Prior Analytics
{"WorkMasterId":4932,"WpPageId":243290,"ParentWpPageId":189130,"Slug":"prior-analytics","Url":"https://chrisdeasy.com/theos/humanities/philosophy/philosophers/aristotle-of-stagira/prior-analytics/","RelativeUrl":"theos/humanities/philosophy/philosophers/aristotle-of-stagira/prior-analytics/","HasFullText":true,"RawHtmlLength":272708,"CleanHtmlLength":215367,"Kicker":"Philosophy Work","Title":"Prior Analytics","Deck":"Founded syllogistic logic by analyzing valid deduction through term relations and formal inference patterns.","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":"350 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 Πρότερα","Language":"Ancient Greek","DisciplineCards":[{"Label":"Primary Discipline","Key":"Discipline:logic"},{"Label":"Secondary Discipline","Key":"Discipline:epistemology"}],"Tradition":"Aristotelian philosophy","FullText":{"Title":"Full Text","Copy":"Full text from MIT Internet Classics Archive: Prior Analytics .","Url":"","Label":"","Kicker":"","Cards":[]},"CoreThesis":["Founded syllogistic logic by analyzing valid deduction through term relations and formal inference patterns."],"Classification":{"AlternateTitles":"Analytica Priora","KeyConcepts":"syllogism; deduction; terms; validity; proof","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\"\u003ePrior 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/prior.html\"\u003eOpen full version\u003c/a\u003e\n \u003c/article\u003e\n \u003c/div\u003e"},{"Kind":"TextSection","Title":"Core Thesis","Paragraphs":["Founded syllogistic logic by analyzing valid deduction through term relations and formal inference patterns."]},{"Kind":"FieldSection","Title":"Classification","Fields":[{"Label":"Alternate Titles","Value":"Analytica Priora"},{"Label":"Key Concepts","Value":"syllogism; deduction; terms; validity; proof"},{"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/prior.html\"\u003eMIT Internet Classics Archive: Prior 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.prior; expires=1-Jan-102 00:00:00 GMT; path=/\"\u003e\n\u003cMETA NAME=\"description\" CONTENT=\"Prior 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, Prior Analytics, Aristotle, Aristotle\"\u003e\n\u003cTITLE\u003eThe Internet Classics Archive | Prior 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\u003ePrior 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\u003ePrior Analytics\u003c/U\u003e.\n\n\u003cBR\u003e\u003cBR\u003e\u003cB\u003eDownload:\u003c/B\u003e A \ntext-only version is \u003cA HREF=\"prior.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\u003ePrior 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 A. J. Jenkinson\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=\"prior.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=\"prior.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\u003eWe must first state the subject of our inquiry and the faculty to which \n\u003cA NAME=\"12\"\u003e\u003c/A\u003eit belongs: its subject is demonstration and the faculty that carries it \n\u003cA NAME=\"13\"\u003e\u003c/A\u003eout demonstrative science. We must next define a premiss, a term, and a \n\u003cA NAME=\"14\"\u003e\u003c/A\u003esyllogism, and the nature of a perfect and of an imperfect syllogism; and \n\u003cA NAME=\"15\"\u003e\u003c/A\u003eafter that, the inclusion or noninclusion of one term in another as in \n\u003cA NAME=\"16\"\u003e\u003c/A\u003ea whole, and what we mean by predicating one term of all, or none, of \n\u003cA NAME=\"17\"\u003e\u003c/A\u003eanother.\n\u003cA NAME=\"18\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eA premiss then is a sentence affirming or denying one thing of \n\u003cA NAME=\"19\"\u003e\u003c/A\u003eanother. This is either universal or particular or indefinite. By universal \n\u003cA NAME=\"20\"\u003e\u003c/A\u003eI mean the statement that something belongs to all or none of something \n\u003cA NAME=\"21\"\u003e\u003c/A\u003eelse; by particular that it belongs to some or not to some or not to all; \n\u003cA NAME=\"22\"\u003e\u003c/A\u003eby indefinite that it does or does not belong, without any mark to show \n\u003cA NAME=\"23\"\u003e\u003c/A\u003ewhether it is universal or particular, e.g. \u0027contraries are subjects of \n\u003cA NAME=\"24\"\u003e\u003c/A\u003ethe same science\u0027, or \u0027pleasure is not good\u0027. The demonstrative premiss \n\u003cA NAME=\"25\"\u003e\u003c/A\u003ediffers from the dialectical, because the demonstrative premiss is the \n\u003cA NAME=\"26\"\u003e\u003c/A\u003eassertion of one of two contradictory statements (the demonstrator does \n\u003cA NAME=\"27\"\u003e\u003c/A\u003enot ask for his premiss, but lays it down), whereas the dialectical premiss \n\u003cA NAME=\"28\"\u003e\u003c/A\u003edepends on the adversary\u0027s choice between two contradictories. But this \n\u003cA NAME=\"29\"\u003e\u003c/A\u003ewill make no difference to the production of a syllogism in either case; \n\u003cA NAME=\"30\"\u003e\u003c/A\u003efor both the demonstrator and the dialectician argue syllogistically after \n\u003cA NAME=\"31\"\u003e\u003c/A\u003estating that something does or does not belong to something else. Therefore \n\u003cA NAME=\"32\"\u003e\u003c/A\u003ea syllogistic premiss without qualification will be an affirmation or denial \n\u003cA NAME=\"33\"\u003e\u003c/A\u003eof something concerning something else in the way we have described; it \n\u003cA NAME=\"34\"\u003e\u003c/A\u003ewill be demonstrative, if it is true and obtained through the first principles \n\u003cA NAME=\"35\"\u003e\u003c/A\u003eof its science; while a dialectical premiss is the giving of a choice between \n\u003cA NAME=\"36\"\u003e\u003c/A\u003etwo contradictories, when a man is proceeding by question, but when he \n\u003cA NAME=\"37\"\u003e\u003c/A\u003eis syllogizing it is the assertion of that which is apparent and generally \n\u003cA NAME=\"38\"\u003e\u003c/A\u003eadmitted, as has been said in the Topics. The nature then of a premiss \n\u003cA NAME=\"39\"\u003e\u003c/A\u003eand the difference between syllogistic, demonstrative, and dialectical \n\u003cA NAME=\"40\"\u003e\u003c/A\u003epremisses, may be taken as sufficiently defined by us in relation to our \n\u003cA NAME=\"41\"\u003e\u003c/A\u003epresent need, but will be stated accurately in the sequel.\n\u003cA NAME=\"42\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eI call that a term into which the premiss is resolved, i.e. both \n\u003cA NAME=\"43\"\u003e\u003c/A\u003ethe predicate and that of which it is predicated, \u0027being\u0027 being added and \n\u003cA NAME=\"44\"\u003e\u003c/A\u003e\u0027not being\u0027 removed, or vice versa.\n\u003cA NAME=\"45\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eA syllogism is discourse in which, certain things being stated, \n\u003cA NAME=\"46\"\u003e\u003c/A\u003esomething other than what is stated follows of necessity from their being \n\u003cA NAME=\"47\"\u003e\u003c/A\u003eso. I mean by the last phrase that they produce the consequence, and by \n\u003cA NAME=\"48\"\u003e\u003c/A\u003ethis, that no further term is required from without in order to make the \n\u003cA NAME=\"49\"\u003e\u003c/A\u003econsequence necessary.\n\u003cA NAME=\"50\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eI call that a perfect syllogism which needs nothing other than \n\u003cA NAME=\"51\"\u003e\u003c/A\u003ewhat has been stated to make plain what necessarily follows; a syllogism \n\u003cA NAME=\"52\"\u003e\u003c/A\u003eis imperfect, if it needs either one or more propositions, which are indeed \n\u003cA NAME=\"53\"\u003e\u003c/A\u003ethe necessary consequences of the terms set down, but have not been expressly \n\u003cA NAME=\"54\"\u003e\u003c/A\u003estated as premisses.\n\u003cA NAME=\"55\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThat one term should be included in another as in a whole is the \n\u003cA NAME=\"56\"\u003e\u003c/A\u003esame as for the other to be predicated of all of the first. And we say \n\u003cA NAME=\"57\"\u003e\u003c/A\u003ethat one term is predicated of all of another, whenever no instance of \n\u003cA NAME=\"58\"\u003e\u003c/A\u003ethe subject can be found of which the other term cannot be asserted: \u0027to \n\u003cA NAME=\"59\"\u003e\u003c/A\u003ebe predicated of none\u0027 must be understood in the same \n\u003cA NAME=\"60\"\u003e\u003c/A\u003eway.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"61\"\u003e\u003c/A\u003e\u003cB\u003ePart 2\u003c/B\u003e\n\n\u003cA NAME=\"62\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eEvery premiss states that something either is or must be or may \n\u003cA NAME=\"63\"\u003e\u003c/A\u003ebe the attribute of something else; of premisses of these three kinds some \n\u003cA NAME=\"64\"\u003e\u003c/A\u003eare affirmative, others negative, in respect of each of the three modes \n\u003cA NAME=\"65\"\u003e\u003c/A\u003eof attribution; again some affirmative and negative premisses are universal, \n\u003cA NAME=\"66\"\u003e\u003c/A\u003eothers particular, others indefinite. It is necessary then that in universal \n\u003cA NAME=\"67\"\u003e\u003c/A\u003eattribution the terms of the negative premiss should be convertible, e.g. \n\u003cA NAME=\"68\"\u003e\u003c/A\u003eif no pleasure is good, then no good will be pleasure; the terms of the \n\u003cA NAME=\"69\"\u003e\u003c/A\u003eaffirmative must be convertible, not however, universally, but in part, \n\u003cA NAME=\"70\"\u003e\u003c/A\u003ee.g. if every pleasure,is good, some good must be pleasure; the particular \n\u003cA NAME=\"71\"\u003e\u003c/A\u003eaffirmative must convert in part (for if some pleasure is good, then some \n\u003cA NAME=\"72\"\u003e\u003c/A\u003egood will be pleasure); but the particular negative need not convert, for \n\u003cA NAME=\"73\"\u003e\u003c/A\u003eif some animal is not man, it does not follow that some man is not \n\u003cA NAME=\"74\"\u003e\u003c/A\u003eanimal.\n\u003cA NAME=\"75\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eFirst then take a universal negative with the terms A and B. If \n\u003cA NAME=\"76\"\u003e\u003c/A\u003eno B is A, neither can any A be B. For if some A (say C) were B, it would \n\u003cA NAME=\"77\"\u003e\u003c/A\u003enot be true that no B is A; for C is a B. But if every B is A then some \n\u003cA NAME=\"78\"\u003e\u003c/A\u003eA is B. For if no A were B, then no B could be A. But we assumed that every \n\u003cA NAME=\"79\"\u003e\u003c/A\u003eB is A. Similarly too, if the premiss is particular. For if some B is A, \n\u003cA NAME=\"80\"\u003e\u003c/A\u003ethen some of the As must be B. For if none were, then no B would be A. \n\u003cA NAME=\"81\"\u003e\u003c/A\u003eBut if some B is not A, there is no necessity that some of the As should \n\u003cA NAME=\"82\"\u003e\u003c/A\u003enot be B; e.g. let B stand for animal and A for man. Not every animal is \n\u003cA NAME=\"83\"\u003e\u003c/A\u003ea man; but every man is an animal.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"84\"\u003e\u003c/A\u003e\u003cB\u003ePart 3\u003c/B\u003e\n\n\u003cA NAME=\"85\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThe same manner of conversion will hold good also in respect of \n\u003cA NAME=\"86\"\u003e\u003c/A\u003enecessary premisses. The universal negative converts universally; each \n\u003cA NAME=\"87\"\u003e\u003c/A\u003eof the affirmatives converts into a particular. If it is necessary that \n\u003cA NAME=\"88\"\u003e\u003c/A\u003eno B is A, it is necessary also that no A is B. For if it is possible that \n\u003cA NAME=\"89\"\u003e\u003c/A\u003esome A is B, it would be possible also that some B is A. If all or some \n\u003cA NAME=\"90\"\u003e\u003c/A\u003eB is A of necessity, it is necessary also that some A is B: for if there \n\u003cA NAME=\"91\"\u003e\u003c/A\u003ewere no necessity, neither would some of the Bs be A necessarily. But the \n\u003cA NAME=\"92\"\u003e\u003c/A\u003eparticular negative does not convert, for the same reason which we have \n\u003cA NAME=\"93\"\u003e\u003c/A\u003ealready stated.\n\u003cA NAME=\"94\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIn respect of possible premisses, since possibility is used in \n\u003cA NAME=\"95\"\u003e\u003c/A\u003eseveral senses (for we say that what is necessary and what is not necessary \n\u003cA NAME=\"96\"\u003e\u003c/A\u003eand what is potential is possible), affirmative statements will all convert \n\u003cA NAME=\"97\"\u003e\u003c/A\u003ein a manner similar to those described. For if it is possible that all \n\u003cA NAME=\"98\"\u003e\u003c/A\u003eor some B is A, it will be possible that some A is B. For if that were \n\u003cA NAME=\"99\"\u003e\u003c/A\u003enot possible, then no B could possibly be A. This has been already proved. \n\u003cA NAME=\"100\"\u003e\u003c/A\u003eBut in negative statements the case is different. Whatever is said to be \n\u003cA NAME=\"101\"\u003e\u003c/A\u003epossible, either because B necessarily is A, or because B is not necessarily \n\u003cA NAME=\"102\"\u003e\u003c/A\u003eA, admits of conversion like other negative statements, e.g. if one should \n\u003cA NAME=\"103\"\u003e\u003c/A\u003esay, it is possible that man is not horse, or that no garment is white. \n\u003cA NAME=\"104\"\u003e\u003c/A\u003eFor in the former case the one term necessarily does not belong to the \n\u003cA NAME=\"105\"\u003e\u003c/A\u003eother; in the latter there is no necessity that it should: and the premiss \n\u003cA NAME=\"106\"\u003e\u003c/A\u003econverts like other negative statements. For if it is possible for no man \n\u003cA NAME=\"107\"\u003e\u003c/A\u003eto be a horse, it is also admissible for no horse to be a man; and if it \n\u003cA NAME=\"108\"\u003e\u003c/A\u003eis admissible for no garment to be white, it is also admissible for nothing \n\u003cA NAME=\"109\"\u003e\u003c/A\u003ewhite to be a garment. For if any white thing must be a garment, then some \n\u003cA NAME=\"110\"\u003e\u003c/A\u003egarment will necessarily be white. This has been already proved. The particular \n\u003cA NAME=\"111\"\u003e\u003c/A\u003enegative also must be treated like those dealt with above. But if anything \n\u003cA NAME=\"112\"\u003e\u003c/A\u003eis said to be possible because it is the general rule and natural (and \n\u003cA NAME=\"113\"\u003e\u003c/A\u003eit is in this way we define the possible), the negative premisses can no \n\u003cA NAME=\"114\"\u003e\u003c/A\u003elonger be converted like the simple negatives; the universal negative premiss \n\u003cA NAME=\"115\"\u003e\u003c/A\u003edoes not convert, and the particular does. This will be plain when we speak \n\u003cA NAME=\"116\"\u003e\u003c/A\u003eabout the possible. At present we may take this much as clear in addition \n\u003cA NAME=\"117\"\u003e\u003c/A\u003eto what has been said: the statement that it is possible that no B is A \n\u003cA NAME=\"118\"\u003e\u003c/A\u003eor some B is not A is affirmative in form: for the expression \u0027is possible\u0027 \n\u003cA NAME=\"119\"\u003e\u003c/A\u003eranks along with \u0027is\u0027, and \u0027is\u0027 makes an affirmation always and in every \n\u003cA NAME=\"120\"\u003e\u003c/A\u003ecase, whatever the terms to which it is added, in predication, e.g. \u0027it \n\u003cA NAME=\"121\"\u003e\u003c/A\u003eis not-good\u0027 or \u0027it is not-white\u0027 or in a word \u0027it is not-this\u0027. But this \n\u003cA NAME=\"122\"\u003e\u003c/A\u003ealso will be proved in the sequel. In conversion these premisses will behave \n\u003cA NAME=\"123\"\u003e\u003c/A\u003elike the other affirmative propositions.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"124\"\u003e\u003c/A\u003e\u003cB\u003ePart 4\u003c/B\u003e\n\n\u003cA NAME=\"125\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eAfter these distinctions we now state by what means, when, and \n\u003cA NAME=\"126\"\u003e\u003c/A\u003ehow every syllogism is produced; subsequently we must speak of demonstration. \n\u003cA NAME=\"127\"\u003e\u003c/A\u003eSyllogism should be discussed before demonstration because syllogism is \n\u003cA NAME=\"128\"\u003e\u003c/A\u003ethe general: the demonstration is a sort of syllogism, but not every syllogism \n\u003cA NAME=\"129\"\u003e\u003c/A\u003eis a demonstration.\n\u003cA NAME=\"130\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWhenever three terms are so related to one another that the last \n\u003cA NAME=\"131\"\u003e\u003c/A\u003eis contained in the middle as in a whole, and the middle is either contained \n\u003cA NAME=\"132\"\u003e\u003c/A\u003ein, or excluded from, the first as in or from a whole, the extremes must \n\u003cA NAME=\"133\"\u003e\u003c/A\u003ebe related by a perfect syllogism. I call that term middle which is itself \n\u003cA NAME=\"134\"\u003e\u003c/A\u003econtained in another and contains another in itself: in position also this \n\u003cA NAME=\"135\"\u003e\u003c/A\u003ecomes in the middle. By extremes I mean both that term which is itself \n\u003cA NAME=\"136\"\u003e\u003c/A\u003econtained in another and that in which another is contained. If A is predicated \n\u003cA NAME=\"137\"\u003e\u003c/A\u003eof all B, and B of all C, A must be predicated of all C: we have already \n\u003cA NAME=\"138\"\u003e\u003c/A\u003eexplained what we mean by \u0027predicated of all\u0027. Similarly also, if A is \n\u003cA NAME=\"139\"\u003e\u003c/A\u003epredicated of no B, and B of all C, it is necessary that no C will be \n\u003cA NAME=\"140\"\u003e\u003c/A\u003eA.\n\u003cA NAME=\"141\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eBut if the first term belongs to all the middle, but the middle \n\u003cA NAME=\"142\"\u003e\u003c/A\u003eto none of the last term, there will be no syllogism in respect of the \n\u003cA NAME=\"143\"\u003e\u003c/A\u003eextremes; for nothing necessary follows from the terms being so related; \n\u003cA NAME=\"144\"\u003e\u003c/A\u003efor it is possible that the first should belong either to all or to none \n\u003cA NAME=\"145\"\u003e\u003c/A\u003eof the last, so that neither a particular nor a universal conclusion is \n\u003cA NAME=\"146\"\u003e\u003c/A\u003enecessary. But if there is no necessary consequence, there cannot be a \n\u003cA NAME=\"147\"\u003e\u003c/A\u003esyllogism by means of these premisses. As an example of a universal affirmative \n\u003cA NAME=\"148\"\u003e\u003c/A\u003erelation between the extremes we may take the terms animal, man, horse; \n\u003cA NAME=\"149\"\u003e\u003c/A\u003eof a universal negative relation, the terms animal, man, stone. Nor again \n\u003cA NAME=\"150\"\u003e\u003c/A\u003ecan syllogism be formed when neither the first term belongs to any of the \n\u003cA NAME=\"151\"\u003e\u003c/A\u003emiddle, nor the middle to any of the last. As an example of a positive \n\u003cA NAME=\"152\"\u003e\u003c/A\u003erelation between the extremes take the terms science, line, medicine: of \n\u003cA NAME=\"153\"\u003e\u003c/A\u003ea negative relation science, line, unit.\n\u003cA NAME=\"154\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIf then the terms are universally related, it is clear in this \n\u003cA NAME=\"155\"\u003e\u003c/A\u003efigure when a syllogism will be possible and when not, and that if a syllogism \n\u003cA NAME=\"156\"\u003e\u003c/A\u003eis possible the terms must be related as described, and if they are so \n\u003cA NAME=\"157\"\u003e\u003c/A\u003erelated there will be a syllogism.\n\u003cA NAME=\"158\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eBut if one term is related universally, the other in part only, \n\u003cA NAME=\"159\"\u003e\u003c/A\u003eto its subject, there must be a perfect syllogism whenever universality \n\u003cA NAME=\"160\"\u003e\u003c/A\u003eis posited with reference to the major term either affirmatively or negatively, \n\u003cA NAME=\"161\"\u003e\u003c/A\u003eand particularity with reference to the minor term affirmatively: but whenever \n\u003cA NAME=\"162\"\u003e\u003c/A\u003ethe universality is posited in relation to the minor term, or the terms \n\u003cA NAME=\"163\"\u003e\u003c/A\u003eare related in any other way, a syllogism is impossible. I call that term \n\u003cA NAME=\"164\"\u003e\u003c/A\u003ethe major in which the middle is contained and that term the minor which \n\u003cA NAME=\"165\"\u003e\u003c/A\u003ecomes under the middle. Let all B be A and some C be B. Then if \u0027predicated \n\u003cA NAME=\"166\"\u003e\u003c/A\u003eof all\u0027 means what was said above, it is necessary that some C is A. And \n\u003cA NAME=\"167\"\u003e\u003c/A\u003eif no B is A but some C is B, it is necessary that some C is not A. The \n\u003cA NAME=\"168\"\u003e\u003c/A\u003emeaning of \u0027predicated of none\u0027 has also been defined. So there will be \n\u003cA NAME=\"169\"\u003e\u003c/A\u003ea perfect syllogism. This holds good also if the premiss BC should be indefinite, \n\u003cA NAME=\"170\"\u003e\u003c/A\u003eprovided that it is affirmative: for we shall have the same syllogism whether \n\u003cA NAME=\"171\"\u003e\u003c/A\u003ethe premiss is indefinite or particular.\n\u003cA NAME=\"172\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eBut if the universality is posited with respect to the minor term \n\u003cA NAME=\"173\"\u003e\u003c/A\u003eeither affirmatively or negatively, a syllogism will not be possible, whether \n\u003cA NAME=\"174\"\u003e\u003c/A\u003ethe major premiss is positive or negative, indefinite or particular: e.g. \n\u003cA NAME=\"175\"\u003e\u003c/A\u003eif some B is or is not A, and all C is B. As an example of a positive relation \n\u003cA NAME=\"176\"\u003e\u003c/A\u003ebetween the extremes take the terms good, state, wisdom: of a negative \n\u003cA NAME=\"177\"\u003e\u003c/A\u003erelation, good, state, ignorance. Again if no C is B, but some B is or \n\u003cA NAME=\"178\"\u003e\u003c/A\u003eis not A or not every B is A, there cannot be a syllogism. Take the terms \n\u003cA NAME=\"179\"\u003e\u003c/A\u003ewhite, horse, swan: white, horse, raven. The same terms may be taken also \n\u003cA NAME=\"180\"\u003e\u003c/A\u003eif the premiss BA is indefinite.\n\u003cA NAME=\"181\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eNor when the major premiss is universal, whether affirmative or \n\u003cA NAME=\"182\"\u003e\u003c/A\u003enegative, and the minor premiss is negative and particular, can there be \n\u003cA NAME=\"183\"\u003e\u003c/A\u003ea syllogism, whether the minor premiss be indefinite or particular: e.g. \n\u003cA NAME=\"184\"\u003e\u003c/A\u003eif all B is A and some C is not B, or if not all C is B. For the major \n\u003cA NAME=\"185\"\u003e\u003c/A\u003eterm may be predicable both of all and of none of the minor, to some of \n\u003cA NAME=\"186\"\u003e\u003c/A\u003ewhich the middle term cannot be attributed. Suppose the terms are animal, \n\u003cA NAME=\"187\"\u003e\u003c/A\u003eman, white: next take some of the white things of which man is not predicated-swan \n\u003cA NAME=\"188\"\u003e\u003c/A\u003eand snow: animal is predicated of all of the one, but of none of the other. \n\u003cA NAME=\"189\"\u003e\u003c/A\u003eConsequently there cannot be a syllogism. Again let no B be A, but let \n\u003cA NAME=\"190\"\u003e\u003c/A\u003esome C not be B. Take the terms inanimate, man, white: then take some white \n\u003cA NAME=\"191\"\u003e\u003c/A\u003ethings of which man is not predicated-swan and snow: the term inanimate \n\u003cA NAME=\"192\"\u003e\u003c/A\u003eis predicated of all of the one, of none of the other.\n\u003cA NAME=\"193\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eFurther since it is indefinite to say some C is not B, and it is \n\u003cA NAME=\"194\"\u003e\u003c/A\u003etrue that some C is not B, whether no C is B, or not all C is B, and since \n\u003cA NAME=\"195\"\u003e\u003c/A\u003eif terms are assumed such that no C is B, no syllogism follows (this has \n\u003cA NAME=\"196\"\u003e\u003c/A\u003ealready been stated) it is clear that this arrangement of terms will not \n\u003cA NAME=\"197\"\u003e\u003c/A\u003eafford a syllogism: otherwise one would have been possible with a universal \n\u003cA NAME=\"198\"\u003e\u003c/A\u003enegative minor premiss. A similar proof may also be given if the universal \n\u003cA NAME=\"199\"\u003e\u003c/A\u003epremiss is negative.\n\u003cA NAME=\"200\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eNor can there in any way be a syllogism if both the relations of \n\u003cA NAME=\"201\"\u003e\u003c/A\u003esubject and predicate are particular, either positively or negatively, \n\u003cA NAME=\"202\"\u003e\u003c/A\u003eor the one negative and the other affirmative, or one indefinite and the \n\u003cA NAME=\"203\"\u003e\u003c/A\u003eother definite, or both indefinite. Terms common to all the above are animal, \n\u003cA NAME=\"204\"\u003e\u003c/A\u003ewhite, horse: animal, white, stone.\n\u003cA NAME=\"205\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is clear then from what has been said that if there is a syllogism \n\u003cA NAME=\"206\"\u003e\u003c/A\u003ein this figure with a particular conclusion, the terms must be related \n\u003cA NAME=\"207\"\u003e\u003c/A\u003eas we have stated: if they are related otherwise, no syllogism is possible \n\u003cA NAME=\"208\"\u003e\u003c/A\u003eanyhow. It is evident also that all the syllogisms in this figure are perfect \n\u003cA NAME=\"209\"\u003e\u003c/A\u003e(for they are all completed by means of the premisses originally taken) \n\u003cA NAME=\"210\"\u003e\u003c/A\u003eand that all conclusions are proved by this figure, viz. universal and \n\u003cA NAME=\"211\"\u003e\u003c/A\u003eparticular, affirmative and negative. Such a figure I call the \n\u003cA NAME=\"212\"\u003e\u003c/A\u003efirst.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"213\"\u003e\u003c/A\u003e\u003cB\u003ePart 5\u003c/B\u003e\n\n\u003cA NAME=\"214\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWhenever the same thing belongs to all of one subject, and to none \n\u003cA NAME=\"215\"\u003e\u003c/A\u003eof another, or to all of each subject or to none of either, I call such \n\u003cA NAME=\"216\"\u003e\u003c/A\u003ea figure the second; by middle term in it I mean that which is predicated \n\u003cA NAME=\"217\"\u003e\u003c/A\u003eof both subjects, by extremes the terms of which this is said, by major \n\u003cA NAME=\"218\"\u003e\u003c/A\u003eextreme that which lies near the middle, by minor that which is further \n\u003cA NAME=\"219\"\u003e\u003c/A\u003eaway from the middle. The middle term stands outside the extremes, and \n\u003cA NAME=\"220\"\u003e\u003c/A\u003eis first in position. A syllogism cannot be perfect anyhow in this figure, \n\u003cA NAME=\"221\"\u003e\u003c/A\u003ebut it may be valid whether the terms are related universally or \n\u003cA NAME=\"222\"\u003e\u003c/A\u003enot.