge. And the originative source of science grasps \n\u003cA NAME=\"1039\"\u003e\u003c/A\u003ethe original basic premiss, while science as a whole is similarly related \n\u003cA NAME=\"1040\"\u003e\u003c/A\u003eas originative source to the whole body of fact.\n\n\u003cA NAME=\"end\"\u003e\u003c/A\u003e\n\u003cbr\u003e\u003cbr\u003e\u003cB\u003eTHE END\u003c/B\u003e\n\u003cBR\u003e\u003cHR SIZE=\"1\" COLOR=\"990033\" NOSHADE\u003e\u003cBR\u003e\n\n\u003cTABLE WIDTH=\"60%\" BORDER=\"0\"\u003e\n\u003cTR VALIGN=\"TOP\"\u003e\n\u003cTD ALIGN=\"LEFT\" WIDTH=\"30%\" NOWRAP\u003e\u003cA HREF=\"posterior.1.i.html\"Book I\u0027; return true;\"\u003e \u003c/A\u003e\n\n\u0026nbsp;\u0026nbsp;\u0026nbsp;\u003c/TD\u003e\n\u003cTD ALIGN=\"CENTER\" NOWRAP\u003e\u003cA HREF=\"posterior.html\"Go to table of contents\u0027; return true;\"\u003eTable of Contents\u003c/A\u003e\u003c/TD\u003e\n\u003cTD ALIGN=\"RIGHT\" WIDTH=\"30%\" NOWRAP\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u003c/TD\u003e\n\u003c/TR\u003e\n\u003c/TABLE\u003e\u003c/BLOCKQUOTE\u003e\n\n\u003cTABLE BORDER=\"0\" CELLSPACING=\"15\"\u003e\n\u003cTR ALIGN=\"CENTER\" VALIGN=\"CENTER\"\u003e\n\u003cTD ALIGN=\"CENTER\" VALIGN=\"BOTTOM\" NOWRAP\u003e\u003ca href=\"/index.html\"Go to home page\u0027; return true;\" TARGET=\"_top\"\u003e \u003c/A\u003e\n\u003cFONT SIZE=\"-1\"\u003e\u003cBR\u003e\u003ca href=\"/index.html\"Go to home page\u0027; return true;\" TARGET=\"_top\"\u003eHome\u003c/A\u003e\u003cBR\u003e\u0026nbsp;\u003c/FONT\u003e\u003c/TD\u003e\n\n\u003cTD ALIGN=\"CENTER\" VALIGN=\"BOTTOM\" NOWRAP\u003e\u003ca href=\"/Browse/index-Aristotle.html\"Browse a list of titles\u0027; return true;\" TARGET=\"_top\"\u003e \u003c/A\u003e\n\u003cFONT SIZE=\"-1\"\u003e\u003cBR\u003e\u003ca href=\"/Browse/index-Aristotle.html\"Browse a list of titles\u0027; return true;\" TARGET=\"_top\"\u003eBrowse and\u003cBR\u003eComment\u003c/A\u003e\u003c/FONT\u003e\u003c/TD\u003e\n\n\u003cTD ALIGN=\"CENTER\" VALIGN=\"BOTTOM\" NOWRAP\u003e\u003ca href=\"/Search/index.html\"Search texts\u0027; return true;\" TARGET=\"_top\"\u003e \u003c/A\u003e\n\u003cFONT SIZE=\"-1\"\u003e\u003cBR\u003e\u003ca href=\"/Search/index.html\"Search texts\u0027; return true;\" TARGET=\"_top\"\u003eSearch\u003c/A\u003e\u003cBR\u003e\u0026nbsp;\u003c/FONT\u003e\u003c/TD\u003e\n\n\u003cTD ALIGN=\"CENTER\" VALIGN=\"BOTTOM\" NOWRAP\u003e\u003ca href=\"/Buy/Aristotle.html\"Buy books and CD-ROMs\u0027; return true;\" TARGET=\"_top\"\u003e \u003c/A\u003e\n\u003cFONT SIZE=\"-1\"\u003e\u003cBR\u003e\u003ca href=\"/Buy/Aristotle.html\"Buy books and CD-ROMs\u0027; return true;\" TARGET=\"_top\"\u003eBuy Books and\u003cBR\u003eCD-ROMs\u003c/A\u003e\u003c/FONT\u003e\u003c/TD\u003e\n\n\u003cTD ALIGN=\"CENTER\" VALIGN=\"BOTTOM\" NOWRAP\u003e\u003ca href=\"/Help/general.html\"Get help\u0027; return true;\" TARGET=\"_top\"\u003e \u003c/A\u003e\n\u003cFONT SIZE=\"-1\"\u003e\u003cBR\u003e\u003ca href=\"/Help/general.html\"Get help\u0027; return true;\" TARGET=\"_top\"\u003eHelp\u003c/A\u003e\u003cBR\u003e\u0026nbsp;\u003c/FONT\u003e\u003c/TD\u003e\n\n\u003c/TR\u003e\n\u003c/TABLE\u003e\n\n\u003cBR\u003e\u003cBR\u003e\u003cFONT SIZE=\"-1\"\u003e\u003cNOBR\u003e\u003ca href=\"/Help/permissions.html\"View information on copyright and permissions\u0027; return true;\"\u003e\u0026copy; 1994-2009\u003c/A\u003e\u003c/NOBR\u003e\u003c/FONT\u003e\u003c/FONT\u003e\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}}