\n\u003cA NAME=\"223\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIf then the terms are related universally a syllogism will be possible, \n\u003cA NAME=\"224\"\u003e\u003c/A\u003ewhenever the middle belongs to all of one subject and to none of another \n\u003cA NAME=\"225\"\u003e\u003c/A\u003e(it does not matter which has the negative relation), but in no other way. \n\u003cA NAME=\"226\"\u003e\u003c/A\u003eLet M be predicated of no N, but of all O. Since, then, the negative relation \n\u003cA NAME=\"227\"\u003e\u003c/A\u003eis convertible, N will belong to no M: but M was assumed to belong to all \n\u003cA NAME=\"228\"\u003e\u003c/A\u003eO: consequently N will belong to no O. This has already been proved. Again \n\u003cA NAME=\"229\"\u003e\u003c/A\u003eif M belongs to all N, but to no O, then N will belong to no O. For if \n\u003cA NAME=\"230\"\u003e\u003c/A\u003eM belongs to no O, O belongs to no M: but M (as was said) belongs to all \n\u003cA NAME=\"231\"\u003e\u003c/A\u003eN: O then will belong to no N: for the first figure has again been formed. \n\u003cA NAME=\"232\"\u003e\u003c/A\u003eBut since the negative relation is convertible, N will belong to no O. \n\u003cA NAME=\"233\"\u003e\u003c/A\u003eThus it will be the same syllogism that proves both \n\u003cA NAME=\"234\"\u003e\u003c/A\u003econclusions.\n\u003cA NAME=\"235\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is possible to prove these results also by reductio ad \n\u003cA NAME=\"236\"\u003e\u003c/A\u003eimpossibile.\n\u003cA NAME=\"237\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is clear then that a syllogism is formed when the terms are \n\u003cA NAME=\"238\"\u003e\u003c/A\u003eso related, but not a perfect syllogism; for necessity is not perfectly \n\u003cA NAME=\"239\"\u003e\u003c/A\u003eestablished merely from the original premisses; others also are \n\u003cA NAME=\"240\"\u003e\u003c/A\u003eneeded.\n\u003cA NAME=\"241\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eBut if M is predicated of every N and O, there cannot be a syllogism. \n\u003cA NAME=\"242\"\u003e\u003c/A\u003eTerms to illustrate a positive relation between the extremes are substance, \n\u003cA NAME=\"243\"\u003e\u003c/A\u003eanimal, man; a negative relation, substance, animal, number-substance being \n\u003cA NAME=\"244\"\u003e\u003c/A\u003ethe middle term.\n\u003cA NAME=\"245\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eNor is a syllogism possible when M is predicated neither of any \n\u003cA NAME=\"246\"\u003e\u003c/A\u003eN nor of any O. Terms to illustrate a positive relation are line, animal, \n\u003cA NAME=\"247\"\u003e\u003c/A\u003eman: a negative relation, line, animal, stone.\n\u003cA NAME=\"248\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is clear then that if a syllogism is formed when the terms are \n\u003cA NAME=\"249\"\u003e\u003c/A\u003euniversally related, the terms must be related as we stated at the outset: \n\u003cA NAME=\"250\"\u003e\u003c/A\u003efor if they are otherwise related no necessary consequence \n\u003cA NAME=\"251\"\u003e\u003c/A\u003efollows.\n\u003cA NAME=\"252\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIf the middle term is related universally to one of the extremes, \n\u003cA NAME=\"253\"\u003e\u003c/A\u003ea particular negative syllogism must result whenever the middle term is \n\u003cA NAME=\"254\"\u003e\u003c/A\u003erelated universally to the major whether positively or negatively, and \n\u003cA NAME=\"255\"\u003e\u003c/A\u003eparticularly to the minor and in a manner opposite to that of the universal \n\u003cA NAME=\"256\"\u003e\u003c/A\u003estatement: by \u0027an opposite manner\u0027 I mean, if the universal statement is \n\u003cA NAME=\"257\"\u003e\u003c/A\u003enegative, the particular is affirmative: if the universal is affirmative, \n\u003cA NAME=\"258\"\u003e\u003c/A\u003ethe particular is negative. For if M belongs to no N, but to some O, it \n\u003cA NAME=\"259\"\u003e\u003c/A\u003eis necessary that N does not belong to some O. For since the negative statement \n\u003cA NAME=\"260\"\u003e\u003c/A\u003eis convertible, N will belong to no M: but M was admitted to belong to \n\u003cA NAME=\"261\"\u003e\u003c/A\u003esome O: therefore N will not belong to some O: for the result is reached \n\u003cA NAME=\"262\"\u003e\u003c/A\u003eby means of the first figure. Again if M belongs to all N, but not to some \n\u003cA NAME=\"263\"\u003e\u003c/A\u003eO, it is necessary that N does not belong to some O: for if N belongs to \n\u003cA NAME=\"264\"\u003e\u003c/A\u003eall O, and M is predicated also of all N, M must belong to all O: but we \n\u003cA NAME=\"265\"\u003e\u003c/A\u003eassumed that M does not belong to some O. And if M belongs to all N but \n\u003cA NAME=\"266\"\u003e\u003c/A\u003enot to all O, we shall conclude that N does not belong to all O: the proof \n\u003cA NAME=\"267\"\u003e\u003c/A\u003eis the same as the above. But if M is predicated of all O, but not of all \n\u003cA NAME=\"268\"\u003e\u003c/A\u003eN, there will be no syllogism. Take the terms animal, substance, raven; \n\u003cA NAME=\"269\"\u003e\u003c/A\u003eanimal, white, raven. Nor will there be a conclusion when M is predicated \n\u003cA NAME=\"270\"\u003e\u003c/A\u003eof no O, but of some N. Terms to illustrate a positive relation between \n\u003cA NAME=\"271\"\u003e\u003c/A\u003ethe extremes are animal, substance, unit: a negative relation, animal, \n\u003cA NAME=\"272\"\u003e\u003c/A\u003esubstance, science.\n\u003cA NAME=\"273\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIf then the universal statement is opposed to the particular, we \n\u003cA NAME=\"274\"\u003e\u003c/A\u003ehave stated when a syllogism will be possible and when not: but if the \n\u003cA NAME=\"275\"\u003e\u003c/A\u003epremisses are similar in form, I mean both negative or both affirmative, \n\u003cA NAME=\"276\"\u003e\u003c/A\u003ea syllogism will not be possible anyhow. First let them be negative, and \n\u003cA NAME=\"277\"\u003e\u003c/A\u003elet the major premiss be universal, e.g. let M belong to no N, and not \n\u003cA NAME=\"278\"\u003e\u003c/A\u003eto some O. It is possible then for N to belong either to all O or to no \n\u003cA NAME=\"279\"\u003e\u003c/A\u003eO. Terms to illustrate the negative relation are black, snow, animal. But \n\u003cA NAME=\"280\"\u003e\u003c/A\u003eit is not possible to find terms of which the extremes are related positively \n\u003cA NAME=\"281\"\u003e\u003c/A\u003eand universally, if M belongs to some O, and does not belong to some O. \n\u003cA NAME=\"282\"\u003e\u003c/A\u003eFor if N belonged to all O, but M to no N, then M would belong to no O: \n\u003cA NAME=\"283\"\u003e\u003c/A\u003ebut we assumed that it belongs to some O. In this way then it is not admissible \n\u003cA NAME=\"284\"\u003e\u003c/A\u003eto take terms: our point must be proved from the indefinite nature of the \n\u003cA NAME=\"285\"\u003e\u003c/A\u003eparticular statement. For since it is true that M does not belong to some \n\u003cA NAME=\"286\"\u003e\u003c/A\u003eO, even if it belongs to no O, and since if it belongs to no O a syllogism \n\u003cA NAME=\"287\"\u003e\u003c/A\u003eis (as we have seen) not possible, clearly it will not be possible now \n\u003cA NAME=\"288\"\u003e\u003c/A\u003eeither.\n\u003cA NAME=\"289\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eAgain let the premisses be affirmative, and let the major premiss \n\u003cA NAME=\"290\"\u003e\u003c/A\u003eas before be universal, e.g. let M belong to all N and to some O. It is \n\u003cA NAME=\"291\"\u003e\u003c/A\u003epossible then for N to belong to all O or to no O. Terms to illustrate \n\u003cA NAME=\"292\"\u003e\u003c/A\u003ethe negative relation are white, swan, stone. But it is not possible to \n\u003cA NAME=\"293\"\u003e\u003c/A\u003etake terms to illustrate the universal affirmative relation, for the reason \n\u003cA NAME=\"294\"\u003e\u003c/A\u003ealready stated: the point must be proved from the indefinite nature of \n\u003cA NAME=\"295\"\u003e\u003c/A\u003ethe particular statement. But if the minor premiss is universal, and M \n\u003cA NAME=\"296\"\u003e\u003c/A\u003ebelongs to no O, and not to some N, it is possible for N to belong either \n\u003cA NAME=\"297\"\u003e\u003c/A\u003eto all O or to no O. Terms for the positive relation are white, animal, \n\u003cA NAME=\"298\"\u003e\u003c/A\u003eraven: for the negative relation, white, stone, raven. If the premisses \n\u003cA NAME=\"299\"\u003e\u003c/A\u003eare affirmative, terms for the negative relation are white, animal, snow; \n\u003cA NAME=\"300\"\u003e\u003c/A\u003efor the positive relation, white, animal, swan. Evidently then, whenever \n\u003cA NAME=\"301\"\u003e\u003c/A\u003ethe premisses are similar in form, and one is universal, the other particular, \n\u003cA NAME=\"302\"\u003e\u003c/A\u003ea syllogism can, not be formed anyhow. Nor is one possible if the middle \n\u003cA NAME=\"303\"\u003e\u003c/A\u003eterm belongs to some of each of the extremes, or does not belong to some \n\u003cA NAME=\"304\"\u003e\u003c/A\u003eof either, or belongs to some of the one, not to some of the other, or \n\u003cA NAME=\"305\"\u003e\u003c/A\u003ebelongs to neither universally, or is related to them indefinitely. Common \n\u003cA NAME=\"306\"\u003e\u003c/A\u003eterms for all the above are white, animal, man: white, animal, inanimate. \n\u003cA NAME=\"307\"\u003e\u003c/A\u003eIt is clear then from what has been said that if the terms are related \n\u003cA NAME=\"308\"\u003e\u003c/A\u003eto one another in the way stated, a syllogism results of necessity; and \n\u003cA NAME=\"309\"\u003e\u003c/A\u003eif there is a syllogism, the terms must be so related. But it is evident \n\u003cA NAME=\"310\"\u003e\u003c/A\u003ealso that all the syllogisms in this figure are imperfect: for all are \n\u003cA NAME=\"311\"\u003e\u003c/A\u003emade perfect by certain supplementary statements, which either are contained \n\u003cA NAME=\"312\"\u003e\u003c/A\u003ein the terms of necessity or are assumed as hypotheses, i.e. when we prove \n\u003cA NAME=\"313\"\u003e\u003c/A\u003eper impossibile. And it is evident that an affirmative conclusion is not \n\u003cA NAME=\"314\"\u003e\u003c/A\u003eattained by means of this figure, but all are negative, whether universal \n\u003cA NAME=\"315\"\u003e\u003c/A\u003eor particular.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"316\"\u003e\u003c/A\u003e\u003cB\u003ePart 6\u003c/B\u003e\n\n\u003cA NAME=\"317\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eBut if one term belongs to all, and another to none, of a third, \n\u003cA NAME=\"318\"\u003e\u003c/A\u003eor if both belong to all, or to none, of it, I call such a figure the third; \n\u003cA NAME=\"319\"\u003e\u003c/A\u003eby middle term in it I mean that of which both the predicates are predicated, \n\u003cA NAME=\"320\"\u003e\u003c/A\u003eby extremes I mean the predicates, by the major extreme that which is further \n\u003cA NAME=\"321\"\u003e\u003c/A\u003efrom the middle, by the minor that which is nearer to it. The middle term \n\u003cA NAME=\"322\"\u003e\u003c/A\u003estands outside the extremes, and is last in position. A syllogism cannot \n\u003cA NAME=\"323\"\u003e\u003c/A\u003ebe perfect in this figure either, but it may be valid whether the terms \n\u003cA NAME=\"324\"\u003e\u003c/A\u003eare related universally or not to the middle term.\n\u003cA NAME=\"325\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIf they are universal, whenever both P and R belong to S, it follows \n\u003cA NAME=\"326\"\u003e\u003c/A\u003ethat P will necessarily belong to some R. For, since the affirmative statement \n\u003cA NAME=\"327\"\u003e\u003c/A\u003eis convertible, S will belong to some R: consequently since P belongs to \n\u003cA NAME=\"328\"\u003e\u003c/A\u003eall S, and S to some R, P must belong to some R: for a syllogism in the \n\u003cA NAME=\"329\"\u003e\u003c/A\u003efirst figure is produced. It is possible to demonstrate this also per impossibile \n\u003cA NAME=\"330\"\u003e\u003c/A\u003eand by exposition. For if both P and R belong to all S, should one of the \n\u003cA NAME=\"331\"\u003e\u003c/A\u003eSs, e.g. N, be taken, both P and R will belong to this, and thus P will \n\u003cA NAME=\"332\"\u003e\u003c/A\u003ebelong to some R.\n\u003cA NAME=\"333\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIf R belongs to all S, and P to no S, there will be a syllogism \n\u003cA NAME=\"334\"\u003e\u003c/A\u003eto prove that P will necessarily not belong to some R. This may be demonstrated \n\u003cA NAME=\"335\"\u003e\u003c/A\u003ein the same way as before by converting the premiss RS. It might be proved \n\u003cA NAME=\"336\"\u003e\u003c/A\u003ealso per impossibile, as in the former cases. But if R belongs to no S, \n\u003cA NAME=\"337\"\u003e\u003c/A\u003eP to all S, there will be no syllogism. Terms for the positive relation \n\u003cA NAME=\"338\"\u003e\u003c/A\u003eare animal, horse, man: for the negative relation animal, inanimate, \n\u003cA NAME=\"339\"\u003e\u003c/A\u003eman.\n\u003cA NAME=\"340\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eNor can there be a syllogism when both terms are asserted of no \n\u003cA NAME=\"341\"\u003e\u003c/A\u003eS. Terms for the positive relation are animal, horse, inanimate; for the \n\u003cA NAME=\"342\"\u003e\u003c/A\u003enegative relation man, horse, inanimate-inanimate being the middle \n\u003cA NAME=\"343\"\u003e\u003c/A\u003eterm.\n\u003cA NAME=\"344\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is clear then in this figure also when a syllogism will be possible \n\u003cA NAME=\"345\"\u003e\u003c/A\u003eand when not, if the terms are related universally. For whenever both the \n\u003cA NAME=\"346\"\u003e\u003c/A\u003eterms are affirmative, there will be a syllogism to prove that one extreme \n\u003cA NAME=\"347\"\u003e\u003c/A\u003ebelongs to some of the other; but when they are negative, no syllogism \n\u003cA NAME=\"348\"\u003e\u003c/A\u003ewill be possible. But when one is negative, the other affirmative, if the \n\u003cA NAME=\"349\"\u003e\u003c/A\u003emajor is negative, the minor affirmative, there will be a syllogism to \n\u003cA NAME=\"350\"\u003e\u003c/A\u003eprove that the one extreme does not belong to some of the other: but if \n\u003cA NAME=\"351\"\u003e\u003c/A\u003ethe relation is reversed, no syllogism will be possible. If one term is \n\u003cA NAME=\"352\"\u003e\u003c/A\u003erelated universally to the middle, the other in part only, when both are \n\u003cA NAME=\"353\"\u003e\u003c/A\u003eaffirmative there must be a syllogism, no matter which of the premisses \n\u003cA NAME=\"354\"\u003e\u003c/A\u003eis universal. For if R belongs to all S, P to some S, P must belong to \n\u003cA NAME=\"355\"\u003e\u003c/A\u003esome R. For since the affirmative statement is convertible S will belong \n\u003cA NAME=\"356\"\u003e\u003c/A\u003eto some P: consequently since R belongs to all S, and S to some P, R must \n\u003cA NAME=\"357\"\u003e\u003c/A\u003ealso belong to some P: therefore P must belong to some \n\u003cA NAME=\"358\"\u003e\u003c/A\u003eR.\n\u003cA NAME=\"359\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eAgain if R belongs to some S, and P to all S, P must belong to \n\u003cA NAME=\"360\"\u003e\u003c/A\u003esome R. This may be demonstrated in the same way as the preceding. And \n\u003cA NAME=\"361\"\u003e\u003c/A\u003eit is possible to demonstrate it also per impossibile and by exposition, \n\u003cA NAME=\"362\"\u003e\u003c/A\u003eas in the former cases. But if one term is affirmative, the other negative, \n\u003cA NAME=\"363\"\u003e\u003c/A\u003eand if the affirmative is universal, a syllogism will be possible whenever \n\u003cA NAME=\"364\"\u003e\u003c/A\u003ethe minor term is affirmative. For if R belongs to all S, but P does not \n\u003cA NAME=\"365\"\u003e\u003c/A\u003ebelong to some S, it is necessary that P does not belong to some R. For \n\u003cA NAME=\"366\"\u003e\u003c/A\u003eif P belongs to all R, and R belongs to all S, then P will belong to all \n\u003cA NAME=\"367\"\u003e\u003c/A\u003eS: but we assumed that it did not. Proof is possible also without reduction \n\u003cA NAME=\"368\"\u003e\u003c/A\u003ead impossibile, if one of the Ss be taken to which P does not \n\u003cA NAME=\"369\"\u003e\u003c/A\u003ebelong.\n\u003cA NAME=\"370\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eBut whenever the major is affirmative, no syllogism will be possible, \n\u003cA NAME=\"371\"\u003e\u003c/A\u003ee.g. if P belongs to all S and R does not belong to some S. Terms for the \n\u003cA NAME=\"372\"\u003e\u003c/A\u003euniversal affirmative relation are animate, man, animal. For the universal \n\u003cA NAME=\"373\"\u003e\u003c/A\u003enegative relation it is not possible to get terms, if R belongs to some \n\u003cA NAME=\"374\"\u003e\u003c/A\u003eS, and does not belong to some S. For if P belongs to all S, and R to some \n\u003cA NAME=\"375\"\u003e\u003c/A\u003eS, then P will belong to some R: but we assumed that it belongs to no R. \n\u003cA NAME=\"376\"\u003e\u003c/A\u003eWe must put the matter as before.\u0027 Since the expression \u0027it does not belong \n\u003cA NAME=\"377\"\u003e\u003c/A\u003eto some\u0027 is indefinite, it may be used truly of that also which belongs \n\u003cA NAME=\"378\"\u003e\u003c/A\u003eto none. But if R belongs to no S, no syllogism is possible, as has been \n\u003cA NAME=\"379\"\u003e\u003c/A\u003eshown. Clearly then no syllogism will be possible here.\n\u003cA NAME=\"380\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eBut if the negative term is universal, whenever the major is negative \n\u003cA NAME=\"381\"\u003e\u003c/A\u003eand the minor affirmative there will be a syllogism. For if P belongs to \n\u003cA NAME=\"382\"\u003e\u003c/A\u003eno S, and R belongs to some S, P will not belong to some R: for we shall \n\u003cA NAME=\"383\"\u003e\u003c/A\u003ehave the first figure again, if the premiss RS is converted.\n\u003cA NAME=\"384\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eBut when the minor is negative, there will be no syllogism. Terms \n\u003cA NAME=\"385\"\u003e\u003c/A\u003efor the positive relation are animal, man, wild: for the negative relation, \n\u003cA NAME=\"386\"\u003e\u003c/A\u003eanimal, science, wild-the middle in both being the term \n\u003cA NAME=\"387\"\u003e\u003c/A\u003ewild.\n\u003cA NAME=\"388\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eNor is a syllogism possible when both are stated in the negative, \n\u003cA NAME=\"389\"\u003e\u003c/A\u003ebut one is universal, the other particular. When the minor is related universally \n\u003cA NAME=\"390\"\u003e\u003c/A\u003eto the middle, take the terms animal, science, wild; animal, man, wild. \n\u003cA NAME=\"391\"\u003e\u003c/A\u003eWhen the major is related universally to the middle, take as terms for \n\u003cA NAME=\"392\"\u003e\u003c/A\u003ea negative relation raven, snow, white. For a positive relation terms cannot \n\u003cA NAME=\"393\"\u003e\u003c/A\u003ebe found, if R belongs to some S, and does not belong to some S. For if \n\u003cA NAME=\"394\"\u003e\u003c/A\u003eP belongs to all R, and R to some S, then P belongs to some S: but we assumed \n\u003cA NAME=\"395\"\u003e\u003c/A\u003ethat it belongs to no S. Our point, then, must be proved from the indefinite \n\u003cA NAME=\"396\"\u003e\u003c/A\u003enature of the particular statement.\n\u003cA NAME=\"397\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eNor is a syllogism possible anyhow, if each of the extremes belongs \n\u003cA NAME=\"398\"\u003e\u003c/A\u003eto some of the middle or does not belong, or one belongs and the other \n\u003cA NAME=\"399\"\u003e\u003c/A\u003edoes not to some of the middle, or one belongs to some of the middle, the \n\u003cA NAME=\"400\"\u003e\u003c/A\u003eother not to all, or if the premisses are indefinite. Common terms for \n\u003cA NAME=\"401\"\u003e\u003c/A\u003eall are animal, man, white: animal, inanimate, white.\n\u003cA NAME=\"402\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is clear then in this figure also when a syllogism will be possible, \n\u003cA NAME=\"403\"\u003e\u003c/A\u003eand when not; and that if the terms are as stated, a syllogism results \n\u003cA NAME=\"404\"\u003e\u003c/A\u003eof necessity, and if there is a syllogism, the terms must be so related. \n\u003cA NAME=\"405\"\u003e\u003c/A\u003eIt is clear also that all the syllogisms in this figure are imperfect (for \n\u003cA NAME=\"406\"\u003e\u003c/A\u003eall are made perfect by certain supplementary assumptions), and that it \n\u003cA NAME=\"407\"\u003e\u003c/A\u003ewill not be possible to reach a universal conclusion by means of this figure, \n\u003cA NAME=\"408\"\u003e\u003c/A\u003ewhether negative or affirmative.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"409\"\u003e\u003c/A\u003e\u003cB\u003ePart 7\u003c/B\u003e\n\n\u003cA NAME=\"410\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is evident also that in all the figures, whenever a proper syllogism \n\u003cA NAME=\"411\"\u003e\u003c/A\u003edoes not result, if both the terms are affirmative or negative nothing \n\u003cA NAME=\"412\"\u003e\u003c/A\u003enecessary follows at all, but if one is affirmative, the other negative, \n\u003cA NAME=\"413\"\u003e\u003c/A\u003eand if the negative is stated universally, a syllogism always results relating \n\u003cA NAME=\"414\"\u003e\u003c/A\u003ethe minor to the major term, e.g. if A belongs to all or some B, and B \n\u003cA NAME=\"415\"\u003e\u003c/A\u003ebelongs to no C: for if the premisses are converted it is necessary that \n\u003cA NAME=\"416\"\u003e\u003c/A\u003eC does not belong to some A. Similarly also in the other figures: a syllogism \n\u003cA NAME=\"417\"\u003e\u003c/A\u003ealways results by means of conversion. It is evident also that the substitution \n\u003cA NAME=\"418\"\u003e\u003c/A\u003eof an indefinite for a particular affirmative will effect the same syllogism \n\u003cA NAME=\"419\"\u003e\u003c/A\u003ein all the figures.\n\u003cA NAME=\"420\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is clear too that all the imperfect syllogisms are made perfect \n\u003cA NAME=\"421\"\u003e\u003c/A\u003eby means of the first figure. For all are brought to a conclusion either \n\u003cA NAME=\"422\"\u003e\u003c/A\u003eostensively or per impossibile. In both ways the first figure is formed: \n\u003cA NAME=\"423\"\u003e\u003c/A\u003eif they are made perfect ostensively, because (as we saw) all are brought \n\u003cA NAME=\"424\"\u003e\u003c/A\u003eto a conclusion by means of conversion, and conversion produces the first \n\u003cA NAME=\"425\"\u003e\u003c/A\u003efigure: if they are proved per impossibile, because on the assumption of \n\u003cA NAME=\"426\"\u003e\u003c/A\u003ethe false statement the syllogism comes about by means of the first figure, \n\u003cA NAME=\"427\"\u003e\u003c/A\u003ee.g. in the last figure, if A and B belong to all C, it follows that A \n\u003cA NAME=\"428\"\u003e\u003c/A\u003ebelongs to some B: for if A belonged to no B, and B belongs to all C, A \n\u003cA NAME=\"429\"\u003e\u003c/A\u003ewould belong to no C: but (as we stated) it belongs to all C. Similarly \n\u003cA NAME=\"430\"\u003e\u003c/A\u003ealso with the rest.\n\u003cA NAME=\"431\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is possible also to reduce all syllogisms to the universal syllogisms \n\u003cA NAME=\"432\"\u003e\u003c/A\u003ein the first figure. Those in the second figure are clearly made perfect \n\u003cA NAME=\"433\"\u003e\u003c/A\u003eby these, though not all in the same way; the universal syllogisms are \n\u003cA NAME=\"434\"\u003e\u003c/A\u003emade perfect by converting the negative premiss, each of the particular \n\u003cA NAME=\"435\"\u003e\u003c/A\u003esyllogisms by reductio ad impossibile. In the first figure particular syllogisms \n\u003cA NAME=\"436\"\u003e\u003c/A\u003eare indeed made perfect by themselves, but it is possible also to prove \n\u003cA NAME=\"437\"\u003e\u003c/A\u003ethem by means of the second figure, reducing them ad impossibile, e.g. \n\u003cA NAME=\"438\"\u003e\u003c/A\u003eif A belongs to all B, and B to some C, it follows that A belongs to some \n\u003cA NAME=\"439\"\u003e\u003c/A\u003eC. For if it belonged to no C, and belongs to all B, then B will belong \n\u003cA NAME=\"440\"\u003e\u003c/A\u003eto no C: this we know by means of the second figure. Similarly also demonstration \n\u003cA NAME=\"441\"\u003e\u003c/A\u003ewill be possible in the case of the negative. For if A belongs to no B, \n\u003cA NAME=\"442\"\u003e\u003c/A\u003eand B belongs to some C, A will not belong to some C: for if it belonged \n\u003cA NAME=\"443\"\u003e\u003c/A\u003eto all C, and belongs to no B, then B will belong to no C: and this (as \n\u003cA NAME=\"444\"\u003e\u003c/A\u003ewe saw) is the middle figure. Consequently, since all syllogisms in the \n\u003cA NAME=\"445\"\u003e\u003c/A\u003emiddle figure can be reduced to universal syllogisms in the first figure, \n\u003cA NAME=\"446\"\u003e\u003c/A\u003eand since particular syllogisms in the first figure can be reduced to syllogisms \n\u003cA NAME=\"447\"\u003e\u003c/A\u003ein the middle figure, it is clear that particular syllogisms can be reduced \n\u003cA NAME=\"448\"\u003e\u003c/A\u003eto universal syllogisms in the first figure. Syllogisms in the third figure, \n\u003cA NAME=\"449\"\u003e\u003c/A\u003eif the terms are universal, are directly made perfect by means of those \n\u003cA NAME=\"450\"\u003e\u003c/A\u003esyllogisms; but, when one of the premisses is particular, by means of the \n\u003cA NAME=\"451\"\u003e\u003c/A\u003eparticular syllogisms in the first figure: and these (we have seen) may \n\u003cA NAME=\"452\"\u003e\u003c/A\u003ebe reduced to the universal syllogisms in the first figure: consequently \n\u003cA NAME=\"453\"\u003e\u003c/A\u003ealso the particular syllogisms in the third figure may be so reduced. It \n\u003cA NAME=\"454\"\u003e\u003c/A\u003eis clear then that all syllogisms may be reduced to the universal syllogisms \n\u003cA NAME=\"455\"\u003e\u003c/A\u003ein the first figure.\n\u003cA NAME=\"456\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWe have stated then how syllogisms which prove that something belongs \n\u003cA NAME=\"457\"\u003e\u003c/A\u003eor does not belong to something else are constituted, both how syllogisms \n\u003cA NAME=\"458\"\u003e\u003c/A\u003eof the same figure are constituted in themselves, and how syllogisms of \n\u003cA NAME=\"459\"\u003e\u003c/A\u003edifferent figures are related to one another.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"460\"\u003e\u003c/A\u003e\u003cB\u003ePart 8\u003c/B\u003e\n\n\u003cA NAME=\"461\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eSince there is a difference according as something belongs, necessarily \n\u003cA NAME=\"462\"\u003e\u003c/A\u003ebelongs, or may belong to something else (for many things belong indeed, \n\u003cA NAME=\"463\"\u003e\u003c/A\u003ebut not necessarily, others neither necessarily nor indeed at all, but \n\u003cA NAME=\"464\"\u003e\u003c/A\u003eit is possible for them to belong), it is clear that there will be different \n\u003cA NAME=\"465\"\u003e\u003c/A\u003esyllogisms to prove each of these relations, and syllogisms with differently \n\u003cA NAME=\"466\"\u003e\u003c/A\u003erelated terms, one syllogism concluding from what is necessary, another \n\u003cA NAME=\"467\"\u003e\u003c/A\u003efrom what is, a third from what is possible.\n\u003cA NAME=\"468\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThere is hardly any difference between syllogisms from necessary \n\u003cA NAME=\"469\"\u003e\u003c/A\u003epremisses and syllogisms from premisses which merely assert. When the terms \n\u003cA NAME=\"470\"\u003e\u003c/A\u003eare put in the same way, then, whether something belongs or necessarily \n\u003cA NAME=\"471\"\u003e\u003c/A\u003ebelongs (or does not belong) to something else, a syllogism will or will \n\u003cA NAME=\"472\"\u003e\u003c/A\u003enot result alike in both cases, the only difference being the addition \n\u003cA NAME=\"473\"\u003e\u003c/A\u003eof the expression \u0027necessarily\u0027 to the terms. For the negative statement \n\u003cA NAME=\"474\"\u003e\u003c/A\u003eis convertible alike in both cases, and we should give the same account \n\u003cA NAME=\"475\"\u003e\u003c/A\u003eof the expressions \u0027to be contained in something as in a whole\u0027 and \u0027to \n\u003cA NAME=\"476\"\u003e\u003c/A\u003ebe predicated of all of something\u0027. With the exceptions to be made below, \n\u003cA NAME=\"477\"\u003e\u003c/A\u003ethe conclusion will be proved to be necessary by means of conversion, in \n\u003cA NAME=\"478\"\u003e\u003c/A\u003ethe same manner as in the case of simple predication. But in the middle \n\u003cA NAME=\"479\"\u003e\u003c/A\u003efigure when the universal statement is affirmative, and the particular \n\u003cA NAME=\"480\"\u003e\u003c/A\u003enegative, and again in the third figure when the universal is affirmative \n\u003cA NAME=\"481\"\u003e\u003c/A\u003eand the particular negative, the demonstration will not take the same form, \n\u003cA NAME=\"482\"\u003e\u003c/A\u003ebut it is necessary by the \u0027exposition\u0027 of a part of the subject of the \n\u003cA NAME=\"483\"\u003e\u003c/A\u003eparticular negative proposition, to which the predicate does not belong, \n\u003cA NAME=\"484\"\u003e\u003c/A\u003eto make the syllogism in reference to this: with terms so chosen the conclusion \n\u003cA NAME=\"485\"\u003e\u003c/A\u003ewill necessarily follow. But if the relation is necessary in respect of \n\u003cA NAME=\"486\"\u003e\u003c/A\u003ethe part taken, it must hold of some of that term in which this part is \n\u003cA NAME=\"487\"\u003e\u003c/A\u003eincluded: for the part taken is just some of that. And each of the resulting \n\u003cA NAME=\"488\"\u003e\u003c/A\u003esyllogisms is in the appropriate figure.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"489\"\u003e\u003c/A\u003e\u003cB\u003ePart 9\u003c/B\u003e\n\n\u003cA NAME=\"490\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt happens sometimes also that when one premiss is necessary the \n\u003cA NAME=\"491\"\u003e\u003c/A\u003econclusion is necessary, not however when either premiss is necessary, \n\u003cA NAME=\"492\"\u003e\u003c/A\u003ebut only when the major is, e.g. if A is taken as necessarily belonging \n\u003cA NAME=\"493\"\u003e\u003c/A\u003eor not belonging to B, but B is taken as simply belonging to C: for if \n\u003cA NAME=\"494\"\u003e\u003c/A\u003ethe premisses are taken in this way, A will necessarily belong or not belong \n\u003cA NAME=\"495\"\u003e\u003c/A\u003eto C. For since necessarily belongs, or does not belong, to every B, and \n\u003cA NAME=\"496\"\u003e\u003c/A\u003esince C is one of the Bs, it is clear that for C also the positive or the \n\u003cA NAME=\"497\"\u003e\u003c/A\u003enegative relation to A will hold necessarily. But if the major premiss \n\u003cA NAME=\"498\"\u003e\u003c/A\u003eis not necessary, but the minor is necessary, the conclusion will not be \n\u003cA NAME=\"499\"\u003e\u003c/A\u003enecessary. For if it were, it would result both through the first figure \n\u003cA NAME=\"500\"\u003e\u003c/A\u003eand through the third that A belongs necessarily to some B. But this is \n\u003cA NAME=\"501\"\u003e\u003c/A\u003efalse; for B may be such that it is possible that A should belong to none \n\u003cA NAME=\"502\"\u003e\u003c/A\u003eof it. Further, an example also makes it clear that the conclusion not \n\u003cA NAME=\"503\"\u003e\u003c/A\u003ebe necessary, e.g. if A were movement, B animal, C man: man is an animal \n\u003cA NAME=\"504\"\u003e\u003c/A\u003enecessarily, but an animal does not move necessarily, nor does man. Similarly \n\u003cA NAME=\"505\"\u003e\u003c/A\u003ealso if the major premiss is negative; for the proof is the \n\u003cA NAME=\"506\"\u003e\u003c/A\u003esame.\n\u003cA NAME=\"507\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIn particular syllogisms, if the universal premiss is necessary, \n\u003cA NAME=\"508\"\u003e\u003c/A\u003ethen the conclusion will be necessary; but if the particular, the conclusion \n\u003cA NAME=\"509\"\u003e\u003c/A\u003ewill not be necessary, whether the universal premiss is negative or affirmative. \n\u003cA NAME=\"510\"\u003e\u003c/A\u003eFirst let the universal be necessary, and let A belong to all B necessarily, \n\u003cA NAME=\"511\"\u003e\u003c/A\u003ebut let B simply belong to some C: it is necessary then that A belongs \n\u003cA NAME=\"512\"\u003e\u003c/A\u003eto some C necessarily: for C falls under B, and A was assumed to belong \n\u003cA NAME=\"513\"\u003e\u003c/A\u003enecessarily to all B. Similarly also if the syllogism should be negative: \n\u003cA NAME=\"514\"\u003e\u003c/A\u003efor the proof will be the same. But if the particular premiss is necessary, \n\u003cA NAME=\"515\"\u003e\u003c/A\u003ethe conclusion will not be necessary: for from the denial of such a conclusion \n\u003cA NAME=\"516\"\u003e\u003c/A\u003enothing impossible results, just as it does not in the universal syllogisms. \n\u003cA NAME=\"517\"\u003e\u003c/A\u003eThe same is true of negative syllogisms. Try the terms movement, animal, \n\u003cA NAME=\"518\"\u003e\u003c/A\u003ewhite.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"519\"\u003e\u003c/A\u003e\u003cB\u003ePart 10\u003c/B\u003e\n\n\u003cA NAME=\"520\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIn the second figure, if the negative premiss is necessary, then \n\u003cA NAME=\"521\"\u003e\u003c/A\u003ethe conclusion will be necessary, but if the affirmative, not necessary. \n\u003cA NAME=\"522\"\u003e\u003c/A\u003eFirst let the negative be necessary; let A be possible of no B, and simply \n\u003cA NAME=\"523\"\u003e\u003c/A\u003ebelong to C. Since then the negative statement is convertible, B is possible \n\u003cA NAME=\"524\"\u003e\u003c/A\u003eof no A. But A belongs to all C; consequently B is possible of no C. For \n\u003cA NAME=\"525\"\u003e\u003c/A\u003eC falls under A. The same result would be obtained if the minor premiss \n\u003cA NAME=\"526\"\u003e\u003c/A\u003ewere negative: for if A is possible be of no C, C is possible of no A: \n\u003cA NAME=\"527\"\u003e\u003c/A\u003ebut A belongs to all B, consequently C is possible of none of the Bs: for \n\u003cA NAME=\"528\"\u003e\u003c/A\u003eagain we have obtained the first figure. Neither then is B possible of \n\u003cA NAME=\"529\"\u003e\u003c/A\u003eC: for conversion is possible without modifying the \n\u003cA NAME=\"530\"\u003e\u003c/A\u003erelation.\n\u003cA NAME=\"531\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eBut if the affirmative premiss is necessary, the conclusion will \n\u003cA NAME=\"532\"\u003e\u003c/A\u003enot be necessary. Let A belong to all B necessarily, but to no C simply. \n\u003cA NAME=\"533\"\u003e\u003c/A\u003eIf then the negative premiss is converted, the first figure results. But \n\u003cA NAME=\"534\"\u003e\u003c/A\u003eit has been proved in the case of the first figure that if the negative \n\u003cA NAME=\"535\"\u003e\u003c/A\u003emajor premiss is not necessary the conclusion will not be necessary either. \n\u003cA NAME=\"536\"\u003e\u003c/A\u003eTherefore the same result will obtain here. Further, if the conclusion \n\u003cA NAME=\"537\"\u003e\u003c/A\u003eis necessary, it follows that C necessarily does not belong to some A. \n\u003cA NAME=\"538\"\u003e\u003c/A\u003eFor if B necessarily belongs to no C, C will necessarily belong to no B. \n\u003cA NAME=\"539\"\u003e\u003c/A\u003eBut B at any rate must belong to some A, if it is true (as was assumed) \n\u003cA NAME=\"540\"\u003e\u003c/A\u003ethat A necessarily belongs to all B. Consequently it is necessary that \n\u003cA NAME=\"541\"\u003e\u003c/A\u003eC does not belong to some A. But nothing prevents such an A being taken \n\u003cA NAME=\"542\"\u003e\u003c/A\u003ethat it is possible for C to belong to all of it. Further one might show \n\u003cA NAME=\"543\"\u003e\u003c/A\u003eby an exposition of terms that the conclusion is not necessary without \n\u003cA NAME=\"544\"\u003e\u003c/A\u003equalification, though it is a necessary conclusion from the premisses. \n\u003cA NAME=\"545\"\u003e\u003c/A\u003eFor example let A be animal, B man, C white, and let the premisses be assumed \n\u003cA NAME=\"546\"\u003e\u003c/A\u003eto correspond to what we had before: it is possible that animal should \n\u003cA NAME=\"547\"\u003e\u003c/A\u003ebelong to nothing white. Man then will not belong to anything white, but \n\u003cA NAME=\"548\"\u003e\u003c/A\u003enot necessarily: for it is possible for man to be born white, not however \n\u003cA NAME=\"549\"\u003e\u003c/A\u003eso long as animal belongs to nothing white. Consequently under these conditions \n\u003cA NAME=\"550\"\u003e\u003c/A\u003ethe conclusion will be necessary, but it is not necessary without \n\u003cA NAME=\"551\"\u003e\u003c/A\u003equalification.\n\u003cA NAME=\"552\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eSimilar results will obtain also in particular syllogisms. For \n\u003cA NAME=\"553\"\u003e\u003c/A\u003ewhenever the negative premiss is both universal and necessary, then the \n\u003cA NAME=\"554\"\u003e\u003c/A\u003econclusion will be necessary: but whenever the affirmative premiss is universal, \n\u003cA NAME=\"555\"\u003e\u003c/A\u003ethe negative particular, the conclusion will not be necessary. First then \n\u003cA NAME=\"556\"\u003e\u003c/A\u003elet the negative premiss be both universal and necessary: let it be possible \n\u003cA NAME=\"557\"\u003e\u003c/A\u003efor no B that A should belong to it, and let A simply belong to some C. \n\u003cA NAME=\"558\"\u003e\u003c/A\u003eSince the negative statement is convertible, it will be possible for no \n\u003cA NAME=\"559\"\u003e\u003c/A\u003eA that B should belong to it: but A belongs to some C; consequently B necessarily \n\u003cA NAME=\"560\"\u003e\u003c/A\u003edoes not belong to some of the Cs. Again let the affirmative premiss be \n\u003cA NAME=\"561\"\u003e\u003c/A\u003eboth universal and necessary, and let the major premiss be affirmative. \n\u003cA NAME=\"562\"\u003e\u003c/A\u003eIf then A necessarily belongs to all B, but does not belong to some C, \n\u003cA NAME=\"563\"\u003e\u003c/A\u003eit is clear that B will not belong to some C, but not necessarily. For \n\u003cA NAME=\"564\"\u003e\u003c/A\u003ethe same terms can be used to demonstrate the point, which were used in \n\u003cA NAME=\"565\"\u003e\u003c/A\u003ethe universal syllogisms. Nor again, if the negative statement is necessary \n\u003cA NAME=\"566\"\u003e\u003c/A\u003ebut particular, will the conclusion be necessary. The point can be demonstrated \n\u003cA NAME=\"567\"\u003e\u003c/A\u003eby means of the same terms.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"568\"\u003e\u003c/A\u003e\u003cB\u003ePart 11\u003c/B\u003e\n\n\u003cA NAME=\"569\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIn the last figure when the terms are related universally to the \n\u003cA NAME=\"570\"\u003e\u003c/A\u003emiddle, and both premisses are affirmative, if one of the two is necessary, \n\u003cA NAME=\"571\"\u003e\u003c/A\u003ethen the conclusion will be necessary. But if one is negative, the other \n\u003cA NAME=\"572\"\u003e\u003c/A\u003eaffirmative, whenever the negative is necessary the conclusion also will \n\u003cA NAME=\"573\"\u003e\u003c/A\u003ebe necessary, but whenever the affirmative is necessary the conclusion \n\u003cA NAME=\"574\"\u003e\u003c/A\u003ewill not be necessary. First let both the premisses be affirmative, and \n\u003cA NAME=\"575\"\u003e\u003c/A\u003elet A and B belong to all C, and let Ac be necessary. Since then B belongs \n\u003cA NAME=\"576\"\u003e\u003c/A\u003eto all C, C also will belong to some B, because the universal is convertible \n\u003cA NAME=\"577\"\u003e\u003c/A\u003einto the particular: consequently if A belongs necessarily to all C, and \n\u003cA NAME=\"578\"\u003e\u003c/A\u003eC belongs to some B, it is necessary that A should belong to some B also. \n\u003cA NAME=\"579\"\u003e\u003c/A\u003eFor B is under C. The first figure then is formed. A similar proof will \n\u003cA NAME=\"580\"\u003e\u003c/A\u003ebe given also if BC is necessary. For C is convertible with some A: consequently \n\u003cA NAME=\"581\"\u003e\u003c/A\u003eif B belongs necessarily to all C, it will belong necessarily also to some \n\u003cA NAME=\"582\"\u003e\u003c/A\u003eA.\n\u003cA NAME=\"583\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eAgain let AC be negative, BC affirmative, and let the negative \n\u003cA NAME=\"584\"\u003e\u003c/A\u003epremiss be necessary. Since then C is convertible with some B, but A necessarily \n\u003cA NAME=\"585\"\u003e\u003c/A\u003ebelongs to no C, A will necessarily not belong to some B either: for B \n\u003cA NAME=\"586\"\u003e\u003c/A\u003eis under C. But if the affirmative is necessary, the conclusion will not \n\u003cA NAME=\"587\"\u003e\u003c/A\u003ebe necessary. For suppose BC is affirmative and necessary, while AC is \n\u003cA NAME=\"588\"\u003e\u003c/A\u003enegative and not necessary. Since then the affirmative is convertible, \n\u003cA NAME=\"589\"\u003e\u003c/A\u003eC also will belong to some B necessarily: consequently if A belongs to \n\u003cA NAME=\"590\"\u003e\u003c/A\u003enone of the Cs, while C belongs to some of the Bs, A will not belong to \n\u003cA NAME=\"591\"\u003e\u003c/A\u003esome of the Bs-but not of necessity; for it has been proved, in the case \n\u003cA NAME=\"592\"\u003e\u003c/A\u003eof the first figure, that if the negative premiss is not necessary, neither \n\u003cA NAME=\"593\"\u003e\u003c/A\u003ewill the conclusion be necessary. Further, the point may be made clear \n\u003cA NAME=\"594\"\u003e\u003c/A\u003eby considering the terms. Let the term A be \u0027good\u0027, let that which B signifies \n\u003cA NAME=\"595\"\u003e\u003c/A\u003ebe \u0027animal\u0027, let the term C be \u0027horse\u0027. It is possible then that the term \n\u003cA NAME=\"596\"\u003e\u003c/A\u003egood should belong to no horse, and it is necessary that the term animal \n\u003cA NAME=\"597\"\u003e\u003c/A\u003eshould belong to every horse: but it is not necessary that some animal \n\u003cA NAME=\"598\"\u003e\u003c/A\u003eshould not be good, since it is possible for every animal to be good. Or \n\u003cA NAME=\"599\"\u003e\u003c/A\u003eif that is not possible, take as the term \u0027awake\u0027 or \u0027asleep\u0027: for every \n\u003cA NAME=\"600\"\u003e\u003c/A\u003eanimal can accept these.\n\u003cA NAME=\"601\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIf, then, the premisses are universal, we have stated when the \n\u003cA NAME=\"602\"\u003e\u003c/A\u003econclusion will be necessary. But if one premiss is universal, the other \n\u003cA NAME=\"603\"\u003e\u003c/A\u003eparticular, and if both are affirmative, whenever the universal is necessary \n\u003cA NAME=\"604\"\u003e\u003c/A\u003ethe conclusion also must be necessary. The demonstration is the same as \n\u003cA NAME=\"605\"\u003e\u003c/A\u003ebefore; for the particular affirmative also is convertible. If then it \n\u003cA NAME=\"606\"\u003e\u003c/A\u003eis necessary that B should belong to all C, and A falls under C, it is \n\u003cA NAME=\"607\"\u003e\u003c/A\u003enecessary that B should belong to some A. But if B must belong to some \n\u003cA NAME=\"608\"\u003e\u003c/A\u003eA, then A must belong to some B: for conversion is possible. Similarly \n\u003cA NAME=\"609\"\u003e\u003c/A\u003ealso if AC should be necessary and universal: for B falls under C. But \n\u003cA NAME=\"610\"\u003e\u003c/A\u003eif the particular premiss is necessary, the conclusion will not be necessary. \n\u003cA NAME=\"611\"\u003e\u003c/A\u003eLet the premiss BC be both particular and necessary, and let A belong to \n\u003cA NAME=\"612\"\u003e\u003c/A\u003eall C, not however necessarily. If the proposition BC is converted the \n\u003cA NAME=\"613\"\u003e\u003c/A\u003efirst figure is formed, and the universal premiss is not necessary, but \n\u003cA NAME=\"614\"\u003e\u003c/A\u003ethe particular is necessary. But when the premisses were thus, the conclusion \n\u003cA NAME=\"615\"\u003e\u003c/A\u003e(as we proved was not necessary: consequently it is not here either. Further, \n\u003cA NAME=\"616\"\u003e\u003c/A\u003ethe point is clear if we look at the terms. Let A be waking, B biped, and \n\u003cA NAME=\"617\"\u003e\u003c/A\u003eC animal. It is necessary that B should belong to some C, but it is possible \n\u003cA NAME=\"618\"\u003e\u003c/A\u003efor A to belong to C, and that A should belong to B is not necessary. For \n\u003cA NAME=\"619\"\u003e\u003c/A\u003ethere is no necessity that some biped should be asleep or awake. Similarly \n\u003cA NAME=\"620\"\u003e\u003c/A\u003eand by means of the same terms proof can be made, should the proposition \n\u003cA NAME=\"621\"\u003e\u003c/A\u003eAc be both particular and necessary.\n\u003cA NAME=\"622\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eBut if one premiss is affirmative, the other negative, whenever \n\u003cA NAME=\"623\"\u003e\u003c/A\u003ethe universal is both negative and necessary the conclusion also will be \n\u003cA NAME=\"624\"\u003e\u003c/A\u003enecessary. For if it is not possible that A should belong to any C, but \n\u003cA NAME=\"625\"\u003e\u003c/A\u003eB belongs to some C, it is necessary that A should not belong to some B. \n\u003cA NAME=\"626\"\u003e\u003c/A\u003eBut whenever the affirmative proposition is necessary, whether universal \n\u003cA NAME=\"627\"\u003e\u003c/A\u003eor particular, or the negative is particular, the conclusion will not be \n\u003cA NAME=\"628\"\u003e\u003c/A\u003enecessary. The proof of this by reduction will be the same as before; but \n\u003cA NAME=\"629\"\u003e\u003c/A\u003eif terms are wanted, when the universal affirmative is necessary, take \n\u003cA NAME=\"630\"\u003e\u003c/A\u003ethe terms \u0027waking\u0027-\u0027animal\u0027-\u0027man\u0027, \u0027man\u0027 being middle, and when the affirmative \n\u003cA NAME=\"631\"\u003e\u003c/A\u003eis particular and necessary, take the terms \u0027waking\u0027-\u0027animal\u0027-\u0027white\u0027: \n\u003cA NAME=\"632\"\u003e\u003c/A\u003efor it is necessary that animal should belong to some white thing, but \n\u003cA NAME=\"633\"\u003e\u003c/A\u003eit is possible that waking should belong to none, and it is not necessary \n\u003cA NAME=\"634\"\u003e\u003c/A\u003ethat waking should not belong to some animal. But when the negative proposition \n\u003cA NAME=\"635\"\u003e\u003c/A\u003ebeing particular is necessary, take the terms \u0027biped\u0027, \u0027moving\u0027, \u0027animal\u0027, \n\u003cA NAME=\"636\"\u003e\u003c/A\u003e\u0027animal\u0027 being middle.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"637\"\u003e\u003c/A\u003e\u003cB\u003ePart 12\u003c/B\u003e\n\n\u003cA NAME=\"638\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is clear then that a simple conclusion is not reached unless \n\u003cA NAME=\"639\"\u003e\u003c/A\u003eboth premisses are simple assertions, but a necessary conclusion is possible \n\u003cA NAME=\"640\"\u003e\u003c/A\u003ealthough one only of the premisses is necessary. But in both cases, whether \n\u003cA NAME=\"641\"\u003e\u003c/A\u003ethe syllogisms are affirmative or negative, it is necessary that one premiss \n\u003cA NAME=\"642\"\u003e\u003c/A\u003eshould be similar to the conclusion. I mean by \u0027similar\u0027, if the conclusion \n\u003cA NAME=\"643\"\u003e\u003c/A\u003eis a simple assertion, the premiss must be simple; if the conclusion is \n\u003cA NAME=\"644\"\u003e\u003c/A\u003enecessary, the premiss must be necessary. Consequently this also is clear, \n\u003cA NAME=\"645\"\u003e\u003c/A\u003ethat the conclusion will be neither necessary nor simple unless a necessary \n\u003cA NAME=\"646\"\u003e\u003c/A\u003eor simple premiss is assumed.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"647\"\u003e\u003c/A\u003e\u003cB\u003ePart 13\u003c/B\u003e\n\n\u003cA NAME=\"648\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003ePerhaps enough has been said about the proof of necessity, how \n\u003cA NAME=\"649\"\u003e\u003c/A\u003eit comes about and how it differs from the proof of a simple statement. \n\u003cA NAME=\"650\"\u003e\u003c/A\u003eWe proceed to discuss that which is possible, when and how and by what \n\u003cA NAME=\"651\"\u003e\u003c/A\u003emeans it can be proved. I use the terms \u0027to be possible\u0027 and \u0027the possible\u0027 \n\u003cA NAME=\"652\"\u003e\u003c/A\u003eof that which is not necessary but, being assumed, results in nothing impossible. \n\u003cA NAME=\"653\"\u003e\u003c/A\u003eWe say indeed ambiguously of the necessary that it is possible. But that \n\u003cA NAME=\"654\"\u003e\u003c/A\u003emy definition of the possible is correct is clear from the phrases by which \n\u003cA NAME=\"655\"\u003e\u003c/A\u003ewe deny or on the contrary affirm possibility. For the expressions \u0027it \n\u003cA NAME=\"656\"\u003e\u003c/A\u003eis not possible to belong\u0027, \u0027it is impossible to belong\u0027, and \u0027it is necessary \n\u003cA NAME=\"657\"\u003e\u003c/A\u003enot to belong\u0027 are either identical or follow from one another; consequently \n\u003cA NAME=\"658\"\u003e\u003c/A\u003etheir opposites also, \u0027it is possible to belong\u0027, \u0027it is not impossible \n\u003cA NAME=\"659\"\u003e\u003c/A\u003eto belong\u0027, and \u0027it is not necessary not to belong\u0027, will either be identical \n\u003cA NAME=\"660\"\u003e\u003c/A\u003eor follow from one another. For of everything the affirmation or the denial \n\u003cA NAME=\"661\"\u003e\u003c/A\u003eholds good. That which is possible then will be not necessary and that \n\u003cA NAME=\"662\"\u003e\u003c/A\u003ewhich is not necessary will be possible. It results that all premisses \n\u003cA NAME=\"663\"\u003e\u003c/A\u003ein the mode of possibility are convertible into one another. I mean not \n\u003cA NAME=\"664\"\u003e\u003c/A\u003ethat the affirmative are convertible into the negative, but that those \n\u003cA NAME=\"665\"\u003e\u003c/A\u003ewhich are affirmative in form admit of conversion by opposition, e.g. \u0027it \n\u003cA NAME=\"666\"\u003e\u003c/A\u003eis possible to belong\u0027 may be converted into \u0027it is possible not to belong\u0027, \n\u003cA NAME=\"667\"\u003e\u003c/A\u003eand \u0027it is possible for A to belong to all B\u0027 into \u0027it is possible for \n\u003cA NAME=\"668\"\u003e\u003c/A\u003eA to belong to no B\u0027 or \u0027not to all B\u0027, and \u0027it is possible for A to belong \n\u003cA NAME=\"669\"\u003e\u003c/A\u003eto some B\u0027 into \u0027it is possible for A not to belong to some B\u0027. And similarly \n\u003cA NAME=\"670\"\u003e\u003c/A\u003ethe other propositions in this mode can be converted. For since that which \n\u003cA NAME=\"671\"\u003e\u003c/A\u003eis possible is not necessary, and that which is not necessary may possibly \n\u003cA NAME=\"672\"\u003e\u003c/A\u003enot belong, it is clear that if it is possible that A should belong to \n\u003cA NAME=\"673\"\u003e\u003c/A\u003eB, it is possible also that it should not belong to B: and if it is possible \n\u003cA NAME=\"674\"\u003e\u003c/A\u003ethat it should belong to all, it is also possible that it should not belong \n\u003cA NAME=\"675\"\u003e\u003c/A\u003eto all. The same holds good in the case of particular affirmations: for \n\u003cA NAME=\"676\"\u003e\u003c/A\u003ethe proof is identical. And such premisses are affirmative and not negative; \n\u003cA NAME=\"677\"\u003e\u003c/A\u003efor \u0027to be possible\u0027 is in the same rank as \u0027to be\u0027, as was said \n\u003cA NAME=\"678\"\u003e\u003c/A\u003eabove.\n\u003cA NAME=\"679\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eHaving made these distinctions we next point out that the expression \n\u003cA NAME=\"680\"\u003e\u003c/A\u003e\u0027to be possible\u0027 is used in two ways. In one it means to happen generally \n\u003cA NAME=\"681\"\u003e\u003c/A\u003eand fall short of necessity, e.g. man\u0027s turning grey or growing or decaying, \n\u003cA NAME=\"682\"\u003e\u003c/A\u003eor generally what naturally belongs to a thing (for this has not its necessity \n\u003cA NAME=\"683\"\u003e\u003c/A\u003eunbroken, since man\u0027s existence is not continuous for ever, although if \n\u003cA NAME=\"684\"\u003e\u003c/A\u003ea man does exist, it comes about either necessarily or generally). In another \n\u003cA NAME=\"685\"\u003e\u003c/A\u003esense the expression means the indefinite, which can be both thus and not \n\u003cA NAME=\"686\"\u003e\u003c/A\u003ethus, e.g. an animal\u0027s walking or an earthquake\u0027s taking place while it \n\u003cA NAME=\"687\"\u003e\u003c/A\u003eis walking, or generally what happens by chance: for none of these inclines \n\u003cA NAME=\"688\"\u003e\u003c/A\u003eby nature in the one way more than in the opposite.\n\u003cA NAME=\"689\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThat which is possible in each of its two senses is convertible \n\u003cA NAME=\"690\"\u003e\u003c/A\u003einto its opposite, not however in the same way: but what is natural is \n\u003cA NAME=\"691\"\u003e\u003c/A\u003econvertible because it does not necessarily belong (for in this sense it \n\u003cA NAME=\"692\"\u003e\u003c/A\u003eis possible that a man should not grow grey) and what is indefinite is \n\u003cA NAME=\"693\"\u003e\u003c/A\u003econvertible because it inclines this way no more than that. Science and \n\u003cA NAME=\"694\"\u003e\u003c/A\u003edemonstrative syllogism are not concerned with things which are indefinite, \n\u003cA NAME=\"695\"\u003e\u003c/A\u003ebecause the middle term is uncertain; but they are concerned with things \n\u003cA NAME=\"696\"\u003e\u003c/A\u003ethat are natural, and as a rule arguments and inquiries are made about \n\u003cA NAME=\"697\"\u003e\u003c/A\u003ethings which are possible in this sense. Syllogisms indeed can be made \n\u003cA NAME=\"698\"\u003e\u003c/A\u003eabout the former, but it is unusual at any rate to inquire about \n\u003cA NAME=\"699\"\u003e\u003c/A\u003ethem.\n\u003cA NAME=\"700\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThese matters will be treated more definitely in the sequel; our \n\u003cA NAME=\"701\"\u003e\u003c/A\u003ebusiness at present is to state the moods and nature of the syllogism made \n\u003cA NAME=\"702\"\u003e\u003c/A\u003efrom possible premisses. The expression \u0027it is possible for this to belong \n\u003cA NAME=\"703\"\u003e\u003c/A\u003eto that\u0027 may be understood in two senses: \u0027that\u0027 may mean either that to \n\u003cA NAME=\"704\"\u003e\u003c/A\u003ewhich \u0027that\u0027 belongs or that to which it may belong; for the expression \n\u003cA NAME=\"705\"\u003e\u003c/A\u003e\u0027A is possible of the subject of B\u0027 means that it is possible either of \n\u003cA NAME=\"706\"\u003e\u003c/A\u003ethat of which B is stated or of that of which B may possibly be stated. \n\u003cA NAME=\"707\"\u003e\u003c/A\u003eIt makes no difference whether we say, A is possible of the subject of \n\u003cA NAME=\"708\"\u003e\u003c/A\u003eB, or all B admits of A. It is clear then that the expression \u0027A may possibly \n\u003cA NAME=\"709\"\u003e\u003c/A\u003ebelong to all B\u0027 might be used in two senses. First then we must state \n\u003cA NAME=\"710\"\u003e\u003c/A\u003ethe nature and characteristics of the syllogism which arises if B is possible \n\u003cA NAME=\"711\"\u003e\u003c/A\u003eof the subject of C, and A is possible of the subject of B. For thus both \n\u003cA NAME=\"712\"\u003e\u003c/A\u003epremisses are assumed in the mode of possibility; but whenever A is possible \n\u003cA NAME=\"713\"\u003e\u003c/A\u003eof that of which B is true, one premiss is a simple assertion, the other \n\u003cA NAME=\"714\"\u003e\u003c/A\u003ea problematic. Consequently we must start from premisses which are similar \n\u003cA NAME=\"715\"\u003e\u003c/A\u003ein form, as in the other cases.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"716\"\u003e\u003c/A\u003e\u003cB\u003ePart 14\u003c/B\u003e\n\n\u003cA NAME=\"717\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWhenever A may possibly belong to all B, and B to all C, there \n\u003cA NAME=\"718\"\u003e\u003c/A\u003ewill be a perfect syllogism to prove that A may possibly belong to all \n\u003cA NAME=\"719\"\u003e\u003c/A\u003eC. This is clear from the definition: for it was in this way that we explained \n\u003cA NAME=\"720\"\u003e\u003c/A\u003e\u0027to be possible for one term to belong to all of another\u0027. Similarly if \n\u003cA NAME=\"721\"\u003e\u003c/A\u003eit is possible for A to belong no B, and for B to belong to all C, then \n\u003cA NAME=\"722\"\u003e\u003c/A\u003eit is possible for A to belong to no C. For the statement that it is possible \n\u003cA NAME=\"723\"\u003e\u003c/A\u003efor A not to belong to that of which B may be true means (as we saw) that \n\u003cA NAME=\"724\"\u003e\u003c/A\u003enone of those things which can possibly fall under the term B is left out \n\u003cA NAME=\"725\"\u003e\u003c/A\u003eof account. But whenever A may belong to all B, and B may belong to no \n\u003cA NAME=\"726\"\u003e\u003c/A\u003eC, then indeed no syllogism results from the premisses assumed, but if \n\u003cA NAME=\"727\"\u003e\u003c/A\u003ethe premiss BC is converted after the manner of problematic propositions, \n\u003cA NAME=\"728\"\u003e\u003c/A\u003ethe same syllogism results as before. For since it is possible that B should \n\u003cA NAME=\"729\"\u003e\u003c/A\u003ebelong to no C, it is possible also that it should belong to all C. This \n\u003cA NAME=\"730\"\u003e\u003c/A\u003ehas been stated above. Consequently if B is possible for all C, and A is \n\u003cA NAME=\"731\"\u003e\u003c/A\u003epossible for all B, the same syllogism again results. Similarly if in both \n\u003cA NAME=\"732\"\u003e\u003c/A\u003ethe premisses the negative is joined with \u0027it is possible\u0027: e.g. if A may \n\u003cA NAME=\"733\"\u003e\u003c/A\u003ebelong to none of the Bs, and B to none of the Cs. No syllogism results \n\u003cA NAME=\"734\"\u003e\u003c/A\u003efrom the assumed premisses, but if they are converted we shall have the \n\u003cA NAME=\"735\"\u003e\u003c/A\u003esame syllogism as before. It is clear then that if the minor premiss is \n\u003cA NAME=\"736\"\u003e\u003c/A\u003enegative, or if both premisses are negative, either no syllogism results, \n\u003cA NAME=\"737\"\u003e\u003c/A\u003eor if one it is not perfect. For the necessity results from the \n\u003cA NAME=\"738\"\u003e\u003c/A\u003econversion.\n\u003cA NAME=\"739\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eBut if one of the premisses is universal, the other particular, \n\u003cA NAME=\"740\"\u003e\u003c/A\u003ewhen the major premiss is universal there will be a perfect syllogism. \n\u003cA NAME=\"741\"\u003e\u003c/A\u003eFor if A is possible for all B, and B for some C, then A is possible for \n\u003cA NAME=\"742\"\u003e\u003c/A\u003esome C. This is clear from the definition of being possible. Again if A \n\u003cA NAME=\"743\"\u003e\u003c/A\u003emay belong to no B, and B may belong to some of the Cs, it is necessary \n\u003cA NAME=\"744\"\u003e\u003c/A\u003ethat A may possibly not belong to some of the Cs. The proof is the same \n\u003cA NAME=\"745\"\u003e\u003c/A\u003eas above. But if the particular premiss is negative, and the universal \n\u003cA NAME=\"746\"\u003e\u003c/A\u003eis affirmative, the major still being universal and the minor particular, \n\u003cA NAME=\"747\"\u003e\u003c/A\u003ee.g. A is possible for all B, B may possibly not belong to some C, then \n\u003cA NAME=\"748\"\u003e\u003c/A\u003ea clear syllogism does not result from the assumed premisses, but if the \n\u003cA NAME=\"749\"\u003e\u003c/A\u003eparticular premiss is converted and it is laid down that B possibly may \n\u003cA NAME=\"750\"\u003e\u003c/A\u003ebelong to some C, we shall have the same conclusion as before, as in the \n\u003cA NAME=\"751\"\u003e\u003c/A\u003ecases given at the beginning.\n\u003cA NAME=\"752\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eBut if the major premiss is the minor universal, whether both are \n\u003cA NAME=\"753\"\u003e\u003c/A\u003eaffirmative, or negative, or different in quality, or if both are indefinite \n\u003cA NAME=\"754\"\u003e\u003c/A\u003eor particular, in no way will a syllogism be possible. For nothing prevents \n\u003cA NAME=\"755\"\u003e\u003c/A\u003eB from reaching beyond A, so that as predicates cover unequal areas. Let \n\u003cA NAME=\"756\"\u003e\u003c/A\u003eC be that by which B extends beyond A. To C it is not possible that A should \n\u003cA NAME=\"757\"\u003e\u003c/A\u003ebelong-either to all or to none or to some or not to some, since premisses \n\u003cA NAME=\"758\"\u003e\u003c/A\u003ein the mode of possibility are convertible and it is possible for B to \n\u003cA NAME=\"759\"\u003e\u003c/A\u003ebelong to more things than A can. Further, this is obvious if we take terms; \n\u003cA NAME=\"760\"\u003e\u003c/A\u003efor if the premisses are as assumed, the major term is both possible for \n\u003cA NAME=\"761\"\u003e\u003c/A\u003enone of the minor and must belong to all of it. Take as terms common to \n\u003cA NAME=\"762\"\u003e\u003c/A\u003eall the cases under consideration \u0027animal\u0027-\u0027white\u0027-\u0027man\u0027, where the major \n\u003cA NAME=\"763\"\u003e\u003c/A\u003ebelongs necessarily to the minor; \u0027animal\u0027-\u0027white\u0027-\u0027garment\u0027, where it \n\u003cA NAME=\"764\"\u003e\u003c/A\u003eis not possible that the major should belong to the minor. It is clear \n\u003cA NAME=\"765\"\u003e\u003c/A\u003ethen that if the terms are related in this manner, no syllogism results. \n\u003cA NAME=\"766\"\u003e\u003c/A\u003eFor every syllogism proves that something belongs either simply or necessarily \n\u003cA NAME=\"767\"\u003e\u003c/A\u003eor possibly. It is clear that there is no proof of the first or of the \n\u003cA NAME=\"768\"\u003e\u003c/A\u003esecond. For the affirmative is destroyed by the negative, and the negative \n\u003cA NAME=\"769\"\u003e\u003c/A\u003eby the affirmative. There remains the proof of possibility. But this is \n\u003cA NAME=\"770\"\u003e\u003c/A\u003eimpossible. For it has been proved that if the terms are related in this \n\u003cA NAME=\"771\"\u003e\u003c/A\u003emanner it is both necessary that the major should belong to all the minor \n\u003cA NAME=\"772\"\u003e\u003c/A\u003eand not possible that it should belong to any. Consequently there cannot \n\u003cA NAME=\"773\"\u003e\u003c/A\u003ebe a syllogism to prove the possibility; for the necessary (as we stated) \n\u003cA NAME=\"774\"\u003e\u003c/A\u003eis not possible.\n\u003cA NAME=\"775\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is clear that if the terms are universal in possible premisses \n\u003cA NAME=\"776\"\u003e\u003c/A\u003ea syllogism always results in the first figure, whether they are affirmative \n\u003cA NAME=\"777\"\u003e\u003c/A\u003eor negative, only a perfect syllogism results in the first case, an imperfect \n\u003cA NAME=\"778\"\u003e\u003c/A\u003ein the second. But possibility must be understood according to the definition \n\u003cA NAME=\"779\"\u003e\u003c/A\u003elaid down, not as covering necessity. This is sometimes \n\u003cA NAME=\"780\"\u003e\u003c/A\u003eforgotten.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"781\"\u003e\u003c/A\u003e\u003cB\u003ePart 15\u003c/B\u003e\n\n\u003cA NAME=\"782\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIf one premiss is a simple proposition, the other a problematic, \n\u003cA NAME=\"783\"\u003e\u003c/A\u003ewhenever the major premiss indicates possibility all the syllogisms will \n\u003cA NAME=\"784\"\u003e\u003c/A\u003ebe perfect and establish possibility in the sense defined; but whenever \n\u003cA NAME=\"785\"\u003e\u003c/A\u003ethe minor premiss indicates possibility all the syllogisms will be imperfect, \n\u003cA NAME=\"786\"\u003e\u003c/A\u003eand those which are negative will establish not possibility according to \n\u003cA NAME=\"787\"\u003e\u003c/A\u003ethe definition, but that the major does not necessarily belong to any, \n\u003cA NAME=\"788\"\u003e\u003c/A\u003eor to all, of the minor. For if this is so, we say it is possible that \n\u003cA NAME=\"789\"\u003e\u003c/A\u003eit should belong to none or not to all. Let A be possible for all B, and \n\u003cA NAME=\"790\"\u003e\u003c/A\u003elet B belong to all C. Since C falls under B, and A is possible for all \n\u003cA NAME=\"791\"\u003e\u003c/A\u003eB, clearly it is possible for all C also. So a perfect syllogism results. \n\u003cA NAME=\"792\"\u003e\u003c/A\u003eLikewise if the premiss AB is negative, and the premiss BC is affirmative, \n\u003cA NAME=\"793\"\u003e\u003c/A\u003ethe former stating possible, the latter simple attribution, a perfect syllogism \n\u003cA NAME=\"794\"\u003e\u003c/A\u003eresults proving that A possibly belongs to no C.\n\u003cA NAME=\"795\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is clear that perfect syllogisms result if the minor premiss \n\u003cA NAME=\"796\"\u003e\u003c/A\u003estates simple belonging: but that syllogisms will result if the modality \n\u003cA NAME=\"797\"\u003e\u003c/A\u003eof the premisses is reversed, must be proved per impossibile. At the same \n\u003cA NAME=\"798\"\u003e\u003c/A\u003etime it will be evident that they are imperfect: for the proof proceeds \n\u003cA NAME=\"799\"\u003e\u003c/A\u003enot from the premisses assumed. First we must state that if B\u0027s being follows \n\u003cA NAME=\"800\"\u003e\u003c/A\u003enecessarily from A\u0027s being, B\u0027s possibility will follow necessarily from \n\u003cA NAME=\"801\"\u003e\u003c/A\u003eA\u0027s possibility. Suppose, the terms being so related, that A is possible, \n\u003cA NAME=\"802\"\u003e\u003c/A\u003eand B is impossible. If then that which is possible, when it is possible \n\u003cA NAME=\"803\"\u003e\u003c/A\u003efor it to be, might happen, and if that which is impossible, when it is \n\u003cA NAME=\"804\"\u003e\u003c/A\u003eimpossible, could not happen, and if at the same time A is possible and \n\u003cA NAME=\"805\"\u003e\u003c/A\u003eB impossible, it would be possible for A to happen without B, and if to \n\u003cA NAME=\"806\"\u003e\u003c/A\u003ehappen, then to be. For that which has happened, when it has happened, \n\u003cA NAME=\"807\"\u003e\u003c/A\u003eis. But we must take the impossible and the possible not only in the sphere \n\u003cA NAME=\"808\"\u003e\u003c/A\u003eof becoming, but also in the spheres of truth and predicability, and the \n\u003cA NAME=\"809\"\u003e\u003c/A\u003evarious other spheres in which we speak of the possible: for it will be \n\u003cA NAME=\"810\"\u003e\u003c/A\u003ealike in all. Further we must understand the statement that B\u0027s being depends \n\u003cA NAME=\"811\"\u003e\u003c/A\u003eon A\u0027s being, not as meaning that if some single thing A is, B will be: \n\u003cA NAME=\"812\"\u003e\u003c/A\u003efor nothing follows of necessity from the being of some one thing, but \n\u003cA NAME=\"813\"\u003e\u003c/A\u003efrom two at least, i.e. when the premisses are related in the manner stated \n\u003cA NAME=\"814\"\u003e\u003c/A\u003eto be that of the syllogism. For if C is predicated of D, and D of F, then \n\u003cA NAME=\"815\"\u003e\u003c/A\u003eC is necessarily predicated of F. And if each is possible, the conclusion \n\u003cA NAME=\"816\"\u003e\u003c/A\u003ealso is possible. If then, for example, one should indicate the premisses \n\u003cA NAME=\"817\"\u003e\u003c/A\u003eby A, and the conclusion by B, it would not only result that if A is necessary \n\u003cA NAME=\"818\"\u003e\u003c/A\u003eB is necessary, but also that if A is possible, B is \n\u003cA NAME=\"819\"\u003e\u003c/A\u003epossible.\n\u003cA NAME=\"820\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eSince this is proved it is evident that if a false and not impossible \n\u003cA NAME=\"821\"\u003e\u003c/A\u003eassumption is made, the consequence of the assumption will also be false \n\u003cA NAME=\"822\"\u003e\u003c/A\u003eand not impossible: e.g. if A is false, but not impossible, and if B is \n\u003cA NAME=\"823\"\u003e\u003c/A\u003ethe consequence of A, B also will be false but not impossible. For since \n\u003cA NAME=\"824\"\u003e\u003c/A\u003eit has been proved that if B\u0027s being is the consequence of A\u0027s being, then \n\u003cA NAME=\"825\"\u003e\u003c/A\u003eB\u0027s possibility will follow from A\u0027s possibility (and A is assumed to be \n\u003cA NAME=\"826\"\u003e\u003c/A\u003epossible), consequently B will be possible: for if it were impossible, \n\u003cA NAME=\"827\"\u003e\u003c/A\u003ethe same thing would at the same time be possible and \n\u003cA NAME=\"828\"\u003e\u003c/A\u003eimpossible.\n\u003cA NAME=\"829\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eSince we have defined these points, let A belong to all B, and \n\u003cA NAME=\"830\"\u003e\u003c/A\u003eB be possible for all C: it is necessary then that should be a possible \n\u003cA NAME=\"831\"\u003e\u003c/A\u003eattribute for all C. Suppose that it is not possible, but assume that B \n\u003cA NAME=\"832\"\u003e\u003c/A\u003ebelongs to all C: this is false but not impossible. If then A is not possible \n\u003cA NAME=\"833\"\u003e\u003c/A\u003efor C but B belongs to all C, then A is not possible for all B: for a syllogism \n\u003cA NAME=\"834\"\u003e\u003c/A\u003eis formed in the third degree. But it was assumed that A is a possible \n\u003cA NAME=\"835\"\u003e\u003c/A\u003eattribute for all B. It is necessary then that A is possible for all C. \n\u003cA NAME=\"836\"\u003e\u003c/A\u003eFor though the assumption we made is false and not impossible, the conclusion \n\u003cA NAME=\"837\"\u003e\u003c/A\u003eis impossible. It is possible also in the first figure to bring about the \n\u003cA NAME=\"838\"\u003e\u003c/A\u003eimpossibility, by assuming that B belongs to C. For if B belongs to all \n\u003cA NAME=\"839\"\u003e\u003c/A\u003eC, and A is possible for all B, then A would be possible for all C. But \n\u003cA NAME=\"840\"\u003e\u003c/A\u003ethe assumption was made that A is not possible for all \n\u003cA NAME=\"841\"\u003e\u003c/A\u003eC.\n\u003cA NAME=\"842\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWe must understand \u0027that which belongs to all\u0027 with no limitation \n\u003cA NAME=\"843\"\u003e\u003c/A\u003ein respect of time, e.g. to the present or to a particular period, but \n\u003cA NAME=\"844\"\u003e\u003c/A\u003esimply without qualification. For it is by the help of such premisses that \n\u003cA NAME=\"845\"\u003e\u003c/A\u003ewe make syllogisms, since if the premiss is understood with reference to \n\u003cA NAME=\"846\"\u003e\u003c/A\u003ethe present moment, there cannot be a syllogism. For nothing perhaps prevents \n\u003cA NAME=\"847\"\u003e\u003c/A\u003e\u0027man\u0027 belonging at a particular time to everything that is moving, i.e. \n\u003cA NAME=\"848\"\u003e\u003c/A\u003eif nothing else were moving: but \u0027moving\u0027 is possible for every horse; \n\u003cA NAME=\"849\"\u003e\u003c/A\u003eyet \u0027man\u0027 is possible for no horse. Further let the major term be \u0027animal\u0027, \n\u003cA NAME=\"850\"\u003e\u003c/A\u003ethe middle \u0027moving\u0027, the the minor \u0027man\u0027. The premisses then will be as \n\u003cA NAME=\"851\"\u003e\u003c/A\u003ebefore, but the conclusion necessary, not possible. For man is necessarily \n\u003cA NAME=\"852\"\u003e\u003c/A\u003eanimal. It is clear then that the universal must be understood simply, \n\u003cA NAME=\"853\"\u003e\u003c/A\u003ewithout limitation in respect of time.\n\u003cA NAME=\"854\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eAgain let the premiss AB be universal and negative, and assume \n\u003cA NAME=\"855\"\u003e\u003c/A\u003ethat A belongs to no B, but B possibly belongs to all C. These propositions \n\u003cA NAME=\"856\"\u003e\u003c/A\u003ebeing laid down, it is necessary that A possibly belongs to no C. Suppose \n\u003cA NAME=\"857\"\u003e\u003c/A\u003ethat it cannot belong, and that B belongs to C, as above. It is necessary \n\u003cA NAME=\"858\"\u003e\u003c/A\u003ethen that A belongs to some B: for we have a syllogism in the third figure: \n\u003cA NAME=\"859\"\u003e\u003c/A\u003ebut this is impossible. Thus it will be possible for A to belong to no \n\u003cA NAME=\"860\"\u003e\u003c/A\u003eC; for if at is supposed false, the consequence is an impossible one. This \n\u003cA NAME=\"861\"\u003e\u003c/A\u003esyllogism then does not establish that which is possible according to the \n\u003cA NAME=\"862\"\u003e\u003c/A\u003edefinition, but that which does not necessarily belong to any part of the \n\u003cA NAME=\"863\"\u003e\u003c/A\u003esubject (for this is the contradictory of the assumption which was made: \n\u003cA NAME=\"864\"\u003e\u003c/A\u003efor it was supposed that A necessarily belongs to some C, but the syllogism \n\u003cA NAME=\"865\"\u003e\u003c/A\u003eper impossibile establishes the contradictory which is opposed to this). \n\u003cA NAME=\"866\"\u003e\u003c/A\u003eFurther, it is clear also from an example that the conclusion will not \n\u003cA NAME=\"867\"\u003e\u003c/A\u003eestablish possibility. Let A be \u0027raven\u0027, B \u0027intelligent\u0027, and C \u0027man\u0027. \n\u003cA NAME=\"868\"\u003e\u003c/A\u003eA then belongs to no B: for no intelligent thing is a raven. But B is possible \n\u003cA NAME=\"869\"\u003e\u003c/A\u003efor all C: for every man may possibly be intelligent. But A necessarily \n\u003cA NAME=\"870\"\u003e\u003c/A\u003ebelongs to no C: so the conclusion does not establish possibility. But \n\u003cA NAME=\"871\"\u003e\u003c/A\u003eneither is it always necessary. Let A be \u0027moving\u0027, B \u0027science\u0027, C \u0027man\u0027. \n\u003cA NAME=\"872\"\u003e\u003c/A\u003eA then will belong to no B; but B is possible for all C. And the conclusion \n\u003cA NAME=\"873\"\u003e\u003c/A\u003ewill not be necessary. For it is not necessary that no man should move; \n\u003cA NAME=\"874\"\u003e\u003c/A\u003erather it is not necessary that any man should move. Clearly then the conclusion \n\u003cA NAME=\"875\"\u003e\u003c/A\u003eestablishes that one term does not necessarily belong to any instance of \n\u003cA NAME=\"876\"\u003e\u003c/A\u003eanother term. But we must take our terms better.\n\u003cA NAME=\"877\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIf the minor premiss is negative and indicates possibility, from \n\u003cA NAME=\"878\"\u003e\u003c/A\u003ethe actual premisses taken there can be no syllogism, but if the problematic \n\u003cA NAME=\"879\"\u003e\u003c/A\u003epremiss is converted, a syllogism will be possible, as before. Let A belong \n\u003cA NAME=\"880\"\u003e\u003c/A\u003eto all B, and let B possibly belong to no C. If the terms are arranged \n\u003cA NAME=\"881\"\u003e\u003c/A\u003ethus, nothing necessarily follows: but if the proposition BC is converted \n\u003cA NAME=\"882\"\u003e\u003c/A\u003eand it is assumed that B is possible for all C, a syllogism results as \n\u003cA NAME=\"883\"\u003e\u003c/A\u003ebefore: for the terms are in the same relative positions. Likewise if both \n\u003cA NAME=\"884\"\u003e\u003c/A\u003ethe relations are negative, if the major premiss states that A does not \n\u003cA NAME=\"885\"\u003e\u003c/A\u003ebelong to B, and the minor premiss indicates that B may possibly belong \n\u003cA NAME=\"886\"\u003e\u003c/A\u003eto no C. Through the premisses actually taken nothing necessary results \n\u003cA NAME=\"887\"\u003e\u003c/A\u003ein any way; but if the problematic premiss is converted, we shall have \n\u003cA NAME=\"888\"\u003e\u003c/A\u003ea syllogism. Suppose that A belongs to no B, and B may possibly belong \n\u003cA NAME=\"889\"\u003e\u003c/A\u003eto no C. Through these comes nothing necessary. But if B is assumed to \n\u003cA NAME=\"890\"\u003e\u003c/A\u003ebe possible for all C (and this is true) and if the premiss AB remains \n\u003cA NAME=\"891\"\u003e\u003c/A\u003eas before, we shall again have the same syllogism. But if it be assumed \n\u003cA NAME=\"892\"\u003e\u003c/A\u003ethat B does not belong to any C, instead of possibly not belonging, there \n\u003cA NAME=\"893\"\u003e\u003c/A\u003ecannot be a syllogism anyhow, whether the premiss AB is negative or affirmative. \n\u003cA NAME=\"894\"\u003e\u003c/A\u003eAs common instances of a necessary and positive relation we may take the \n\u003cA NAME=\"895\"\u003e\u003c/A\u003eterms white-animal-snow: of a necessary and negative relation, white-animal-pitch. \n\u003cA NAME=\"896\"\u003e\u003c/A\u003eClearly then if the terms are universal, and one of the premisses is assertoric, \n\u003cA NAME=\"897\"\u003e\u003c/A\u003ethe other problematic, whenever the minor premiss is problematic a syllogism \n\u003cA NAME=\"898\"\u003e\u003c/A\u003ealways results, only sometimes it results from the premisses that are taken, \n\u003cA NAME=\"899\"\u003e\u003c/A\u003esometimes it requires the conversion of one premiss. We have stated when \n\u003cA NAME=\"900\"\u003e\u003c/A\u003eeach of these happens and the reason why. But if one of the relations is \n\u003cA NAME=\"901\"\u003e\u003c/A\u003euniversal, the other particular, then whenever the major premiss is universal \n\u003cA NAME=\"902\"\u003e\u003c/A\u003eand problematic, whether affirmative or negative, and the particular is \n\u003cA NAME=\"903\"\u003e\u003c/A\u003eaffirmative and assertoric, there will be a perfect syllogism, just as \n\u003cA NAME=\"904\"\u003e\u003c/A\u003ewhen the terms are universal. The demonstration is the same as before. \n\u003cA NAME=\"905\"\u003e\u003c/A\u003eBut whenever the major premiss is universal, but assertoric, not problematic, \n\u003cA NAME=\"906\"\u003e\u003c/A\u003eand the minor is particular and problematic, whether both premisses are \n\u003cA NAME=\"907\"\u003e\u003c/A\u003enegative or affirmative, or one is negative, the other affirmative, in \n\u003cA NAME=\"908\"\u003e\u003c/A\u003eall cases there will be an imperfect syllogism. Only some of them will \n\u003cA NAME=\"909\"\u003e\u003c/A\u003ebe proved per impossibile, others by the conversion of the problematic \n\u003cA NAME=\"910\"\u003e\u003c/A\u003epremiss, as has been shown above. And a syllogism will be possible by means \n\u003cA NAME=\"911\"\u003e\u003c/A\u003eof conversion when the major premiss is universal and assertoric, whether \n\u003cA NAME=\"912\"\u003e\u003c/A\u003epositive or negative, and the minor particular, negative, and problematic, \n\u003cA NAME=\"913\"\u003e\u003c/A\u003ee.g. if A belongs to all B or to no B, and B may possibly not belong to \n\u003cA NAME=\"914\"\u003e\u003c/A\u003esome C. For if the premiss BC is converted in respect of possibility, a \n\u003cA NAME=\"915\"\u003e\u003c/A\u003esyllogism results. But whenever the particular premiss is assertoric and \n\u003cA NAME=\"916\"\u003e\u003c/A\u003enegative, there cannot be a syllogism. As instances of the positive relation \n\u003cA NAME=\"917\"\u003e\u003c/A\u003ewe may take the terms white-animal-snow; of the negative, white-animal-pitch. \n\u003cA NAME=\"918\"\u003e\u003c/A\u003eFor the demonstration must be made through the indefinite nature of the \n\u003cA NAME=\"919\"\u003e\u003c/A\u003eparticular premiss. But if the minor premiss is universal, and the major \n\u003cA NAME=\"920\"\u003e\u003c/A\u003eparticular, whether either premiss is negative or affirmative, problematic \n\u003cA NAME=\"921\"\u003e\u003c/A\u003eor assertoric, nohow is a syllogism possible. Nor is a syllogism possible \n\u003cA NAME=\"922\"\u003e\u003c/A\u003ewhen the premisses are particular or indefinite, whether problematic or \n\u003cA NAME=\"923\"\u003e\u003c/A\u003eassertoric, or the one problematic, the other assertoric. The demonstration \n\u003cA NAME=\"924\"\u003e\u003c/A\u003eis the same as above. As instances of the necessary and positive relation \n\u003cA NAME=\"925\"\u003e\u003c/A\u003ewe may take the terms animal-white-man; of the necessary and negative relation, \n\u003cA NAME=\"926\"\u003e\u003c/A\u003eanimal-white-garment. It is evident then that if the major premiss is universal, \n\u003cA NAME=\"927\"\u003e\u003c/A\u003ea syllogism always results, but if the minor is universal nothing at all \n\u003cA NAME=\"928\"\u003e\u003c/A\u003ecan ever be proved.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"929\"\u003e\u003c/A\u003e\u003cB\u003ePart 16\u003c/B\u003e\n\n\u003cA NAME=\"930\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWhenever one premiss is necessary, the other problematic, there \n\u003cA NAME=\"931\"\u003e\u003c/A\u003ewill be a syllogism when the terms are related as before; and a perfect \n\u003cA NAME=\"932\"\u003e\u003c/A\u003esyllogism when the minor premiss is necessary. If the premisses are affirmative \n\u003cA NAME=\"933\"\u003e\u003c/A\u003ethe conclusion will be problematic, not assertoric, whether the premisses \n\u003cA NAME=\"934\"\u003e\u003c/A\u003eare universal or not: but if one is affirmative, the other negative, when \n\u003cA NAME=\"935\"\u003e\u003c/A\u003ethe affirmative is necessary the conclusion will be problematic, not negative \n\u003cA NAME=\"936\"\u003e\u003c/A\u003eassertoric; but when the negative is necessary the conclusion will be problematic \n\u003cA NAME=\"937\"\u003e\u003c/A\u003enegative, and assertoric negative, whether the premisses are universal \n\u003cA NAME=\"938\"\u003e\u003c/A\u003eor not. Possibility in the conclusion must be understood in the same manner \n\u003cA NAME=\"939\"\u003e\u003c/A\u003eas before. There cannot be an inference to the necessary negative proposition: \n\u003cA NAME=\"940\"\u003e\u003c/A\u003efor \u0027not necessarily to belong\u0027 is different from \u0027necessarily not to \n\u003cA NAME=\"941\"\u003e\u003c/A\u003ebelong\u0027.\n\u003cA NAME=\"942\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIf the premisses are affirmative, clearly the conclusion which \n\u003cA NAME=\"943\"\u003e\u003c/A\u003efollows is not necessary. Suppose A necessarily belongs to all B, and let \n\u003cA NAME=\"944\"\u003e\u003c/A\u003eB be possible for all C. We shall have an imperfect syllogism to prove \n\u003cA NAME=\"945\"\u003e\u003c/A\u003ethat A may belong to all C. That it is imperfect is clear from the proof: \n\u003cA NAME=\"946\"\u003e\u003c/A\u003efor it will be proved in the same manner as above. Again, let A be possible \n\u003cA NAME=\"947\"\u003e\u003c/A\u003efor all B, and let B necessarily belong to all C. We shall then have a \n\u003cA NAME=\"948\"\u003e\u003c/A\u003esyllogism to prove that A may belong to all C, not that A does belong to \n\u003cA NAME=\"949\"\u003e\u003c/A\u003eall C: and it is perfect, not imperfect: for it is completed directly through \n\u003cA NAME=\"950\"\u003e\u003c/A\u003ethe original premisses.\n\u003cA NAME=\"951\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eBut if the premisses are not similar in quality, suppose first \n\u003cA NAME=\"952\"\u003e\u003c/A\u003ethat the negative premiss is necessary, and let necessarily A not be possible \n\u003cA NAME=\"953\"\u003e\u003c/A\u003efor any B, but let B be possible for all C. It is necessary then that A \n\u003cA NAME=\"954\"\u003e\u003c/A\u003ebelongs to no C. For suppose A to belong to all C or to some C. Now we \n\u003cA NAME=\"955\"\u003e\u003c/A\u003eassumed that A is not possible for any B. Since then the negative proposition \n\u003cA NAME=\"956\"\u003e\u003c/A\u003eis convertible, B is not possible for any A. But A is supposed to belong \n\u003cA NAME=\"957\"\u003e\u003c/A\u003eto all C or to some C. Consequently B will not be possible for any C or \n\u003cA NAME=\"958\"\u003e\u003c/A\u003efor all C. But it was originally laid down that B is possible for all C. \n\u003cA NAME=\"959\"\u003e\u003c/A\u003eAnd it is clear that the possibility of belonging can be inferred, since \n\u003cA NAME=\"960\"\u003e\u003c/A\u003ethe fact of not belonging is inferred. Again, let the affirmative premiss \n\u003cA NAME=\"961\"\u003e\u003c/A\u003ebe necessary, and let A possibly not belong to any B, and let B necessarily \n\u003cA NAME=\"962\"\u003e\u003c/A\u003ebelong to all C. The syllogism will be perfect, but it will establish a \n\u003cA NAME=\"963\"\u003e\u003c/A\u003eproblematic negative, not an assertoric negative. For the major premiss \n\u003cA NAME=\"964\"\u003e\u003c/A\u003ewas problematic, and further it is not possible to prove the assertoric \n\u003cA NAME=\"965\"\u003e\u003c/A\u003econclusion per impossibile. For if it were supposed that A belongs to some \n\u003cA NAME=\"966\"\u003e\u003c/A\u003eC, and it is laid down that A possibly does not belong to any B, no impossible \n\u003cA NAME=\"967\"\u003e\u003c/A\u003erelation between B and C follows from these premisses. But if the minor \n\u003cA NAME=\"968\"\u003e\u003c/A\u003epremiss is negative, when it is problematic a syllogism is possible by \n\u003cA NAME=\"969\"\u003e\u003c/A\u003econversion, as above; but when it is necessary no syllogism can be formed. \n\u003cA NAME=\"970\"\u003e\u003c/A\u003eNor again when both premisses are negative, and the minor is necessary. \n\u003cA NAME=\"971\"\u003e\u003c/A\u003eThe same terms as before serve both for the positive relation-white-animal-snow, \n\u003cA NAME=\"972\"\u003e\u003c/A\u003eand for the negative relation-white-animal-pitch.\n\u003cA NAME=\"973\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThe same relation will obtain in particular syllogisms. Whenever \n\u003cA NAME=\"974\"\u003e\u003c/A\u003ethe negative proposition is necessary, the conclusion will be negative \n\u003cA NAME=\"975\"\u003e\u003c/A\u003eassertoric: e.g. if it is not possible that A should belong to any B, but \n\u003cA NAME=\"976\"\u003e\u003c/A\u003eB may belong to some of the Cs, it is necessary that A should not belong \n\u003cA NAME=\"977\"\u003e\u003c/A\u003eto some of the Cs. For if A belongs to all C, but cannot belong to any \n\u003cA NAME=\"978\"\u003e\u003c/A\u003eB, neither can B belong to any A. So if A belongs to all C, to none of \n\u003cA NAME=\"979\"\u003e\u003c/A\u003ethe Cs can B belong. But it was laid down that B may belong to some C. \n\u003cA NAME=\"980\"\u003e\u003c/A\u003eBut when the particular affirmative in the negative syllogism, e.g. BC \n\u003cA NAME=\"981\"\u003e\u003c/A\u003ethe minor premiss, or the universal proposition in the affirmative syllogism, \n\u003cA NAME=\"982\"\u003e\u003c/A\u003ee.g. AB the major premiss, is necessary, there will not be an assertoric \n\u003cA NAME=\"983\"\u003e\u003c/A\u003econclusion. The demonstration is the same as before. But if the minor premiss \n\u003cA NAME=\"984\"\u003e\u003c/A\u003eis universal, and problematic, whether affirmative or negative, and the \n\u003cA NAME=\"985\"\u003e\u003c/A\u003emajor premiss is particular and necessary, there cannot be a syllogism. \n\u003cA NAME=\"986\"\u003e\u003c/A\u003ePremisses of this kind are possible both where the relation is positive \n\u003cA NAME=\"987\"\u003e\u003c/A\u003eand necessary, e.g. animal-white-man, and where it is necessary and negative, \n\u003cA NAME=\"988\"\u003e\u003c/A\u003ee.g. animal-white-garment. But when the universal is necessary, the particular \n\u003cA NAME=\"989\"\u003e\u003c/A\u003eproblematic, if the universal is negative we may take the terms animal-white-raven \n\u003cA NAME=\"990\"\u003e\u003c/A\u003eto illustrate the positive relation, or animal-white-pitch to illustrate \n\u003cA NAME=\"991\"\u003e\u003c/A\u003ethe negative; and if the universal is affirmative we may take the terms \n\u003cA NAME=\"992\"\u003e\u003c/A\u003eanimal-white-swan to illustrate the positive relation, and animal-white-snow \n\u003cA NAME=\"993\"\u003e\u003c/A\u003eto illustrate the negative and necessary relation. Nor again is a syllogism \n\u003cA NAME=\"994\"\u003e\u003c/A\u003epossible when the premisses are indefinite, or both particular. Terms applicable \n\u003cA NAME=\"995\"\u003e\u003c/A\u003ein either case to illustrate the positive relation are animal-white-man: \n\u003cA NAME=\"996\"\u003e\u003c/A\u003eto illustrate the negative, animal-white-inanimate. For the relation of \n\u003cA NAME=\"997\"\u003e\u003c/A\u003eanimal to some white, and of white to some inanimate, is both necessary \n\u003cA NAME=\"998\"\u003e\u003c/A\u003eand positive and necessary and negative. Similarly if the relation is problematic: \n\u003cA NAME=\"999\"\u003e\u003c/A\u003eso the terms may be used for all cases.\n\u003cA NAME=\"1000\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eClearly then from what has been said a syllogism results or not \n\u003cA NAME=\"1001\"\u003e\u003c/A\u003efrom similar relations of the terms whether we are dealing with simple \n\u003cA NAME=\"1002\"\u003e\u003c/A\u003eexistence or necessity, with this exception, that if the negative premiss \n\u003cA NAME=\"1003\"\u003e\u003c/A\u003eis assertoric the conclusion is problematic, but if the negative premiss \n\u003cA NAME=\"1004\"\u003e\u003c/A\u003eis necessary the conclusion is both problematic and negative assertoric. \n\u003cA NAME=\"1005\"\u003e\u003c/A\u003e[It is clear also that all the syllogisms are imperfect and are perfected \n\u003cA NAME=\"1006\"\u003e\u003c/A\u003eby means of the figures above mentioned.]\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"1007\"\u003e\u003c/A\u003e\u003cB\u003ePart 17\u003c/B\u003e\n\n\u003cA NAME=\"1008\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIn the second figure whenever both premisses are problematic, no \n\u003cA NAME=\"1009\"\u003e\u003c/A\u003esyllogism is possible, whether the premisses are affirmative or negative, \n\u003cA NAME=\"1010\"\u003e\u003c/A\u003euniversal or particular. But when one premiss is assertoric, the other \n\u003cA NAME=\"1011\"\u003e\u003c/A\u003eproblematic, if the affirmative is assertoric no syllogism is possible, \n\u003cA NAME=\"1012\"\u003e\u003c/A\u003ebut if the universal negative is assertoric a conclusion can always be \n\u003cA NAME=\"1013\"\u003e\u003c/A\u003edrawn. Similarly when one premiss is necessary, the other problematic. \n\u003cA NAME=\"1014\"\u003e\u003c/A\u003eHere also we must understand the term \u0027possible\u0027 in the conclusion, in \n\u003cA NAME=\"1015\"\u003e\u003c/A\u003ethe same sense as before.\n\u003cA NAME=\"1016\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eFirst we must point out that the negative problematic proposition \n\u003cA NAME=\"1017\"\u003e\u003c/A\u003eis not convertible, e.g. if A may belong to no B, it does not follow that \n\u003cA NAME=\"1018\"\u003e\u003c/A\u003eB may belong to no A. For suppose it to follow and assume that B may belong \n\u003cA NAME=\"1019\"\u003e\u003c/A\u003eto no A. Since then problematic affirmations are convertible with negations, \n\u003cA NAME=\"1020\"\u003e\u003c/A\u003ewhether they are contraries or contradictories, and since B may belong \n\u003cA NAME=\"1021\"\u003e\u003c/A\u003eto no A, it is clear that B may belong to all A. But this is false: for \n\u003cA NAME=\"1022\"\u003e\u003c/A\u003eif all this can be that, it does not follow that all that can be this: \n\u003cA NAME=\"1023\"\u003e\u003c/A\u003econsequently the negative proposition is not convertible. Further, these \n\u003cA NAME=\"1024\"\u003e\u003c/A\u003epropositions are not incompatible, \u0027A may belong to no B\u0027, \u0027B necessarily \n\u003cA NAME=\"1025\"\u003e\u003c/A\u003edoes not belong to some of the As\u0027; e.g. it is possible that no man should \n\u003cA NAME=\"1026\"\u003e\u003c/A\u003ebe white (for it is also possible that every man should be white), but \n\u003cA NAME=\"1027\"\u003e\u003c/A\u003eit is not true to say that it is possible that no white thing should be \n\u003cA NAME=\"1028\"\u003e\u003c/A\u003ea man: for many white things are necessarily not men, and the necessary \n\u003cA NAME=\"1029\"\u003e\u003c/A\u003e(as we saw) other than the possible.\n\u003cA NAME=\"1030\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eMoreover it is not possible to prove the convertibility of these \n\u003cA NAME=\"1031\"\u003e\u003c/A\u003epropositions by a reductio ad absurdum, i.e. by claiming assent to the \n\u003cA NAME=\"1032\"\u003e\u003c/A\u003efollowing argument: \u0027since it is false that B may belong to no A, it is \n\u003cA NAME=\"1033\"\u003e\u003c/A\u003etrue that it cannot belong to no A, for the one statement is the contradictory \n\u003cA NAME=\"1034\"\u003e\u003c/A\u003eof the other. But if this is so, it is true that B necessarily belongs \n\u003cA NAME=\"1035\"\u003e\u003c/A\u003eto some of the As: consequently A necessarily belongs to some of the Bs. \n\u003cA NAME=\"1036\"\u003e\u003c/A\u003eBut this is impossible.\u0027 The argument cannot be admitted, for it does not \n\u003cA NAME=\"1037\"\u003e\u003c/A\u003efollow that some A is necessarily B, if it is not possible that no A should \n\u003cA NAME=\"1038\"\u003e\u003c/A\u003ebe B. For the latter expression is used in two senses, one if A some is \n\u003cA NAME=\"1039\"\u003e\u003c/A\u003enecessarily B, another if some A is necessarily not B. For it is not true \n\u003cA NAME=\"1040\"\u003e\u003c/A\u003eto say that that which necessarily does not belong to some of the As may \n\u003cA NAME=\"1041\"\u003e\u003c/A\u003epossibly not belong to any A, just as it is not true to say that what necessarily \n\u003cA NAME=\"1042\"\u003e\u003c/A\u003ebelongs to some A may possibly belong to all A. If any one then should \n\u003cA NAME=\"1043\"\u003e\u003c/A\u003eclaim that because it is not possible for C to belong to all D, it necessarily \n\u003cA NAME=\"1044\"\u003e\u003c/A\u003edoes not belong to some D, he would make a false assumption: for it does \n\u003cA NAME=\"1045\"\u003e\u003c/A\u003ebelong to all D, but because in some cases it belongs necessarily, therefore \n\u003cA NAME=\"1046\"\u003e\u003c/A\u003ewe say that it is not possible for it to belong to all. Hence both the \n\u003cA NAME=\"1047\"\u003e\u003c/A\u003epropositions \u0027A necessarily belongs to some B\u0027 and \u0027A necessarily does \n\u003cA NAME=\"1048\"\u003e\u003c/A\u003enot belong to some B\u0027 are opposed to the proposition \u0027A belongs to all \n\u003cA NAME=\"1049\"\u003e\u003c/A\u003eB\u0027. Similarly also they are opposed to the proposition \u0027A may belong to \n\u003cA NAME=\"1050\"\u003e\u003c/A\u003eno B\u0027. It is clear then that in relation to what is possible and not possible, \n\u003cA NAME=\"1051\"\u003e\u003c/A\u003ein the sense originally defined, we must assume, not that A necessarily \n\u003cA NAME=\"1052\"\u003e\u003c/A\u003ebelongs to some B, but that A necessarily does not belong to some B. But \n\u003cA NAME=\"1053\"\u003e\u003c/A\u003eif this is assumed, no absurdity results: consequently no syllogism. It \n\u003cA NAME=\"1054\"\u003e\u003c/A\u003eis clear from what has been said that the negative proposition is not \n\u003cA NAME=\"1055\"\u003e\u003c/A\u003econvertible.\n\u003cA NAME=\"1056\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThis being proved, suppose it possible that A may belong to no \n\u003cA NAME=\"1057\"\u003e\u003c/A\u003eB and to all C. By means of conversion no syllogism will result: for the \n\u003cA NAME=\"1058\"\u003e\u003c/A\u003emajor premiss, as has been said, is not convertible. Nor can a proof be \n\u003cA NAME=\"1059\"\u003e\u003c/A\u003eobtained by a reductio ad absurdum: for if it is assumed that B can belong \n\u003cA NAME=\"1060\"\u003e\u003c/A\u003eto all C, no false consequence results: for A may belong both to all C \n\u003cA NAME=\"1061\"\u003e\u003c/A\u003eand to no C. In general, if there is a syllogism, it is clear that its \n\u003cA NAME=\"1062\"\u003e\u003c/A\u003econclusion will be problematic because neither of the premisses is assertoric; \n\u003cA NAME=\"1063\"\u003e\u003c/A\u003eand this must be either affirmative or negative. But neither is possible. \n\u003cA NAME=\"1064\"\u003e\u003c/A\u003eSuppose the conclusion is affirmative: it will be proved by an example \n\u003cA NAME=\"1065\"\u003e\u003c/A\u003ethat the predicate cannot belong to the subject. Suppose the conclusion \n\u003cA NAME=\"1066\"\u003e\u003c/A\u003eis negative: it will be proved that it is not problematic but necessary. \n\u003cA NAME=\"1067\"\u003e\u003c/A\u003eLet A be white, B man, C horse. It is possible then for A to belong to \n\u003cA NAME=\"1068\"\u003e\u003c/A\u003eall of the one and to none of the other. But it is not possible for B to \n\u003cA NAME=\"1069\"\u003e\u003c/A\u003ebelong nor not to belong to C. That it is not possible for it to belong, \n\u003cA NAME=\"1070\"\u003e\u003c/A\u003eis clear. For no horse is a man. Neither is it possible for it not to belong. \n\u003cA NAME=\"1071\"\u003e\u003c/A\u003eFor it is necessary that no horse should be a man, but the necessary we \n\u003cA NAME=\"1072\"\u003e\u003c/A\u003efound to be different from the possible. No syllogism then results. A similar \n\u003cA NAME=\"1073\"\u003e\u003c/A\u003eproof can be given if the major premiss is negative, the minor affirmative, \n\u003cA NAME=\"1074\"\u003e\u003c/A\u003eor if both are affirmative or negative. The demonstration can be made by \n\u003cA NAME=\"1075\"\u003e\u003c/A\u003emeans of the same terms. And whenever one premiss is universal, the other \n\u003cA NAME=\"1076\"\u003e\u003c/A\u003eparticular, or both are particular or indefinite, or in whatever other \n\u003cA NAME=\"1077\"\u003e\u003c/A\u003eway the premisses can be altered, the proof will always proceed through \n\u003cA NAME=\"1078\"\u003e\u003c/A\u003ethe same terms. Clearly then, if both the premisses are problematic, no \n\u003cA NAME=\"1079\"\u003e\u003c/A\u003esyllogism results.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"1080\"\u003e\u003c/A\u003e\u003cB\u003ePart 18\u003c/B\u003e\n\n\u003cA NAME=\"1081\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eBut if one premiss is assertoric, the other problematic, if the \n\u003cA NAME=\"1082\"\u003e\u003c/A\u003eaffirmative is assertoric and the negative problematic no syllogism will \n\u003cA NAME=\"1083\"\u003e\u003c/A\u003ebe possible, whether the premisses are universal or particular. The proof \n\u003cA NAME=\"1084\"\u003e\u003c/A\u003eis the same as above, and by means of the same terms. But when the affirmative \n\u003cA NAME=\"1085\"\u003e\u003c/A\u003epremiss is problematic, and the negative assertoric, we shall have a syllogism. \n\u003cA NAME=\"1086\"\u003e\u003c/A\u003eSuppose A belongs to no B, but can belong to all C. If the negative proposition \n\u003cA NAME=\"1087\"\u003e\u003c/A\u003eis converted, B will belong to no A. But ex hypothesi can belong to all \n\u003cA NAME=\"1088\"\u003e\u003c/A\u003eC: so a syllogism is made, proving by means of the first figure that B \n\u003cA NAME=\"1089\"\u003e\u003c/A\u003emay belong to no C. Similarly also if the minor premiss is negative. But \n\u003cA NAME=\"1090\"\u003e\u003c/A\u003eif both premisses are negative, one being assertoric, the other problematic, \n\u003cA NAME=\"1091\"\u003e\u003c/A\u003enothing follows necessarily from these premisses as they stand, but if \n\u003cA NAME=\"1092\"\u003e\u003c/A\u003ethe problematic premiss is converted into its complementary affirmative \n\u003cA NAME=\"1093\"\u003e\u003c/A\u003ea syllogism is formed to prove that B may belong to no C, as before: for \n\u003cA NAME=\"1094\"\u003e\u003c/A\u003ewe shall again have the first figure. But if both premisses are affirmative, \n\u003cA NAME=\"1095\"\u003e\u003c/A\u003eno syllogism will be possible. This arrangement of terms is possible both \n\u003cA NAME=\"1096\"\u003e\u003c/A\u003ewhen the relation is positive, e.g. health, animal, man, and when it is \n\u003cA NAME=\"1097\"\u003e\u003c/A\u003enegative, e.g. health, horse, man.\n\u003cA NAME=\"1098\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThe same will hold good if the syllogisms are particular. Whenever \n\u003cA NAME=\"1099\"\u003e\u003c/A\u003ethe affirmative proposition is assertoric, whether universal or particular, \n\u003cA NAME=\"1100\"\u003e\u003c/A\u003eno syllogism is possible (this is proved similarly and by the same examples \n\u003cA NAME=\"1101\"\u003e\u003c/A\u003eas above), but when the negative proposition is assertoric, a conclusion \n\u003cA NAME=\"1102\"\u003e\u003c/A\u003ecan be drawn by means of conversion, as before. Again if both the relations \n\u003cA NAME=\"1103\"\u003e\u003c/A\u003eare negative, and the assertoric proposition is universal, although no \n\u003cA NAME=\"1104\"\u003e\u003c/A\u003econclusion follows from the actual premisses, a syllogism can\r\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.prior; expires=1-Jan-102 00:00:00 GMT; path=/\"\u003e\n\u003cMETA NAME=\"description\" CONTENT=\"Prior 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, Prior Analytics, Aristotle, Aristotle\"\u003e\n\u003cTITLE\u003eThe Internet Classics Archive | Prior 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\u003ePrior 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\u003ePrior Analytics\u003c/U\u003e.\n\n\u003cBR\u003e\u003cBR\u003e\u003cB\u003eDownload:\u003c/B\u003e A \ntext-only version is \u003cA HREF=\"prior.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\u003ePrior 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 A. J. Jenkinson\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=\"prior.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=\"prior.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\u003eWe have already explained the number of the figures, the character and \n\u003cA NAME=\"12\"\u003e\u003c/A\u003enumber of the premisses, when and how a syllogism is formed; further what \n\u003cA NAME=\"13\"\u003e\u003c/A\u003ewe must look for when a refuting and establishing propositions, and how \n\u003cA NAME=\"14\"\u003e\u003c/A\u003ewe should investigate a given problem in any branch of inquiry, also by \n\u003cA NAME=\"15\"\u003e\u003c/A\u003ewhat means we shall obtain principles appropriate to each subject. Since \n\u003cA NAME=\"16\"\u003e\u003c/A\u003esome syllogisms are universal, others particular, all the universal syllogisms \n\u003cA NAME=\"17\"\u003e\u003c/A\u003egive more than one result, and of particular syllogisms the affirmative \n\u003cA NAME=\"18\"\u003e\u003c/A\u003eyield more than one, the negative yield only the stated conclusion. For \n\u003cA NAME=\"19\"\u003e\u003c/A\u003eall propositions are convertible save only the particular negative: and \n\u003cA NAME=\"20\"\u003e\u003c/A\u003ethe conclusion states one definite thing about another definite thing. \n\u003cA NAME=\"21\"\u003e\u003c/A\u003eConsequently all syllogisms save the particular negative yield more than \n\u003cA NAME=\"22\"\u003e\u003c/A\u003eone conclusion, e.g. if A has been proved to to all or to some B, then \n\u003cA NAME=\"23\"\u003e\u003c/A\u003eB must belong to some A: and if A has been proved to belong to no B, then \n\u003cA NAME=\"24\"\u003e\u003c/A\u003eB belongs to no A. This is a different conclusion from the former. But \n\u003cA NAME=\"25\"\u003e\u003c/A\u003eif A does not belong to some B, it is not necessary that B should not belong \n\u003cA NAME=\"26\"\u003e\u003c/A\u003eto some A: for it may possibly belong to all A.\n\u003cA NAME=\"27\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThis then is the reason common to all syllogisms whether universal \n\u003cA NAME=\"28\"\u003e\u003c/A\u003eor particular. But it is possible to give another reason concerning those \n\u003cA NAME=\"29\"\u003e\u003c/A\u003ewhich are universal. For all the things that are subordinate to the middle \n\u003cA NAME=\"30\"\u003e\u003c/A\u003eterm or to the conclusion may be proved by the same syllogism, if the former \n\u003cA NAME=\"31\"\u003e\u003c/A\u003eare placed in the middle, the latter in the conclusion; e.g. if the conclusion \n\u003cA NAME=\"32\"\u003e\u003c/A\u003eAB is proved through C, whatever is subordinate to B or C must accept the \n\u003cA NAME=\"33\"\u003e\u003c/A\u003epredicate A: for if D is included in B as in a whole, and B is included \n\u003cA NAME=\"34\"\u003e\u003c/A\u003ein A, then D will be included in A. Again if E is included in C as in a \n\u003cA NAME=\"35\"\u003e\u003c/A\u003ewhole, and C is included in A, then E will be included in A. Similarly \n\u003cA NAME=\"36\"\u003e\u003c/A\u003eif the syllogism is negative. In the second figure it will be possible \n\u003cA NAME=\"37\"\u003e\u003c/A\u003eto infer only that which is subordinate to the conclusion, e.g. if A belongs \n\u003cA NAME=\"38\"\u003e\u003c/A\u003eto no B and to all C; we conclude that B belongs to no C. If then D is \n\u003cA NAME=\"39\"\u003e\u003c/A\u003esubordinate to C, clearly B does not belong to it. But that B does not \n\u003cA NAME=\"40\"\u003e\u003c/A\u003ebelong to what is subordinate to A is not clear by means of the syllogism. \n\u003cA NAME=\"41\"\u003e\u003c/A\u003eAnd yet B does not belong to E, if E is subordinate to A. But while it \n\u003cA NAME=\"42\"\u003e\u003c/A\u003ehas been proved through the syllogism that B belongs to no C, it has been \n\u003cA NAME=\"43\"\u003e\u003c/A\u003eassumed without proof that B does not belong to A, consequently it does \n\u003cA NAME=\"44\"\u003e\u003c/A\u003enot result through the syllogism that B does not belong to \n\u003cA NAME=\"45\"\u003e\u003c/A\u003eE.\n\u003cA NAME=\"46\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eBut in particular syllogisms there will be no necessity of inferring \n\u003cA NAME=\"47\"\u003e\u003c/A\u003ewhat is subordinate to the conclusion (for a syllogism does not result \n\u003cA NAME=\"48\"\u003e\u003c/A\u003ewhen this premiss is particular), but whatever is subordinate to the middle \n\u003cA NAME=\"49\"\u003e\u003c/A\u003eterm may be inferred, not however through the syllogism, e.g. if A belongs \n\u003cA NAME=\"50\"\u003e\u003c/A\u003eto all B and B to some C. Nothing can be inferred about that which is subordinate \n\u003cA NAME=\"51\"\u003e\u003c/A\u003eto C; something can be inferred about that which is subordinate to B, but \n\u003cA NAME=\"52\"\u003e\u003c/A\u003enot through the preceding syllogism. Similarly in the other figures. That \n\u003cA NAME=\"53\"\u003e\u003c/A\u003ewhich is subordinate to the conclusion cannot be proved; the other subordinate \n\u003cA NAME=\"54\"\u003e\u003c/A\u003ecan be proved, only not through the syllogism, just as in the universal \n\u003cA NAME=\"55\"\u003e\u003c/A\u003esyllogisms what is subordinate to the middle term is proved (as we saw) \n\u003cA NAME=\"56\"\u003e\u003c/A\u003efrom a premiss which is not demonstrated: consequently either a conclusion \n\u003cA NAME=\"57\"\u003e\u003c/A\u003eis not possible in the case of universal syllogisms or else it is possible \n\u003cA NAME=\"58\"\u003e\u003c/A\u003ealso in the case of particular syllogisms.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"59\"\u003e\u003c/A\u003e\u003cB\u003ePart 2\u003c/B\u003e\n\n\u003cA NAME=\"60\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is possible for the premisses of the syllogism to be true, or \n\u003cA NAME=\"61\"\u003e\u003c/A\u003eto be false, or to be the one true, the other false. The conclusion is \n\u003cA NAME=\"62\"\u003e\u003c/A\u003eeither true or false necessarily. From true premisses it is not possible \n\u003cA NAME=\"63\"\u003e\u003c/A\u003eto draw a false conclusion, but a true conclusion may be drawn from false \n\u003cA NAME=\"64\"\u003e\u003c/A\u003epremisses, true however only in respect to the fact, not to the reason. \n\u003cA NAME=\"65\"\u003e\u003c/A\u003eThe reason cannot be established from false premisses: why this is so will \n\u003cA NAME=\"66\"\u003e\u003c/A\u003ebe explained in the sequel.\n\u003cA NAME=\"67\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eFirst then that it is not possible to draw a false conclusion from \n\u003cA NAME=\"68\"\u003e\u003c/A\u003etrue premisses, is made clear by this consideration. If it is necessary \n\u003cA NAME=\"69\"\u003e\u003c/A\u003ethat B should be when A is, it is necessary that A should not be when B \n\u003cA NAME=\"70\"\u003e\u003c/A\u003eis not. If then A is true, B must be true: otherwise it will turn out that \n\u003cA NAME=\"71\"\u003e\u003c/A\u003ethe same thing both is and is not at the same time. But this is impossible. \n\u003cA NAME=\"72\"\u003e\u003c/A\u003eLet it not, because A is laid down as a single term, be supposed that it \n\u003cA NAME=\"73\"\u003e\u003c/A\u003eis possible, when a single fact is given, that something should necessarily \n\u003cA NAME=\"74\"\u003e\u003c/A\u003eresult. For that is not possible. For what results necessarily is the conclusion, \n\u003cA NAME=\"75\"\u003e\u003c/A\u003eand the means by which this comes about are at the least three terms, and \n\u003cA NAME=\"76\"\u003e\u003c/A\u003etwo relations of subject and predicate or premisses. If then it is true \n\u003cA NAME=\"77\"\u003e\u003c/A\u003ethat A belongs to all that to which B belongs, and that B belongs to all \n\u003cA NAME=\"78\"\u003e\u003c/A\u003ethat to which C belongs, it is necessary that A should belong to all that \n\u003cA NAME=\"79\"\u003e\u003c/A\u003eto which C belongs, and this cannot be false: for then the same thing will \n\u003cA NAME=\"80\"\u003e\u003c/A\u003ebelong and not belong at the same time. So A is posited as one thing, being \n\u003cA NAME=\"81\"\u003e\u003c/A\u003etwo premisses taken together. The same holds good of negative syllogisms: \n\u003cA NAME=\"82\"\u003e\u003c/A\u003eit is not possible to prove a false conclusion from true \n\u003cA NAME=\"83\"\u003e\u003c/A\u003epremisses.\n\u003cA NAME=\"84\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eBut from what is false a true conclusion may be drawn, whether \n\u003cA NAME=\"85\"\u003e\u003c/A\u003eboth the premisses are false or only one, provided that this is not either \n\u003cA NAME=\"86\"\u003e\u003c/A\u003eof the premisses indifferently, if it is taken as wholly false: but if \n\u003cA NAME=\"87\"\u003e\u003c/A\u003ethe premiss is not taken as wholly false, it does not matter which of the \n\u003cA NAME=\"88\"\u003e\u003c/A\u003etwo is false. (1) Let A belong to the whole of C, but to none of the Bs, \n\u003cA NAME=\"89\"\u003e\u003c/A\u003eneither let B belong to C. This is possible, e.g. animal belongs to no \n\u003cA NAME=\"90\"\u003e\u003c/A\u003estone, nor stone to any man. If then A is taken to belong to all B and \n\u003cA NAME=\"91\"\u003e\u003c/A\u003eB to all C, A will belong to all C; consequently though both the premisses \n\u003cA NAME=\"92\"\u003e\u003c/A\u003eare false the conclusion is true: for every man is an animal. Similarly \n\u003cA NAME=\"93\"\u003e\u003c/A\u003ewith the negative. For it is possible that neither A nor B should belong \n\u003cA NAME=\"94\"\u003e\u003c/A\u003eto any C, although A belongs to all B, e.g. if the same terms are taken \n\u003cA NAME=\"95\"\u003e\u003c/A\u003eand man is put as middle: for neither animal nor man belongs to any stone, \n\u003cA NAME=\"96\"\u003e\u003c/A\u003ebut animal belongs to every man. Consequently if one term is taken to belong \n\u003cA NAME=\"97\"\u003e\u003c/A\u003eto none of that to which it does belong, and the other term is taken to \n\u003cA NAME=\"98\"\u003e\u003c/A\u003ebelong to all of that to which it does not belong, though both the premisses \n\u003cA NAME=\"99\"\u003e\u003c/A\u003eare false the conclusion will be true. (2) A similar proof may be given \n\u003cA NAME=\"100\"\u003e\u003c/A\u003eif each premiss is partially false.\n\u003cA NAME=\"101\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003e(3) But if one only of the premisses is false, when the first premiss \n\u003cA NAME=\"102\"\u003e\u003c/A\u003eis wholly false, e.g. AB, the conclusion will not be true, but if the premiss \n\u003cA NAME=\"103\"\u003e\u003c/A\u003eBC is wholly false, a true conclusion will be possible. I mean by \u0027wholly \n\u003cA NAME=\"104\"\u003e\u003c/A\u003efalse\u0027 the contrary of the truth, e.g. if what belongs to none is assumed \n\u003cA NAME=\"105\"\u003e\u003c/A\u003eto belong to all, or if what belongs to all is assumed to belong to none. \n\u003cA NAME=\"106\"\u003e\u003c/A\u003eLet A belong to no B, and B to all C. If then the premiss BC which I take \n\u003cA NAME=\"107\"\u003e\u003c/A\u003eis true, and the premiss AB is wholly false, viz. that A belongs to all \n\u003cA NAME=\"108\"\u003e\u003c/A\u003eB, it is impossible that the conclusion should be true: for A belonged \n\u003cA NAME=\"109\"\u003e\u003c/A\u003eto none of the Cs, since A belonged to nothing to which B belonged, and \n\u003cA NAME=\"110\"\u003e\u003c/A\u003eB belonged to all C. Similarly there cannot be a true conclusion if A belongs \n\u003cA NAME=\"111\"\u003e\u003c/A\u003eto all B, and B to all C, but while the true premiss BC is assumed, the \n\u003cA NAME=\"112\"\u003e\u003c/A\u003ewholly false premiss AB is also assumed, viz. that A belongs to nothing \n\u003cA NAME=\"113\"\u003e\u003c/A\u003eto which B belongs: here the conclusion must be false. For A will belong \n\u003cA NAME=\"114\"\u003e\u003c/A\u003eto all C, since A belongs to everything to which B belongs, and B to all \n\u003cA NAME=\"115\"\u003e\u003c/A\u003eC. It is clear then that when the first premiss is wholly false, whether \n\u003cA NAME=\"116\"\u003e\u003c/A\u003eaffirmative or negative, and the other premiss is true, the conclusion \n\u003cA NAME=\"117\"\u003e\u003c/A\u003ecannot be true.\n\u003cA NAME=\"118\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003e(4) But if the premiss is not wholly false, a true conclusion is \n\u003cA NAME=\"119\"\u003e\u003c/A\u003epossible. For if A belongs to all C and to some B, and if B belongs to \n\u003cA NAME=\"120\"\u003e\u003c/A\u003eall C, e.g. animal to every swan and to some white thing, and white to \n\u003cA NAME=\"121\"\u003e\u003c/A\u003eevery swan, then if we take as premisses that A belongs to all B, and B \n\u003cA NAME=\"122\"\u003e\u003c/A\u003eto all C, A will belong to all C truly: for every swan is an animal. Similarly \n\u003cA NAME=\"123\"\u003e\u003c/A\u003eif the statement AB is negative. For it is possible that A should belong \n\u003cA NAME=\"124\"\u003e\u003c/A\u003eto some B and to no C, and that B should belong to all C, e.g. animal to \n\u003cA NAME=\"125\"\u003e\u003c/A\u003esome white thing, but to no snow, and white to all snow. If then one should \n\u003cA NAME=\"126\"\u003e\u003c/A\u003eassume that A belongs to no B, and B to all C, then will belong to no \n\u003cA NAME=\"127\"\u003e\u003c/A\u003eC.\n\u003cA NAME=\"128\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003e(5) But if the premiss AB, which is assumed, is wholly true, and \n\u003cA NAME=\"129\"\u003e\u003c/A\u003ethe premiss BC is wholly false, a true syllogism will be possible: for \n\u003cA NAME=\"130\"\u003e\u003c/A\u003enothing prevents A belonging to all B and to all C, though B belongs to \n\u003cA NAME=\"131\"\u003e\u003c/A\u003eno C, e.g. these being species of the same genus which are not subordinate \n\u003cA NAME=\"132\"\u003e\u003c/A\u003eone to the other: for animal belongs both to horse and to man, but horse \n\u003cA NAME=\"133\"\u003e\u003c/A\u003eto no man. If then it is assumed that A belongs to all B and B to all C, \n\u003cA NAME=\"134\"\u003e\u003c/A\u003ethe conclusion will be true, although the premiss BC is wholly false. Similarly \n\u003cA NAME=\"135\"\u003e\u003c/A\u003eif the premiss AB is negative. For it is possible that A should belong \n\u003cA NAME=\"136\"\u003e\u003c/A\u003eneither to any B nor to any C, and that B should not belong to any C, e.g. \n\u003cA NAME=\"137\"\u003e\u003c/A\u003ea genus to species of another genus: for animal belongs neither to music \n\u003cA NAME=\"138\"\u003e\u003c/A\u003enor to the art of healing, nor does music belong to the art of healing. \n\u003cA NAME=\"139\"\u003e\u003c/A\u003eIf then it is assumed that A belongs to no B, and B to all C, the conclusion \n\u003cA NAME=\"140\"\u003e\u003c/A\u003ewill be true.\n\u003cA NAME=\"141\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003e(6) And if the premiss BC is not wholly false but in part only, \n\u003cA NAME=\"142\"\u003e\u003c/A\u003eeven so the conclusion may be true. For nothing prevents A belonging to \n\u003cA NAME=\"143\"\u003e\u003c/A\u003ethe whole of B and of C, while B belongs to some C, e.g. a genus to its \n\u003cA NAME=\"144\"\u003e\u003c/A\u003especies and difference: for animal belongs to every man and to every footed \n\u003cA NAME=\"145\"\u003e\u003c/A\u003ething, and man to some footed things though not to all. If then it is assumed \n\u003cA NAME=\"146\"\u003e\u003c/A\u003ethat A belongs to all B, and B to all C, A will belong to all C: and this \n\u003cA NAME=\"147\"\u003e\u003c/A\u003eex hypothesi is true. Similarly if the premiss AB is negative. For it is \n\u003cA NAME=\"148\"\u003e\u003c/A\u003epossible that A should neither belong to any B nor to any C, though B belongs \n\u003cA NAME=\"149\"\u003e\u003c/A\u003eto some C, e.g. a genus to the species of another genus and its difference: \n\u003cA NAME=\"150\"\u003e\u003c/A\u003efor animal neither belongs to any wisdom nor to any instance of \u0027speculative\u0027, \n\u003cA NAME=\"151\"\u003e\u003c/A\u003ebut wisdom belongs to some instance of \u0027speculative\u0027. If then it should \n\u003cA NAME=\"152\"\u003e\u003c/A\u003ebe assumed that A belongs to no B, and B to all C, will belong to no C: \n\u003cA NAME=\"153\"\u003e\u003c/A\u003eand this ex hypothesi is true.\n\u003cA NAME=\"154\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIn particular syllogisms it is possible when the first premiss \n\u003cA NAME=\"155\"\u003e\u003c/A\u003eis wholly false, and the other true, that the conclusion should be true; \n\u003cA NAME=\"156\"\u003e\u003c/A\u003ealso when the first premiss is false in part, and the other true; and when \n\u003cA NAME=\"157\"\u003e\u003c/A\u003ethe first is true, and the particular is false; and when both are false. \n\u003cA NAME=\"158\"\u003e\u003c/A\u003e(7) For nothing prevents A belonging to no B, but to some C, and B to some \n\u003cA NAME=\"159\"\u003e\u003c/A\u003eC, e.g. animal belongs to no snow, but to some white thing, and snow to \n\u003cA NAME=\"160\"\u003e\u003c/A\u003esome white thing. If then snow is taken as middle, and animal as first \n\u003cA NAME=\"161\"\u003e\u003c/A\u003eterm, and it is assumed that A belongs to the whole of B, and B to some \n\u003cA NAME=\"162\"\u003e\u003c/A\u003eC, then the premiss BC is wholly false, the premiss BC true, and the conclusion \n\u003cA NAME=\"163\"\u003e\u003c/A\u003etrue. Similarly if the premiss AB is negative: for it is possible that \n\u003cA NAME=\"164\"\u003e\u003c/A\u003eA should belong to the whole of B, but not to some C, although B belongs \n\u003cA NAME=\"165\"\u003e\u003c/A\u003eto some C, e.g. animal belongs to every man, but does not follow some white, \n\u003cA NAME=\"166\"\u003e\u003c/A\u003ebut man belongs to some white; consequently if man be taken as middle term \n\u003cA NAME=\"167\"\u003e\u003c/A\u003eand it is assumed that A belongs to no B but B belongs to some C, the conclusion \n\u003cA NAME=\"168\"\u003e\u003c/A\u003ewill be true although the premiss AB is wholly false. (If the premiss AB \n\u003cA NAME=\"169\"\u003e\u003c/A\u003eis false in part, the conclusion may be true. For nothing prevents A belonging \n\u003cA NAME=\"170\"\u003e\u003c/A\u003eboth to B and to some C, and B belonging to some C, e.g. animal to something \n\u003cA NAME=\"171\"\u003e\u003c/A\u003ebeautiful and to something great, and beautiful belonging to something \n\u003cA NAME=\"172\"\u003e\u003c/A\u003egreat. If then A is assumed to belong to all B, and B to some C, the a \n\u003cA NAME=\"173\"\u003e\u003c/A\u003epremiss AB will be partially false, the premiss BC will be true, and the \n\u003cA NAME=\"174\"\u003e\u003c/A\u003econclusion true. Similarly if the premiss AB is negative. For the same \n\u003cA NAME=\"175\"\u003e\u003c/A\u003eterms will serve, and in the same positions, to prove the \n\u003cA NAME=\"176\"\u003e\u003c/A\u003epoint.\n\u003cA NAME=\"177\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003e(9) Again if the premiss AB is true, and the premiss BC is false, \n\u003cA NAME=\"178\"\u003e\u003c/A\u003ethe conclusion may be true. For nothing prevents A belonging to the whole \n\u003cA NAME=\"179\"\u003e\u003c/A\u003eof B and to some C, while B belongs to no C, e.g. animal to every swan \n\u003cA NAME=\"180\"\u003e\u003c/A\u003eand to some black things, though swan belongs to no black thing. Consequently \n\u003cA NAME=\"181\"\u003e\u003c/A\u003eif it should be assumed that A belongs to all B, and B to some C, the conclusion \n\u003cA NAME=\"182\"\u003e\u003c/A\u003ewill be true, although the statement Bc is false. Similarly if the premiss \n\u003cA NAME=\"183\"\u003e\u003c/A\u003eAB is negative. For it is possible that A should belong to no B, and not \n\u003cA NAME=\"184\"\u003e\u003c/A\u003eto some C, while B belongs to no C, e.g. a genus to the species of another \n\u003cA NAME=\"185\"\u003e\u003c/A\u003egenus and to the accident of its own species: for animal belongs to no \n\u003cA NAME=\"186\"\u003e\u003c/A\u003enumber and not to some white things, and number belongs to nothing white. \n\u003cA NAME=\"187\"\u003e\u003c/A\u003eIf then number is taken as middle, and it is assumed that A belongs to \n\u003cA NAME=\"188\"\u003e\u003c/A\u003eno B, and B to some C, then A will not belong to some C, which ex hypothesi \n\u003cA NAME=\"189\"\u003e\u003c/A\u003eis true. And the premiss AB is true, the premiss BC \n\u003cA NAME=\"190\"\u003e\u003c/A\u003efalse.\n\u003cA NAME=\"191\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003e(10) Also if the premiss AB is partially false, and the premiss \n\u003cA NAME=\"192\"\u003e\u003c/A\u003eBC is false too, the conclusion may be true. For nothing prevents A belonging \n\u003cA NAME=\"193\"\u003e\u003c/A\u003eto some B and to some C, though B belongs to no C, e.g. if B is the contrary \n\u003cA NAME=\"194\"\u003e\u003c/A\u003eof C, and both are accidents of the same genus: for animal belongs to some \n\u003cA NAME=\"195\"\u003e\u003c/A\u003ewhite things and to some black things, but white belongs to no black thing. \n\u003cA NAME=\"196\"\u003e\u003c/A\u003eIf then it is assumed that A belongs to all B, and B to some C, the conclusion \n\u003cA NAME=\"197\"\u003e\u003c/A\u003ewill be true. Similarly if the premiss AB is negative: for the same terms \n\u003cA NAME=\"198\"\u003e\u003c/A\u003earranged in the same way will serve for the proof.\n\u003cA NAME=\"199\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003e(11) Also though both premisses are false the conclusion may be \n\u003cA NAME=\"200\"\u003e\u003c/A\u003etrue. For it is possible that A may belong to no B and to some C, while \n\u003cA NAME=\"201\"\u003e\u003c/A\u003eB belongs to no C, e.g. a genus in relation to the species of another genus, \n\u003cA NAME=\"202\"\u003e\u003c/A\u003eand to the accident of its own species: for animal belongs to no number, \n\u003cA NAME=\"203\"\u003e\u003c/A\u003ebut to some white things, and number to nothing white. If then it is assumed \n\u003cA NAME=\"204\"\u003e\u003c/A\u003ethat A belongs to all B and B to some C, the conclusion will be true, though \n\u003cA NAME=\"205\"\u003e\u003c/A\u003eboth premisses are false. Similarly also if the premiss AB is negative. \n\u003cA NAME=\"206\"\u003e\u003c/A\u003eFor nothing prevents A belonging to the whole of B, and not to some C, \n\u003cA NAME=\"207\"\u003e\u003c/A\u003ewhile B belongs to no C, e.g. animal belongs to every swan, and not to \n\u003cA NAME=\"208\"\u003e\u003c/A\u003esome black things, and swan belongs to nothing black. Consequently if it \n\u003cA NAME=\"209\"\u003e\u003c/A\u003eis assumed that A belongs to no B, and B to some C, then A does not belong \n\u003cA NAME=\"210\"\u003e\u003c/A\u003eto some C. The conclusion then is true, but the premisses arc \n\u003cA NAME=\"211\"\u003e\u003c/A\u003efalse.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"212\"\u003e\u003c/A\u003e\u003cB\u003ePart 3\u003c/B\u003e\n\n\u003cA NAME=\"213\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIn the middle figure it is possible in every way to reach a true \n\u003cA NAME=\"214\"\u003e\u003c/A\u003econclusion through false premisses, whether the syllogisms are universal \n\u003cA NAME=\"215\"\u003e\u003c/A\u003eor particular, viz. when both premisses are wholly false; when each is \n\u003cA NAME=\"216\"\u003e\u003c/A\u003epartially false; when one is true, the other wholly false (it does not \n\u003cA NAME=\"217\"\u003e\u003c/A\u003ematter which of the two premisses is false); if both premisses are partially \n\u003cA NAME=\"218\"\u003e\u003c/A\u003efalse; if one is quite true, the other partially false; if one is wholly \n\u003cA NAME=\"219\"\u003e\u003c/A\u003efalse, the other partially true. For (1) if A belongs to no B and to all \n\u003cA NAME=\"220\"\u003e\u003c/A\u003eC, e.g. animal to no stone and to every horse, then if the premisses are \n\u003cA NAME=\"221\"\u003e\u003c/A\u003estated contrariwise and it is assumed that A belongs to all B and to no \n\u003cA NAME=\"222\"\u003e\u003c/A\u003eC, though the premisses are wholly false they will yield a true conclusion. \n\u003cA NAME=\"223\"\u003e\u003c/A\u003eSimilarly if A belongs to all B and to no C: for we shall have the same \n\u003cA NAME=\"224\"\u003e\u003c/A\u003esyllogism.\n\u003cA NAME=\"225\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003e(2) Again if one premiss is wholly false, the other wholly true: \n\u003cA NAME=\"226\"\u003e\u003c/A\u003efor nothing prevents A belonging to all B and to all C, though B belongs \n\u003cA NAME=\"227\"\u003e\u003c/A\u003eto no C, e.g. a genus to its co-ordinate species. For animal belongs to \n\u003cA NAME=\"228\"\u003e\u003c/A\u003eevery horse and man, and no man is a horse. If then it is assumed that \n\u003cA NAME=\"229\"\u003e\u003c/A\u003eanimal belongs to all of the one, and none of the other, the one premiss \n\u003cA NAME=\"230\"\u003e\u003c/A\u003ewill be wholly false, the other wholly true, and the conclusion will be \n\u003cA NAME=\"231\"\u003e\u003c/A\u003etrue whichever term the negative statement concerns.\n\u003cA NAME=\"232\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003e(3) Also if one premiss is partially false, the other wholly true. \n\u003cA NAME=\"233\"\u003e\u003c/A\u003eFor it is possible that A should belong to some B and to all C, though \n\u003cA NAME=\"234\"\u003e\u003c/A\u003eB belongs to no C, e.g. animal to some white things and to every raven, \n\u003cA NAME=\"235\"\u003e\u003c/A\u003ethough white belongs to no raven. If then it is assumed that A belongs \n\u003cA NAME=\"236\"\u003e\u003c/A\u003eto no B, but to the whole of C, the premiss AB is partially false, the \n\u003cA NAME=\"237\"\u003e\u003c/A\u003epremiss AC wholly true, and the conclusion true. Similarly if the negative \n\u003cA NAME=\"238\"\u003e\u003c/A\u003estatement is transposed: the proof can be made by means of the same terms. \n\u003cA NAME=\"239\"\u003e\u003c/A\u003eAlso if the affirmative premiss is partially false, the negative wholly \n\u003cA NAME=\"240\"\u003e\u003c/A\u003etrue, a true conclusion is possible. For nothing prevents A belonging to \n\u003cA NAME=\"241\"\u003e\u003c/A\u003esome B, but not to C as a whole, while B belongs to no C, e.g. animal belongs \n\u003cA NAME=\"242\"\u003e\u003c/A\u003eto some white things, but to no pitch, and white belongs to no pitch. Consequently \n\u003cA NAME=\"243\"\u003e\u003c/A\u003eif it is assumed that A belongs to the whole of B, but to no C, the premiss \n\u003cA NAME=\"244\"\u003e\u003c/A\u003eAB is partially false, the premiss AC is wholly true, and the conclusion \n\u003cA NAME=\"245\"\u003e\u003c/A\u003eis true.\n\u003cA NAME=\"246\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003e(4) And if both the premisses are partially false, the conclusion \n\u003cA NAME=\"247\"\u003e\u003c/A\u003emay be true. For it is possible that A should belong to some B and to some \n\u003cA NAME=\"248\"\u003e\u003c/A\u003eC, and B to no C, e.g. animal to some white things and to some black things, \n\u003cA NAME=\"249\"\u003e\u003c/A\u003ethough white belongs to nothing black. If then it is assumed that A belongs \n\u003cA NAME=\"250\"\u003e\u003c/A\u003eto all B and to no C, both premisses are partially false, but the conclusion \n\u003cA NAME=\"251\"\u003e\u003c/A\u003eis true. Similarly, if the negative premiss is transposed, the proof can \n\u003cA NAME=\"252\"\u003e\u003c/A\u003ebe made by means of the same terms.\n\u003cA NAME=\"253\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is clear also that our thesis holds in particular syllogisms. \n\u003cA NAME=\"254\"\u003e\u003c/A\u003eFor (5) nothing prevents A belonging to all B and to some C, though B does \n\u003cA NAME=\"255\"\u003e\u003c/A\u003enot belong to some C, e.g. animal to every man and to some white things, \n\u003cA NAME=\"256\"\u003e\u003c/A\u003ethough man will not belong to some white things. If then it is stated that \n\u003cA NAME=\"257\"\u003e\u003c/A\u003eA belongs to no B and to some C, the universal premiss is wholly false, \n\u003cA NAME=\"258\"\u003e\u003c/A\u003ethe particular premiss is true, and the conclusion is true. Similarly if \n\u003cA NAME=\"259\"\u003e\u003c/A\u003ethe premiss AB is affirmative: for it is possible that A should belong \n\u003cA NAME=\"260\"\u003e\u003c/A\u003eto no B, and not to some C, though B does not belong to some C, e.g. animal \n\u003cA NAME=\"261\"\u003e\u003c/A\u003ebelongs to nothing lifeless, and does not belong to some white things, \n\u003cA NAME=\"262\"\u003e\u003c/A\u003eand lifeless will not belong to some white things. If then it is stated \n\u003cA NAME=\"263\"\u003e\u003c/A\u003ethat A belongs to all B and not to some C, the premiss AB which is universal \n\u003cA NAME=\"264\"\u003e\u003c/A\u003eis wholly false, the premiss AC is true, and the conclusion is true. Also \n\u003cA NAME=\"265\"\u003e\u003c/A\u003ea true conclusion is possible when the universal premiss is true, and the \n\u003cA NAME=\"266\"\u003e\u003c/A\u003eparticular is false. For nothing prevents A following neither B nor C at \n\u003cA NAME=\"267\"\u003e\u003c/A\u003eall, while B does not belong to some C, e.g. animal belongs to no number \n\u003cA NAME=\"268\"\u003e\u003c/A\u003enor to anything lifeless, and number does not follow some lifeless things. \n\u003cA NAME=\"269\"\u003e\u003c/A\u003eIf then it is stated that A belongs to no B and to some C, the conclusion \n\u003cA NAME=\"270\"\u003e\u003c/A\u003ewill be true, and the universal premiss true, but the particular false. \n\u003cA NAME=\"271\"\u003e\u003c/A\u003eSimilarly if the premiss which is stated universally is affirmative. For \n\u003cA NAME=\"272\"\u003e\u003c/A\u003eit is possible that should A belong both to B and to C as wholes, though \n\u003cA NAME=\"273\"\u003e\u003c/A\u003eB does not follow some C, e.g. a genus in relation to its species and difference: \n\u003cA NAME=\"274\"\u003e\u003c/A\u003efor animal follows every man and footed things as a whole, but man does \n\u003cA NAME=\"275\"\u003e\u003c/A\u003enot follow every footed thing. Consequently if it is assumed that A belongs \n\u003cA NAME=\"276\"\u003e\u003c/A\u003eto the whole of B, but does not belong to some C, the universal premiss \n\u003cA NAME=\"277\"\u003e\u003c/A\u003eis true, the particular false, and the conclusion true.\n\u003cA NAME=\"278\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003e(6) It is clear too that though both premisses are false they may \n\u003cA NAME=\"279\"\u003e\u003c/A\u003eyield a true conclusion, since it is possible that A should belong both \n\u003cA NAME=\"280\"\u003e\u003c/A\u003eto B and to C as wholes, though B does not follow some C. For if it is \n\u003cA NAME=\"281\"\u003e\u003c/A\u003eassumed that A belongs to no B and to some C, the premisses are both false, \n\u003cA NAME=\"282\"\u003e\u003c/A\u003ebut the conclusion is true. Similarly if the universal premiss is affirmative \n\u003cA NAME=\"283\"\u003e\u003c/A\u003eand the particular negative. For it is possible that A should follow no \n\u003cA NAME=\"284\"\u003e\u003c/A\u003eB and all C, though B does not belong to some C, e.g. animal follows no \n\u003cA NAME=\"285\"\u003e\u003c/A\u003escience but every man, though science does not follow every man. If then \n\u003cA NAME=\"286\"\u003e\u003c/A\u003eA is assumed to belong to the whole of B, and not to follow some C, the \n\u003cA NAME=\"287\"\u003e\u003c/A\u003epremisses are false but the conclusion is true.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"288\"\u003e\u003c/A\u003e\u003cB\u003ePart 4\u003c/B\u003e\n\n\u003cA NAME=\"289\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIn the last figure a true conclusion may come through what is false, \n\u003cA NAME=\"290\"\u003e\u003c/A\u003ealike when both premisses are wholly false, when each is partly false, \n\u003cA NAME=\"291\"\u003e\u003c/A\u003ewhen one premiss is wholly true, the other false, when one premiss is partly \n\u003cA NAME=\"292\"\u003e\u003c/A\u003efalse, the other wholly true, and vice versa, and in every other way in \n\u003cA NAME=\"293\"\u003e\u003c/A\u003ewhich it is possible to alter the premisses. For (1) nothing prevents neither \n\u003cA NAME=\"294\"\u003e\u003c/A\u003eA nor B from belonging to any C, while A belongs to some B, e.g. neither \n\u003cA NAME=\"295\"\u003e\u003c/A\u003eman nor footed follows anything lifeless, though man belongs to some footed \n\u003cA NAME=\"296\"\u003e\u003c/A\u003ethings. If then it is assumed that A and B belong to all C, the premisses \n\u003cA NAME=\"297\"\u003e\u003c/A\u003ewill be wholly false, but the conclusion true. Similarly if one premiss \n\u003cA NAME=\"298\"\u003e\u003c/A\u003eis negative, the other affirmative. For it is possible that B should belong \n\u003cA NAME=\"299\"\u003e\u003c/A\u003eto no C, but A to all C, and that should not belong to some B, e.g. black \n\u003cA NAME=\"300\"\u003e\u003c/A\u003ebelongs to no swan, animal to every swan, and animal not to everything \n\u003cA NAME=\"301\"\u003e\u003c/A\u003eblack. Consequently if it is assumed that B belongs to all C, and A to \n\u003cA NAME=\"302\"\u003e\u003c/A\u003eno C, A will not belong to some B: and the conclusion is true, though the \n\u003cA NAME=\"303\"\u003e\u003c/A\u003epremisses are false.\n\u003cA NAME=\"304\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003e(2) Also if each premiss is partly false, the conclusion may be \n\u003cA NAME=\"305\"\u003e\u003c/A\u003etrue. For nothing prevents both A and B from belonging to some C while \n\u003cA NAME=\"306\"\u003e\u003c/A\u003eA belongs to some B, e.g. white and beautiful belong to some animals, and \n\u003cA NAME=\"307\"\u003e\u003c/A\u003ewhite to some beautiful things. If then it is stated that A and B belong \n\u003cA NAME=\"308\"\u003e\u003c/A\u003eto all C, the premisses are partially false, but the conclusion is true. \n\u003cA NAME=\"309\"\u003e\u003c/A\u003eSimilarly if the premiss AC is stated as negative. For nothing prevents \n\u003cA NAME=\"310\"\u003e\u003c/A\u003eA from not belonging, and B from belonging, to some C, while A does not \n\u003cA NAME=\"311\"\u003e\u003c/A\u003ebelong to all B, e.g. white does not belong to some animals, beautiful \n\u003cA NAME=\"312\"\u003e\u003c/A\u003ebelongs to some animals, and white does not belong to everything beautiful. \n\u003cA NAME=\"313\"\u003e\u003c/A\u003eConsequently if it is assumed that A belongs to no C, and B to all C, both \n\u003cA NAME=\"314\"\u003e\u003c/A\u003epremisses are partly false, but the conclusion is true.\n\u003cA NAME=\"315\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003e(3) Similarly if one of the premisses assumed is wholly false, \n\u003cA NAME=\"316\"\u003e\u003c/A\u003ethe other wholly true. For it is possible that both A and B should follow \n\u003cA NAME=\"317\"\u003e\u003c/A\u003eall C, though A does not belong to some B, e.g. animal and white follow \n\u003cA NAME=\"318\"\u003e\u003c/A\u003eevery swan, though animal does not belong to everything white. Taking these \n\u003cA NAME=\"319\"\u003e\u003c/A\u003ethen as terms, if one assumes that B belongs to the whole of C, but A does \n\u003cA NAME=\"320\"\u003e\u003c/A\u003enot belong to C at all, the premiss BC will be wholly true, the premiss \n\u003cA NAME=\"321\"\u003e\u003c/A\u003eAC wholly false, and the conclusion true. Similarly if the statement BC \n\u003cA NAME=\"322\"\u003e\u003c/A\u003eis false, the statement AC true, the conclusion may be true. The same terms \n\u003cA NAME=\"323\"\u003e\u003c/A\u003ewill serve for the proof. Also if both the premisses assumed are affirmative, \n\u003cA NAME=\"324\"\u003e\u003c/A\u003ethe conclusion may be true. For nothing prevents B from following all C, \n\u003cA NAME=\"325\"\u003e\u003c/A\u003eand A from not belonging to C at all, though A belongs to some B, e.g. \n\u003cA NAME=\"326\"\u003e\u003c/A\u003eanimal belongs to every swan, black to no swan, and black to some animals. \n\u003cA NAME=\"327\"\u003e\u003c/A\u003eConsequently if it is assumed that A and B belong to every C, the premiss \n\u003cA NAME=\"328\"\u003e\u003c/A\u003eBC is wholly true, the premiss AC is wholly false, and the conclusion is \n\u003cA NAME=\"329\"\u003e\u003c/A\u003etrue. Similarly if the premiss AC which is assumed is true: the proof can \n\u003cA NAME=\"330\"\u003e\u003c/A\u003ebe made through the same terms.\n\u003cA NAME=\"331\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003e(4) Again if one premiss is wholly true, the other partly false, \n\u003cA NAME=\"332\"\u003e\u003c/A\u003ethe conclusion may be true. For it is possible that B should belong to \n\u003cA NAME=\"333\"\u003e\u003c/A\u003eall C, and A to some C, while A belongs to some B, e.g. biped belongs to \n\u003cA NAME=\"334\"\u003e\u003c/A\u003eevery man, beautiful not to every man, and beautiful to some bipeds. If \n\u003cA NAME=\"335\"\u003e\u003c/A\u003ethen it is assumed that both A and B belong to the whole of C, the premiss \n\u003cA NAME=\"336\"\u003e\u003c/A\u003eBC is wholly true, the premiss AC partly false, the conclusion true. Similarly \n\u003cA NAME=\"337\"\u003e\u003c/A\u003eif of the premisses assumed AC is true and BC partly false, a true conclusion \n\u003cA NAME=\"338\"\u003e\u003c/A\u003eis possible: this can be proved, if the same terms as before are transposed. \n\u003cA NAME=\"339\"\u003e\u003c/A\u003eAlso the conclusion may be true if one premiss is negative, the other affirmative. \n\u003cA NAME=\"340\"\u003e\u003c/A\u003eFor since it is possible that B should belong to the whole of C, and A \n\u003cA NAME=\"341\"\u003e\u003c/A\u003eto some C, and, when they are so, that A should not belong to all B, therefore \n\u003cA NAME=\"342\"\u003e\u003c/A\u003eit is assumed that B belongs to the whole of C, and A to no C, the negative \n\u003cA NAME=\"343\"\u003e\u003c/A\u003epremiss is partly false, the other premiss wholly true, and the conclusion \n\u003cA NAME=\"344\"\u003e\u003c/A\u003eis true. Again since it has been proved that if A belongs to no C and B \n\u003cA NAME=\"345\"\u003e\u003c/A\u003eto some C, it is possible that A should not belong to some C, it is clear \n\u003cA NAME=\"346\"\u003e\u003c/A\u003ethat if the premiss AC is wholly true, and the premiss BC partly false, \n\u003cA NAME=\"347\"\u003e\u003c/A\u003eit is possible that the conclusion should be true. For if it is assumed \n\u003cA NAME=\"348\"\u003e\u003c/A\u003ethat A belongs to no C, and B to all C, the premiss AC is wholly true, \n\u003cA NAME=\"349\"\u003e\u003c/A\u003eand the premiss BC is partly false.\n\u003cA NAME=\"350\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003e(5) It is clear also in the case of particular syllogisms that \n\u003cA NAME=\"351\"\u003e\u003c/A\u003ea true conclusion may come through what is false, in every possible way. \n\u003cA NAME=\"352\"\u003e\u003c/A\u003eFor the same terms must be taken as have been taken when the premisses \n\u003cA NAME=\"353\"\u003e\u003c/A\u003eare universal, positive terms in positive syllogisms, negative terms in \n\u003cA NAME=\"354\"\u003e\u003c/A\u003enegative. For it makes no difference to the setting out of the terms, whether \n\u003cA NAME=\"355\"\u003e\u003c/A\u003eone assumes that what belongs to none belongs to all or that what belongs \n\u003cA NAME=\"356\"\u003e\u003c/A\u003eto some belongs to all. The same applies to negative \n\u003cA NAME=\"357\"\u003e\u003c/A\u003estatements.\n\u003cA NAME=\"358\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is clear then that if the conclusion is false, the premisses \n\u003cA NAME=\"359\"\u003e\u003c/A\u003eof the argument must be false, either all or some of them; but when the \n\u003cA NAME=\"360\"\u003e\u003c/A\u003econclusion is true, it is not necessary that the premisses should be true, \n\u003cA NAME=\"361\"\u003e\u003c/A\u003eeither one or all, yet it is possible, though no part of the syllogism \n\u003cA NAME=\"362\"\u003e\u003c/A\u003eis true, that the conclusion may none the less be true; but it is not necessitated. \n\u003cA NAME=\"363\"\u003e\u003c/A\u003eThe reason is that when two things are so related to one another, that \n\u003cA NAME=\"364\"\u003e\u003c/A\u003eif the one is, the other necessarily is, then if the latter is not, the \n\u003cA NAME=\"365\"\u003e\u003c/A\u003eformer will not be either, but if the latter is, it is not necessary that \n\u003cA NAME=\"366\"\u003e\u003c/A\u003ethe former should be. But it is impossible that the same thing should be \n\u003cA NAME=\"367\"\u003e\u003c/A\u003enecessitated by the being and by the not-being of the same thing. I mean, \n\u003cA NAME=\"368\"\u003e\u003c/A\u003efor example, that it is impossible that B should necessarily be great since \n\u003cA NAME=\"369\"\u003e\u003c/A\u003eA is white and that B should necessarily be great since A is not white. \n\u003cA NAME=\"370\"\u003e\u003c/A\u003eFor whenever since this, A, is white it is necessary that that, B, should \n\u003cA NAME=\"371\"\u003e\u003c/A\u003ebe great, and since B is great that C should not be white, then it is necessary \n\u003cA NAME=\"372\"\u003e\u003c/A\u003eif is white that C should not be white. And whenever it is necessary, since \n\u003cA NAME=\"373\"\u003e\u003c/A\u003eone of two things is, that the other should be, it is necessary, if the \n\u003cA NAME=\"374\"\u003e\u003c/A\u003elatter is not, that the former (viz. A) should not be. If then B is not \n\u003cA NAME=\"375\"\u003e\u003c/A\u003egreat A cannot be white. But if, when A is not white, it is necessary that \n\u003cA NAME=\"376\"\u003e\u003c/A\u003eB should be great, it necessarily results that if B is not great, B itself \n\u003cA NAME=\"377\"\u003e\u003c/A\u003eis great. (But this is impossible.) For if B is not great, A will necessarily \n\u003cA NAME=\"378\"\u003e\u003c/A\u003enot be white. If then when this is not white B must be great, it results \n\u003cA NAME=\"379\"\u003e\u003c/A\u003ethat if B is not great, it is great, just as if it were proved through \n\u003cA NAME=\"380\"\u003e\u003c/A\u003ethree terms.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"381\"\u003e\u003c/A\u003e\u003cB\u003ePart 5\u003c/B\u003e\n\n\u003cA NAME=\"382\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eCircular and reciprocal proof means proof by means of the conclusion, \n\u003cA NAME=\"383\"\u003e\u003c/A\u003ei.e. by converting one of the premisses simply and inferring the premiss \n\u003cA NAME=\"384\"\u003e\u003c/A\u003ewhich was assumed in the original syllogism: e.g. suppose it has been necessary \n\u003cA NAME=\"385\"\u003e\u003c/A\u003eto prove that A belongs to all C, and it has been proved through B; suppose \n\u003cA NAME=\"386\"\u003e\u003c/A\u003ethat A should now be proved to belong to B by assuming that A belongs to \n\u003cA NAME=\"387\"\u003e\u003c/A\u003eC, and C to B-so A belongs to B: but in the first syllogism the converse \n\u003cA NAME=\"388\"\u003e\u003c/A\u003ewas assumed, viz. that B belongs to C. Or suppose it is necessary to prove \n\u003cA NAME=\"389\"\u003e\u003c/A\u003ethat B belongs to C, and A is assumed to belong to C, which was the conclusion \n\u003cA NAME=\"390\"\u003e\u003c/A\u003eof the first syllogism, and B to belong to A but the converse was assumed \n\u003cA NAME=\"391\"\u003e\u003c/A\u003ein the earlier syllogism, viz. that A belongs to B. In no other way is \n\u003cA NAME=\"392\"\u003e\u003c/A\u003ereciprocal proof possible. If another term is taken as middle, the proof \n\u003cA NAME=\"393\"\u003e\u003c/A\u003eis not circular: for neither of the propositions assumed is the same as \n\u003cA NAME=\"394\"\u003e\u003c/A\u003ebefore: if one of the accepted terms is taken as middle, only one of the \n\u003cA NAME=\"395\"\u003e\u003c/A\u003epremisses of the first syllogism can be assumed in the second: for if both \n\u003cA NAME=\"396\"\u003e\u003c/A\u003eof them are taken the same conclusion as before will result: but it must \n\u003cA NAME=\"397\"\u003e\u003c/A\u003ebe different. If the terms are not convertible, one of the premisses from \n\u003cA NAME=\"398\"\u003e\u003c/A\u003ewhich the syllogism results must be undemonstrated: for it is not possible \n\u003cA NAME=\"399\"\u003e\u003c/A\u003eto demonstrate through these terms that the third belongs to the middle \n\u003cA NAME=\"400\"\u003e\u003c/A\u003eor the middle to the first. If the terms are convertible, it is possible \n\u003cA NAME=\"401\"\u003e\u003c/A\u003eto demonstrate everything reciprocally, e.g. if A and B and C are convertible \n\u003cA NAME=\"402\"\u003e\u003c/A\u003ewith one another. Suppose the proposition AC has been demonstrated through \n\u003cA NAME=\"403\"\u003e\u003c/A\u003eB as middle term, and again the proposition AB through the conclusion and \n\u003cA NAME=\"404\"\u003e\u003c/A\u003ethe premiss BC converted, and similarly the proposition BC through the \n\u003cA NAME=\"405\"\u003e\u003c/A\u003econclusion and the premiss AB converted. But it is necessary to prove both \n\u003cA NAME=\"406\"\u003e\u003c/A\u003ethe premiss CB, and the premiss BA: for we have used these alone without \n\u003cA NAME=\"407\"\u003e\u003c/A\u003edemonstrating them. If then it is assumed that B belongs to all C, and \n\u003cA NAME=\"408\"\u003e\u003c/A\u003eC to all A, we shall have a syllogism relating B to A. Again if it is assumed \n\u003cA NAME=\"409\"\u003e\u003c/A\u003ethat C belongs to all A, and A to all B, C must belong to all B. In both \n\u003cA NAME=\"410\"\u003e\u003c/A\u003ethese syllogisms the premiss CA has been assumed without being demonstrated: \n\u003cA NAME=\"411\"\u003e\u003c/A\u003ethe other premisses had ex hypothesi been proved. Consequently if we succeed \n\u003cA NAME=\"412\"\u003e\u003c/A\u003ein demonstrating this premiss, all the premisses will have been proved \n\u003cA NAME=\"413\"\u003e\u003c/A\u003ereciprocally. If then it is assumed that C belongs to all B, and B to all \n\u003cA NAME=\"414\"\u003e\u003c/A\u003eA, both the premisses assumed have been proved, and C must belong to A. \n\u003cA NAME=\"415\"\u003e\u003c/A\u003eIt is clear then that only if the terms are convertible is circular and \n\u003cA NAME=\"416\"\u003e\u003c/A\u003ereciprocal demonstration possible (if the terms are not convertible, the \n\u003cA NAME=\"417\"\u003e\u003c/A\u003ematter stands as we said above). But it turns out in these also that we \n\u003cA NAME=\"418\"\u003e\u003c/A\u003euse for the demonstration the very thing that is being proved: for C is \n\u003cA NAME=\"419\"\u003e\u003c/A\u003eproved of B, and B of by assuming that C is said of and C is proved of \n\u003cA NAME=\"420\"\u003e\u003c/A\u003eA through these premisses, so that we use the conclusion for the \n\u003cA NAME=\"421\"\u003e\u003c/A\u003edemonstration.\n\u003cA NAME=\"422\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIn negative syllogisms reciprocal proof is as follows. Let B belong \n\u003cA NAME=\"423\"\u003e\u003c/A\u003eto all C, and A to none of the Bs: we conclude that A belongs to none of \n\u003cA NAME=\"424\"\u003e\u003c/A\u003ethe Cs. If again it is necessary to prove that A belongs to none of the \n\u003cA NAME=\"425\"\u003e\u003c/A\u003eBs (which was previously assumed) A must belong to no C, and C to all B: \n\u003cA NAME=\"426\"\u003e\u003c/A\u003ethus the previous premiss is reversed. If it is necessary to prove that \n\u003cA NAME=\"427\"\u003e\u003c/A\u003eB belongs to C, the proposition AB must no longer be converted as before: \n\u003cA NAME=\"428\"\u003e\u003c/A\u003efor the premiss \u0027B belongs to no A\u0027 is identical with the premiss \u0027A belongs \n\u003cA NAME=\"429\"\u003e\u003c/A\u003eto no B\u0027. But we must assume that B belongs to all of that to none of which \n\u003cA NAME=\"430\"\u003e\u003c/A\u003elongs. Let A belong to none of the Cs (which was the previous conclusion) \n\u003cA NAME=\"431\"\u003e\u003c/A\u003eand assume that B belongs to all of that to none of which A belongs. It \n\u003cA NAME=\"432\"\u003e\u003c/A\u003eis necessary then that B should belong to all C. Consequently each of the \n\u003cA NAME=\"433\"\u003e\u003c/A\u003ethree propositions has been made a conclusion, and this is circular demonstration, \n\u003cA NAME=\"434\"\u003e\u003c/A\u003eto assume the conclusion and the converse of one of the premisses, and \n\u003cA NAME=\"435\"\u003e\u003c/A\u003ededuce the remaining premiss.\n\u003cA NAME=\"436\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIn particular syllogisms it is not possible to demonstrate the \n\u003cA NAME=\"437\"\u003e\u003c/A\u003euniversal premiss through the other propositions, but the particular premiss \n\u003cA NAME=\"438\"\u003e\u003c/A\u003ecan be demonstrated. Clearly it is impossible to demonstrate the universal \n\u003cA NAME=\"439\"\u003e\u003c/A\u003epremiss: for what is universal is proved through propositions which are \n\u003cA NAME=\"440\"\u003e\u003c/A\u003euniversal, but the conclusion is not universal, and the proof must start \n\u003cA NAME=\"441\"\u003e\u003c/A\u003efrom the conclusion and the other premiss. Further a syllogism cannot be \n\u003cA NAME=\"442\"\u003e\u003c/A\u003emade at all if the other premiss is converted: for the result is that both \n\u003cA NAME=\"443\"\u003e\u003c/A\u003epremisses are particular. But the particular premiss may be proved. Suppose \n\u003cA NAME=\"444\"\u003e\u003c/A\u003ethat A has been proved of some C through B. If then it is assumed that \n\u003cA NAME=\"445\"\u003e\u003c/A\u003eB belongs to all A and the conclusion is retained, B will belong to some \n\u003cA NAME=\"446\"\u003e\u003c/A\u003eC: for we obtain the first figure and A is middle. But if the syllogism \n\u003cA NAME=\"447\"\u003e\u003c/A\u003eis negative, it is not possible to prove the universal premiss, for the \n\u003cA NAME=\"448\"\u003e\u003c/A\u003ereason given above. But it is possible to prove the particular premiss, \n\u003cA NAME=\"449\"\u003e\u003c/A\u003eif the proposition AB is converted as in the universal syllogism, i.e \u0027B \n\u003cA NAME=\"450\"\u003e\u003c/A\u003ebelongs to some of that to some of which A does not belong\u0027: otherwise \n\u003cA NAME=\"451\"\u003e\u003c/A\u003eno syllogism results because the particular premiss is \n\u003cA NAME=\"452\"\u003e\u003c/A\u003enegative.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"453\"\u003e\u003c/A\u003e\u003cB\u003ePart 6\u003c/B\u003e\n\n\u003cA NAME=\"454\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIn the second figure it is not possible to prove an affirmative \n\u003cA NAME=\"455\"\u003e\u003c/A\u003eproposition in this way, but a negative proposition may be proved. An affirmative \n\u003cA NAME=\"456\"\u003e\u003c/A\u003eproposition is not proved because both premisses of the new syllogism are \n\u003cA NAME=\"457\"\u003e\u003c/A\u003enot affirmative (for the conclusion is negative) but an affirmative proposition \n\u003cA NAME=\"458\"\u003e\u003c/A\u003eis (as we saw) proved from premisses which are both affirmative. The negative \n\u003cA NAME=\"459\"\u003e\u003c/A\u003eis proved as follows. Let A belong to all B, and to no C: we conclude that \n\u003cA NAME=\"460\"\u003e\u003c/A\u003eB belongs to no C. If then it is assumed that B belongs to all A, it is \n\u003cA NAME=\"461\"\u003e\u003c/A\u003enecessary that A should belong to no C: for we get the second figure, with \n\u003cA NAME=\"462\"\u003e\u003c/A\u003eB as middle. But if the premiss AB was negative, and the other affirmative, \n\u003cA NAME=\"463\"\u003e\u003c/A\u003ewe shall have the first figure. For C belongs to all A and B to no C, consequently \n\u003cA NAME=\"464\"\u003e\u003c/A\u003eB belongs to no A: neither then does A belong to B. Through the conclusion, \n\u003cA NAME=\"465\"\u003e\u003c/A\u003etherefore, and one premiss, we get no syllogism, but if another premiss \n\u003cA NAME=\"466\"\u003e\u003c/A\u003eis assumed in addition, a syllogism will be possible. But if the syllogism \n\u003cA NAME=\"467\"\u003e\u003c/A\u003enot universal, the universal premiss cannot be proved, for the same reason \n\u003cA NAME=\"468\"\u003e\u003c/A\u003eas we gave above, but the particular premiss can be proved whenever the \n\u003cA NAME=\"469\"\u003e\u003c/A\u003euniversal statement is affirmative. Let A belong to all B, and not to all \n\u003cA NAME=\"470\"\u003e\u003c/A\u003eC: the conclusion is BC. If then it is assumed that B belongs to all A, \n\u003cA NAME=\"471\"\u003e\u003c/A\u003ebut not to all C, A will not belong to some C, B being middle. But if the \n\u003cA NAME=\"472\"\u003e\u003c/A\u003euniversal premiss is negative, the premiss AC will not be demonstrated \n\u003cA NAME=\"473\"\u003e\u003c/A\u003eby the conversion of AB: for it turns out that either both or one of the \n\u003cA NAME=\"474\"\u003e\u003c/A\u003epremisses is negative; consequently a syllogism will not be possible. But \n\u003cA NAME=\"475\"\u003e\u003c/A\u003ethe proof will proceed as in the universal syllogisms, if it is assumed \n\u003cA NAME=\"476\"\u003e\u003c/A\u003ethat A belongs to some of that to some of which B does not \n\u003cA NAME=\"477\"\u003e\u003c/A\u003ebelong.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"478\"\u003e\u003c/A\u003e\u003cB\u003ePart 7\u003c/B\u003e\n\n\u003cA NAME=\"479\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIn the third figure, when both premisses are taken universally, \n\u003cA NAME=\"480\"\u003e\u003c/A\u003eit is not possible to prove them reciprocally: for that which is universal \n\u003cA NAME=\"481\"\u003e\u003c/A\u003eis proved through statements which are universal, but the conclusion in \n\u003cA NAME=\"482\"\u003e\u003c/A\u003ethis figure is always particular, so that it is clear that it is not possible \n\u003cA NAME=\"483\"\u003e\u003c/A\u003eat all to prove through this figure the universal premiss. But if one premiss \n\u003cA NAME=\"484\"\u003e\u003c/A\u003eis universal, the other particular, proof of the latter will sometimes \n\u003cA NAME=\"485\"\u003e\u003c/A\u003ebe possible, sometimes not. When both the premisses assumed are affirmative, \n\u003cA NAME=\"486\"\u003e\u003c/A\u003eand the universal concerns the minor extreme, proof will be possible, but \n\u003cA NAME=\"487\"\u003e\u003c/A\u003ewhen it concerns the other extreme, impossible. Let A belong to all C and \n\u003cA NAME=\"488\"\u003e\u003c/A\u003eB to some C: the conclusion is the statement AB. If then it is assumed \n\u003cA NAME=\"489\"\u003e\u003c/A\u003ethat C belongs to all A, it has been proved that C belongs to some B, but \n\u003cA NAME=\"490\"\u003e\u003c/A\u003ethat B belongs to some C has not been proved. And yet it is necessary, \n\u003cA NAME=\"491\"\u003e\u003c/A\u003eif C belongs to some B, that B should belong to some C. But it is not the \n\u003cA NAME=\"492\"\u003e\u003c/A\u003esame that this should belong to that, and that to this: but we must assume \n\u003cA NAME=\"493\"\u003e\u003c/A\u003ebesides that if this belongs to some of that, that belongs to some of this. \n\u003cA NAME=\"494\"\u003e\u003c/A\u003eBut if this is assumed the syllogism no longer results from the conclusion \n\u003cA NAME=\"495\"\u003e\u003c/A\u003eand the other premiss. But if B belongs to all C, and A to some C, it will \n\u003cA NAME=\"496\"\u003e\u003c/A\u003ebe possible to prove the proposition AC, when it is assumed that C belongs \n\u003cA NAME=\"497\"\u003e\u003c/A\u003eto all B, and A to some B. For if C belongs to all B and A to some B, it \n\u003cA NAME=\"498\"\u003e\u003c/A\u003eis necessary that A should belong to some C, B being middle. And whenever \n\u003cA NAME=\"499\"\u003e\u003c/A\u003eone premiss is affirmative the other negative, and the affirmative is universal, \n\u003cA NAME=\"500\"\u003e\u003c/A\u003ethe other premiss can be proved. Let B belong to all C, and A not to some \n\u003cA NAME=\"501\"\u003e\u003c/A\u003eC: the conclusion is that A does not belong to some B. If then it is assumed \n\u003cA NAME=\"502\"\u003e\u003c/A\u003efurther that C belongs to all B, it is necessary that A should not belong \n\u003cA NAME=\"503\"\u003e\u003c/A\u003eto some C, B being middle. But when the negative premiss is universal, \n\u003cA NAME=\"504\"\u003e\u003c/A\u003ethe other premiss is not except as before, viz. if it is assumed that that \n\u003cA NAME=\"505\"\u003e\u003c/A\u003ebelongs to some of that, to some of which this does not belong, e.g. if \n\u003cA NAME=\"506\"\u003e\u003c/A\u003eA belongs to no C, and B to some C: the conclusion is that A does not belong \n\u003cA NAME=\"507\"\u003e\u003c/A\u003eto some B. If then it is assumed that C belongs to some of that to some \n\u003cA NAME=\"508\"\u003e\u003c/A\u003eof which does not belong, it is necessary that C should belong to some \n\u003cA NAME=\"509\"\u003e\u003c/A\u003eof the Bs. In no other way is it possible by converting the universal premiss \n\u003cA NAME=\"510\"\u003e\u003c/A\u003eto prove the other: for in no other way can a syllogism be \n\u003cA NAME=\"511\"\u003e\u003c/A\u003eformed.\n\u003cA NAME=\"512\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is clear then that in the first figure reciprocal proof is made \n\u003cA NAME=\"513\"\u003e\u003c/A\u003eboth through the third and through the first figure-if the conclusion is \n\u003cA NAME=\"514\"\u003e\u003c/A\u003eaffirmative through the first; if the conclusion is negative through the \n\u003cA NAME=\"515\"\u003e\u003c/A\u003elast. For it is assumed that that belongs to all of that to none of which \n\u003cA NAME=\"516\"\u003e\u003c/A\u003ethis belongs. In the middle figure, when the syllogism is universal, proof \n\u003cA NAME=\"517\"\u003e\u003c/A\u003eis possible through the second figure and through the first, but when particular \n\u003cA NAME=\"518\"\u003e\u003c/A\u003ethrough the second and the last. In the third figure all proofs are made \n\u003cA NAME=\"519\"\u003e\u003c/A\u003ethrough itself. It is clear also that in the third figure and in the middle \n\u003cA NAME=\"520\"\u003e\u003c/A\u003efigure those syllogisms which are not made through those figures themselves \n\u003cA NAME=\"521\"\u003e\u003c/A\u003eeither are not of the nature of circular proof or are \n\u003cA NAME=\"522\"\u003e\u003c/A\u003eimperfect.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"523\"\u003e\u003c/A\u003e\u003cB\u003ePart 8\u003c/B\u003e\n\n\u003cA NAME=\"524\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eTo convert a syllogism means to alter the conclusion and make another \n\u003cA NAME=\"525\"\u003e\u003c/A\u003esyllogism to prove that either the extreme cannot belong to the middle \n\u003cA NAME=\"526\"\u003e\u003c/A\u003eor the middle to the last term. For it is necessary, if the conclusion \n\u003cA NAME=\"527\"\u003e\u003c/A\u003ehas been changed into its opposite and one of the premisses stands, that \n\u003cA NAME=\"528\"\u003e\u003c/A\u003ethe other premiss should be destroyed. For if it should stand, the conclusion \n\u003cA NAME=\"529\"\u003e\u003c/A\u003ealso must stand. It makes a difference whether the conclusion is converted \n\u003cA NAME=\"530\"\u003e\u003c/A\u003einto its contradictory or into its contrary. For the same syllogism does \n\u003cA NAME=\"531\"\u003e\u003c/A\u003enot result whichever form the conversion takes. This will be made clear \n\u003cA NAME=\"532\"\u003e\u003c/A\u003eby the sequel. By contradictory opposition I mean the opposition of \u0027to \n\u003cA NAME=\"533\"\u003e\u003c/A\u003eall\u0027 to \u0027not to all\u0027, and of \u0027to some\u0027 to \u0027to none\u0027; by contrary opposition \n\u003cA NAME=\"534\"\u003e\u003c/A\u003eI mean the opposition of \u0027to all\u0027 to \u0027to none\u0027, and of \u0027to some\u0027 to \u0027not \n\u003cA NAME=\"535\"\u003e\u003c/A\u003eto some\u0027. Suppose that A been proved of C, through B as middle term. If \n\u003cA NAME=\"536\"\u003e\u003c/A\u003ethen it should be assumed that A belongs to no C, but to all B, B will \n\u003cA NAME=\"537\"\u003e\u003c/A\u003ebelong to no C. And if A belongs to no C, and B to all C, A will belong, \n\u003cA NAME=\"538\"\u003e\u003c/A\u003enot to no B at all, but not to all B. For (as we saw) the universal is \n\u003cA NAME=\"539\"\u003e\u003c/A\u003enot proved through the last figure. In a word it is not possible to refute \n\u003cA NAME=\"540\"\u003e\u003c/A\u003euniversally by conversion the premiss which concerns the major extreme: \n\u003cA NAME=\"541\"\u003e\u003c/A\u003efor the refutation always proceeds through the third since it is necessary \n\u003cA NAME=\"542\"\u003e\u003c/A\u003eto take both premisses in reference to the minor extreme. Similarly if \n\u003cA NAME=\"543\"\u003e\u003c/A\u003ethe syllogism is negative. Suppose it has been proved that A belongs to \n\u003cA NAME=\"544\"\u003e\u003c/A\u003eno C through B. Then if it is assumed that A belongs to all C, and to no \n\u003cA NAME=\"545\"\u003e\u003c/A\u003eB, B will belong to none of the Cs. And if A and B belong to all C, A will \n\u003cA NAME=\"546\"\u003e\u003c/A\u003ebelong to some B: but in the original premiss it belonged to no \n\u003cA NAME=\"547\"\u003e\u003c/A\u003eB.\n\u003cA NAME=\"548\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIf the conclusion is converted into its contradictory, the syllogisms \n\u003cA NAME=\"549\"\u003e\u003c/A\u003ewill be contradictory and not universal. For one premiss is particular, \n\u003cA NAME=\"550\"\u003e\u003c/A\u003eso that the conclusion also will be particular. Let the syllogism be affirmative, \n\u003cA NAME=\"551\"\u003e\u003c/A\u003eand let it be converted as stated. Then if A belongs not to all C, but \n\u003cA NAME=\"552\"\u003e\u003c/A\u003eto all B, B will belong not to all C. And if A belongs not to all C, but \n\u003cA NAME=\"553\"\u003e\u003c/A\u003eB belongs to all C, A will belong not to all B. Similarly if the syllogism \n\u003cA NAME=\"554\"\u003e\u003c/A\u003eis negative. For if A belongs to some C, and to no B, B will belong, not \n\u003cA NAME=\"555\"\u003e\u003c/A\u003eto no C at all, but-not to some C. And if A belongs to some C, and B to \n\u003cA NAME=\"556\"\u003e\u003c/A\u003eall C, as was originally assumed, A will belong to some \n\u003cA NAME=\"557\"\u003e\u003c/A\u003eB.\n\u003cA NAME=\"558\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIn particular syllogisms when the conclusion is converted into \n\u003cA NAME=\"559\"\u003e\u003c/A\u003eits contradictory, both premisses may be refuted, but when it is converted \n\u003cA NAME=\"560\"\u003e\u003c/A\u003einto its contrary, neither. For the result is no longer, as in the universal \n\u003cA NAME=\"561\"\u003e\u003c/A\u003esyllogisms, refutation in which the conclusion reached by O, conversion \n\u003cA NAME=\"562\"\u003e\u003c/A\u003elacks universality, but no refutation at all. Suppose that A has been proved \n\u003cA NAME=\"563\"\u003e\u003c/A\u003eof some C. If then it is assumed that A belongs to no C, and B to some \n\u003cA NAME=\"564\"\u003e\u003c/A\u003eC, A will not belong to some B: and if A belongs to no C, but to all B, \n\u003cA NAME=\"565\"\u003e\u003c/A\u003eB will belong to no C. Thus both premisses are refuted. But neither can \n\u003cA NAME=\"566\"\u003e\u003c/A\u003ebe refuted if the conclusion is converted into its contrary. For if A does \n\u003cA NAME=\"567\"\u003e\u003c/A\u003enot belong to some C, but to all B, then B will not belong to some C. But \n\u003cA NAME=\"568\"\u003e\u003c/A\u003ethe original premiss is not yet refuted: for it is possible that B should \n\u003cA NAME=\"569\"\u003e\u003c/A\u003ebelong to some C, and should not belong to some C. The universal premiss \n\u003cA NAME=\"570\"\u003e\u003c/A\u003eAB cannot be affected by a syllogism at all: for if A does not belong to \n\u003cA NAME=\"571\"\u003e\u003c/A\u003esome of the Cs, but B belongs to some of the Cs, neither of the premisses \n\u003cA NAME=\"572\"\u003e\u003c/A\u003eis universal. Similarly if the syllogism is negative: for if it should \n\u003cA NAME=\"573\"\u003e\u003c/A\u003ebe assumed that A belongs to all C, both premisses are refuted: but if \n\u003cA NAME=\"574\"\u003e\u003c/A\u003ethe assumption is that A belongs to some C, neither premiss is refuted. \n\u003cA NAME=\"575\"\u003e\u003c/A\u003eThe proof is the same as before.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"576\"\u003e\u003c/A\u003e\u003cB\u003ePart 9\u003c/B\u003e\n\n\u003cA NAME=\"577\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIn the second figure it is not possible to refute the premiss which \n\u003cA NAME=\"578\"\u003e\u003c/A\u003econcerns the major extreme by establishing something contrary to it, whichever \n\u003cA NAME=\"579\"\u003e\u003c/A\u003eform the conversion of the conclusion may take. For the conclusion of the \n\u003cA NAME=\"580\"\u003e\u003c/A\u003erefutation will always be in the third figure, and in this figure (as we \n\u003cA NAME=\"581\"\u003e\u003c/A\u003esaw) there is no universal syllogism. The other premiss can be refuted \n\u003cA NAME=\"582\"\u003e\u003c/A\u003ein a manner similar to the conversion: I mean, if the conclusion of the \n\u003cA NAME=\"583\"\u003e\u003c/A\u003efirst syllogism is converted into its contrary, the conclusion of the refutation \n\u003cA NAME=\"584\"\u003e\u003c/A\u003ewill be the contrary of the minor premiss of the first, if into its contradictory, \n\u003cA NAME=\"585\"\u003e\u003c/A\u003ethe contradictory. Let A belong to all B and to no C: conclusion BC. If \n\u003cA NAME=\"586\"\u003e\u003c/A\u003ethen it is assumed that B belongs to all C, and the proposition AB stands, \n\u003cA NAME=\"587\"\u003e\u003c/A\u003eA will belong to all C, since the first figure is produced. If B belongs \n\u003cA NAME=\"588\"\u003e\u003c/A\u003eto all C, and A to no C, then A belongs not to all B: the figure is the \n\u003cA NAME=\"589\"\u003e\u003c/A\u003elast. But if the conclusion BC is converted into its contradictory, the \n\u003cA NAME=\"590\"\u003e\u003c/A\u003epremiss AB will be refuted as before, the premiss, AC by its contradictory. \n\u003cA NAME=\"591\"\u003e\u003c/A\u003eFor if B belongs to some C, and A to no C, then A will not belong to some \n\u003cA NAME=\"592\"\u003e\u003c/A\u003eB. Again if B belongs to some C, and A to all B, A will belong to some \n\u003cA NAME=\"593\"\u003e\u003c/A\u003eC, so that the syllogism results in the contradictory of the minor premiss. \n\u003cA NAME=\"594\"\u003e\u003c/A\u003eA similar proof can be given if the premisses are transposed in respect \n\u003cA NAME=\"595\"\u003e\u003c/A\u003eof their quality.\n\u003cA NAME=\"596\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIf the syllogism is particular, when the conclusion is converted \n\u003cA NAME=\"597\"\u003e\u003c/A\u003einto its contrary neither premiss can be refuted, as also happened in the \n\u003cA NAME=\"598\"\u003e\u003c/A\u003efirst figure,\u0027 if the conclusion is converted into its contradictory, both \n\u003cA NAME=\"599\"\u003e\u003c/A\u003epremisses can be refuted. Suppose that A belongs to no B, and to some C: \n\u003cA NAME=\"600\"\u003e\u003c/A\u003ethe conclusion is BC. If then it is assumed that B belongs to some C, and \n\u003cA NAME=\"601\"\u003e\u003c/A\u003ethe statement AB stands, the conclusion will be that A does not belong \n\u003cA NAME=\"602\"\u003e\u003c/A\u003eto some C. But the original statement has not been refuted: for it is possible \n\u003cA NAME=\"603\"\u003e\u003c/A\u003ethat A should belong to some C and also not to some C. Again if B belongs \n\u003cA NAME=\"604\"\u003e\u003c/A\u003eto some C and A to some C, no syllogism will be possible: for neither of \n\u003cA NAME=\"605\"\u003e\u003c/A\u003ethe premisses taken is universal. Consequently the proposition AB is not \n\u003cA NAME=\"606\"\u003e\u003c/A\u003erefuted. But if the conclusion is converted into its contradictory, both \n\u003cA NAME=\"607\"\u003e\u003c/A\u003epremisses can be refuted. For if B belongs to all C, and A to no B, A will \n\u003cA NAME=\"608\"\u003e\u003c/A\u003ebelong to no C: but it was assumed to belong to some C. Again if B belongs \n\u003cA NAME=\"609\"\u003e\u003c/A\u003eto all C and A to some C, A will belong to some B. The same proof can be \n\u003cA NAME=\"610\"\u003e\u003c/A\u003egiven if the universal statement is affirmative.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"611\"\u003e\u003c/A\u003e\u003cB\u003ePart 10\u003c/B\u003e\n\n\u003cA NAME=\"612\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIn the third figure when the conclusion is converted into its contrary, \n\u003cA NAME=\"613\"\u003e\u003c/A\u003eneither of the premisses can be refuted in any of the syllogisms, but when \n\u003cA NAME=\"614\"\u003e\u003c/A\u003ethe conclusion is converted into its contradictory, both premisses may \n\u003cA NAME=\"615\"\u003e\u003c/A\u003ebe refuted and in all the moods. Suppose it has been proved that A belongs \n\u003cA NAME=\"616\"\u003e\u003c/A\u003eto some B, C being taken as middle, and the premisses being universal. \n\u003cA NAME=\"617\"\u003e\u003c/A\u003eIf then it is assumed that A does not belong to some B, but B belongs to \n\u003cA NAME=\"618\"\u003e\u003c/A\u003eall C, no syllogism is formed about A and C. Nor if A does not belong to \n\u003cA NAME=\"619\"\u003e\u003c/A\u003esome B, but belongs to all C, will a syllogism be possible about B and \n\u003cA NAME=\"620\"\u003e\u003c/A\u003eC. A similar proof can be given if the premisses are not universal. For \n\u003cA NAME=\"621\"\u003e\u003c/A\u003eeither both premisses arrived at by the conversion must be particular, \n\u003cA NAME=\"622\"\u003e\u003c/A\u003eor the universal premiss must refer to the minor extreme. But we found \n\u003cA NAME=\"623\"\u003e\u003c/A\u003ethat no syllogism is possible thus either in the first or in the middle \n\u003cA NAME=\"624\"\u003e\u003c/A\u003efigure. But if the conclusion is converted into its contradictory, both \n\u003cA NAME=\"625\"\u003e\u003c/A\u003ethe premisses can be refuted. For if A belongs to no B, and B to all C, \n\u003cA NAME=\"626\"\u003e\u003c/A\u003ethen A belongs to no C: again if A belongs to no B, and to all C, B belongs \n\u003cA NAME=\"627\"\u003e\u003c/A\u003eto no C. And similarly if one of the premisses is not universal. For if \n\u003cA NAME=\"628\"\u003e\u003c/A\u003eA belongs to no B, and B to some C, A will not belong to some C: if A belongs \n\u003cA NAME=\"629\"\u003e\u003c/A\u003eto no B, and to C, B will belong to no C.\n\u003cA NAME=\"630\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eSimilarly if the original syllogism is negative. Suppose it has \n\u003cA NAME=\"631\"\u003e\u003c/A\u003ebeen proved that A does not belong to some B, BC being affirmative, AC \n\u003cA NAME=\"632\"\u003e\u003c/A\u003ebeing negative: for it was thus that, as we saw, a syllogism could be made. \n\u003cA NAME=\"633\"\u003e\u003c/A\u003eWhenever then the contrary of the conclusion is assumed a syllogism will \n\u003cA NAME=\"634\"\u003e\u003c/A\u003enot be possible. For if A belongs to some B, and B to all C, no syllogism \n\u003cA NAME=\"635\"\u003e\u003c/A\u003eis possible (as we saw) about A and C. Nor, if A belongs to some B, and \n\u003cA NAME=\"636\"\u003e\u003c/A\u003eto no C, was a syllogism possible concerning B and C. Therefore the premisses \n\u003cA NAME=\"637\"\u003e\u003c/A\u003eare not refuted. But when the contradictory of the conclusion is assumed, \n\u003cA NAME=\"638\"\u003e\u003c/A\u003ethey are refuted. For if A belongs to all B, and B to C, A belongs to all \n\u003cA NAME=\"639\"\u003e\u003c/A\u003eC: but A was supposed originally to belong to no C. Again if A belongs \n\u003cA NAME=\"640\"\u003e\u003c/A\u003eto all B, and to no C, then B belongs to no C: but it was supposed to belong \n\u003cA NAME=\"641\"\u003e\u003c/A\u003eto all C. A similar proof is possible if the premisses are not universal. \n\u003cA NAME=\"642\"\u003e\u003c/A\u003eFor AC becomes universal and negative, the other premiss particular and \n\u003cA NAME=\"643\"\u003e\u003c/A\u003eaffirmative. If then A belongs to all B, and B to some C, it results that \n\u003cA NAME=\"644\"\u003e\u003c/A\u003eA belongs to some C: but it was supposed to belong to no C. Again if A \n\u003cA NAME=\"645\"\u003e\u003c/A\u003ebelongs to all B, and to no C, then B belongs to no C: but it was assumed \n\u003cA NAME=\"646\"\u003e\u003c/A\u003eto belong to some C. If A belongs to some B and B to some C, no syllogism \n\u003cA NAME=\"647\"\u003e\u003c/A\u003eresults: nor yet if A belongs to some B, and to no C. Thus in one way the \n\u003cA NAME=\"648\"\u003e\u003c/A\u003epremisses are refuted, in the other way they are not.\n\u003cA NAME=\"649\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eFrom what has been said it is clear how a syllogism results in \n\u003cA NAME=\"650\"\u003e\u003c/A\u003eeach figure when the conclusion is converted; when a result contrary to \n\u003cA NAME=\"651\"\u003e\u003c/A\u003ethe premiss, and when a result contradictory to the premiss, is obtained. \n\u003cA NAME=\"652\"\u003e\u003c/A\u003eIt is clear that in the first figure the syllogisms are formed through \n\u003cA NAME=\"653\"\u003e\u003c/A\u003ethe middle and the last figures, and the premiss which concerns the minor \n\u003cA NAME=\"654\"\u003e\u003c/A\u003eextreme is alway refuted through the middle figure, the premiss which concerns \n\u003cA NAME=\"655\"\u003e\u003c/A\u003ethe major through the last figure. In the second figure syllogisms proceed \n\u003cA NAME=\"656\"\u003e\u003c/A\u003ethrough the first and the last figures, and the premiss which concerns \n\u003cA NAME=\"657\"\u003e\u003c/A\u003ethe minor extreme is always refuted through the first figure, the premiss \n\u003cA NAME=\"658\"\u003e\u003c/A\u003ewhich concerns the major extreme through the last. In the third figure \n\u003cA NAME=\"659\"\u003e\u003c/A\u003ethe refutation proceeds through the first and the middle figures; the premiss \n\u003cA NAME=\"660\"\u003e\u003c/A\u003ewhich concerns the major is always refuted through the first figure, the \n\u003cA NAME=\"661\"\u003e\u003c/A\u003epremiss which concerns the minor through the middle \n\u003cA NAME=\"662\"\u003e\u003c/A\u003efigure.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"663\"\u003e\u003c/A\u003e\u003cB\u003ePart 11\u003c/B\u003e\n\n\u003cA NAME=\"664\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is clear then what conversion is, how it is effected in each \n\u003cA NAME=\"665\"\u003e\u003c/A\u003efigure, and what syllogism results. The syllogism per impossibile is proved \n\u003cA NAME=\"666\"\u003e\u003c/A\u003ewhen the contradictory of the conclusion stated and another premiss is \n\u003cA NAME=\"667\"\u003e\u003c/A\u003eassumed; it can be made in all the figures. For it resembles conversion, \n\u003cA NAME=\"668\"\u003e\u003c/A\u003ediffering only in this: conversion takes place after a syllogism has been \n\u003cA NAME=\"669\"\u003e\u003c/A\u003eformed and both the premisses have been taken, but a reduction to the impossible \n\u003cA NAME=\"670\"\u003e\u003c/A\u003etakes place not because the contradictory has been agreed to already, but \n\u003cA NAME=\"671\"\u003e\u003c/A\u003ebecause it is clear that it is true. The terms are alike in both, and the \n\u003cA NAME=\"672\"\u003e\u003c/A\u003epremisses of both are taken in the same way. For example if A belongs to \n\u003cA NAME=\"673\"\u003e\u003c/A\u003eall B, C being middle, then if it is supposed that A does not belong to \n\u003cA NAME=\"674\"\u003e\u003c/A\u003eall B or belongs to no B, but to all C (which was admitted to be true), \n\u003cA NAME=\"675\"\u003e\u003c/A\u003eit follows that C belongs to no B or not to all B. But this is impossible: \n\u003cA NAME=\"676\"\u003e\u003c/A\u003econsequently the supposition is false: its contradictory then is true. \n\u003cA NAME=\"677\"\u003e\u003c/A\u003eSimilarly in the other figures: for whatever moods admit of conversion \n\u003cA NAME=\"678\"\u003e\u003c/A\u003eadmit also of the reduction per impossibile.\n\u003cA NAME=\"679\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eAll the problems can be proved per impossibile in all the figures, \n\u003cA NAME=\"680\"\u003e\u003c/A\u003eexcepting the universal affirmative, which is proved in the middle and \n\u003cA NAME=\"681\"\u003e\u003c/A\u003ethird figures, but not in the first. Suppose that A belongs not to all \n\u003cA NAME=\"682\"\u003e\u003c/A\u003eB, or to no B, and take besides another premiss concerning either of the \n\u003cA NAME=\"683\"\u003e\u003c/A\u003eterms, viz. that C belongs to all A, or that B belongs to all D; thus we \n\u003cA NAME=\"684\"\u003e\u003c/A\u003eget the first figure. If then it is supposed that A does not belong to \n\u003cA NAME=\"685\"\u003e\u003c/A\u003eall B, no syllogism results whichever term the assumed premiss concerns; \n\u003cA NAME=\"686\"\u003e\u003c/A\u003ebut if it is supposed that A belongs to no B, when the premiss BD is assumed \n\u003cA NAME=\"687\"\u003e\u003c/A\u003eas well we shall prove syllogistically what is false, but not the problem \n\u003cA NAME=\"688\"\u003e\u003c/A\u003eproposed. For if A belongs to no B, and B belongs to all D, A belongs to \n\u003cA NAME=\"689\"\u003e\u003c/A\u003eno D. Let this be impossible: it is false then A belongs to no B. But the \n\u003cA NAME=\"690\"\u003e\u003c/A\u003euniversal affirmative is not necessarily true if the universal negative \n\u003cA NAME=\"691\"\u003e\u003c/A\u003eis false. But if the premiss CA is assumed as well, no syllogism results, \n\u003cA NAME=\"692\"\u003e\u003c/A\u003enor does it do so when it is supposed that A does not belong to all B. \n\u003cA NAME=\"693\"\u003e\u003c/A\u003eConsequently it is clear that the universal affirmative cannot be proved \n\u003cA NAME=\"694\"\u003e\u003c/A\u003ein the first figure per impossibile.\n\u003cA NAME=\"695\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eBut the particular affirmative and the universal and particular \n\u003cA NAME=\"696\"\u003e\u003c/A\u003enegatives can all be proved. Suppose that A belongs to no B, and let it \n\u003cA NAME=\"697\"\u003e\u003c/A\u003ehave been assumed that B belongs to all or to some C. Then it is necessary \n\u003cA NAME=\"698\"\u003e\u003c/A\u003ethat A should belong to no C or not to all C. But this is impossible (for \n\u003cA NAME=\"699\"\u003e\u003c/A\u003elet it be true and clear that A belongs to all C): consequently if this \n\u003cA NAME=\"700\"\u003e\u003c/A\u003eis false, it is necessary that A should belong to some B. But if the other \n\u003cA NAME=\"701\"\u003e\u003c/A\u003epremiss assumed relates to A, no syllogism will be possible. Nor can a \n\u003cA NAME=\"702\"\u003e\u003c/A\u003econclusion be drawn when the contrary of the conclusion is supposed, e.g. \n\u003cA NAME=\"703\"\u003e\u003c/A\u003ethat A does not belong to some B. Clearly then we must suppose the \n\u003cA NAME=\"704\"\u003e\u003c/A\u003econtradictory.\n\u003cA NAME=\"705\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eAgain suppose that A belongs to some B, and let it have been assumed \n\u003cA NAME=\"706\"\u003e\u003c/A\u003ethat C belongs to all A. It is necessary then that C should belong to some \n\u003cA NAME=\"707\"\u003e\u003c/A\u003eB. But let this be impossible, so that the supposition is false: in that \n\u003cA NAME=\"708\"\u003e\u003c/A\u003ecase it is true that A belongs to no B. We may proceed in the same way \n\u003cA NAME=\"709\"\u003e\u003c/A\u003eif the proposition CA has been taken as negative. But if the premiss assumed \n\u003cA NAME=\"710\"\u003e\u003c/A\u003econcerns B, no syllogism will be possible. If the contrary is supposed, \n\u003cA NAME=\"711\"\u003e\u003c/A\u003ewe shall have a syllogism and an impossible conclusion, but the problem \n\u003cA NAME=\"712\"\u003e\u003c/A\u003ein hand is not proved. Suppose that A belongs to all B, and let it have \n\u003cA NAME=\"713\"\u003e\u003c/A\u003ebeen assumed that C belongs to all A. It is necessary then that C should \n\u003cA NAME=\"714\"\u003e\u003c/A\u003ebelong to all B. But this is impossible, so that it is false that A belongs \n\u003cA NAME=\"715\"\u003e\u003c/A\u003eto all B. But we have not yet shown it to be necessary that A belongs to \n\u003cA NAME=\"716\"\u003e\u003c/A\u003eno B, if it does not belong to all B. Similarly if the other premiss taken \n\u003cA NAME=\"717\"\u003e\u003c/A\u003econcerns B; we shall have a syllogism and a conclusion which is impossible, \n\u003cA NAME=\"718\"\u003e\u003c/A\u003ebut the hypothesis is not refuted. Therefore it is the contradictory that \n\u003cA NAME=\"719\"\u003e\u003c/A\u003ewe must suppose.\n\u003cA NAME=\"720\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eTo prove that A does not belong to all B, we must suppose that \n\u003cA NAME=\"721\"\u003e\u003c/A\u003eit belongs to all B: for if A belongs to all B, and C to all A, then C \n\u003cA NAME=\"722\"\u003e\u003c/A\u003ebelongs to all B; so that if this is impossible, the hypothesis is false. \n\u003cA NAME=\"723\"\u003e\u003c/A\u003eSimilarly if the other premiss assumed concerns B. The same results if \n\u003cA NAME=\"724\"\u003e\u003c/A\u003ethe original proposition CA was negative: for thus also we get a syllogism. \n\u003cA NAME=\"725\"\u003e\u003c/A\u003eBut if the negative proposition concerns B, nothing is proved. If the hypothesis \n\u003cA NAME=\"726\"\u003e\u003c/A\u003eis that A belongs not to all but to some B, it is not proved that A belongs \n\u003cA NAME=\"727\"\u003e\u003c/A\u003enot to all B, but that it belongs to no B. For if A belongs to some B, \n\u003cA NAME=\"728\"\u003e\u003c/A\u003eand C to all A, then C will belong to some B. If then this is impossible, \n\u003cA NAME=\"729\"\u003e\u003c/A\u003eit is false that A belongs to some B; consequently it is true that A belongs \n\u003cA NAME=\"730\"\u003e\u003c/A\u003eto no B. But if this is proved, the truth is refuted as well; for the original \n\u003cA NAME=\"731\"\u003e\u003c/A\u003econclusion was that A belongs to some B, and does not belong to some B. \n\u003cA NAME=\"732\"\u003e\u003c/A\u003eFurther the impossible does not result from the hypothesis: for then the \n\u003cA NAME=\"733\"\u003e\u003c/A\u003ehypothesis would be false, since it is impossible to draw a false conclusion \n\u003cA NAME=\"734\"\u003e\u003c/A\u003efrom true premisses: but in fact it is true: for A belongs to some B. Consequently \n\u003cA NAME=\"735\"\u003e\u003c/A\u003ewe must not suppose that A belongs to some B, but that it belongs to all \n\u003cA NAME=\"736\"\u003e\u003c/A\u003eB. Similarly if we should be proving that A does not belong to some B: \n\u003cA NAME=\"737\"\u003e\u003c/A\u003efor if \u0027not to belong to some\u0027 and \u0027to belong not to all\u0027 have the same \n\u003cA NAME=\"738\"\u003e\u003c/A\u003emeaning, the demonstration of both will be identical.\n\u003cA NAME=\"739\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is clear then that not the contrary but the contradictory ought \n\u003cA NAME=\"740\"\u003e\u003c/A\u003eto be supposed in all the syllogisms. For thus we shall have necessity \n\u003cA NAME=\"741\"\u003e\u003c/A\u003eof inference, and the claim we make is one that will be generally accepted. \n\u003cA NAME=\"742\"\u003e\u003c/A\u003eFor if of everything one or other of two contradictory statements holds \n\u003cA NAME=\"743\"\u003e\u003c/A\u003egood, then if it is proved that the negation does not hold, the affirmation \n\u003cA NAME=\"744\"\u003e\u003c/A\u003emust be true. Again if it is not admitted that the affirmation is true, \n\u003cA NAME=\"745\"\u003e\u003c/A\u003ethe claim that the negation is true will be generally accepted. But in \n\u003cA NAME=\"746\"\u003e\u003c/A\u003eneither way does it suit to maintain the contrary: for it is not necessary \n\u003cA NAME=\"747\"\u003e\u003c/A\u003ethat if the universal negative is false, the universal affirmative should \n\u003cA NAME=\"748\"\u003e\u003c/A\u003ebe true, nor is it generally accepted that if the one is false the other \n\u003cA NAME=\"749\"\u003e\u003c/A\u003eis true.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"750\"\u003e\u003c/A\u003e\u003cB\u003ePart 12\u003c/B\u003e\n\n\u003cA NAME=\"751\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is clear then that in the first figure all problems except the \n\u003cA NAME=\"752\"\u003e\u003c/A\u003euniversal affirmative are proved per impossibile. But in the middle and \n\u003cA NAME=\"753\"\u003e\u003c/A\u003ethe last figures this also is proved. Suppose that A does not belong to \n\u003cA NAME=\"754\"\u003e\u003c/A\u003eall B, and let it have been assumed that A belongs to all C. If then A \n\u003cA NAME=\"755\"\u003e\u003c/A\u003ebelongs not to all B, but to all C, C will not belong to all B. But this \n\u003cA NAME=\"756\"\u003e\u003c/A\u003eis impossible (for suppose it to be clear that C belongs to all B): consequently \n\u003cA NAME=\"757\"\u003e\u003c/A\u003ethe hypothesis is false. It is true then that A belongs to all B. But if \n\u003cA NAME=\"758\"\u003e\u003c/A\u003ethe contrary is supposed, we shall have a syllogism and a result which \n\u003cA NAME=\"759\"\u003e\u003c/A\u003eis impossible: but the problem in hand is not proved. For if A belongs \n\u003cA NAME=\"760\"\u003e\u003c/A\u003eto no B, and to all C, C will belong to no B. This is impossible; so that \n\u003cA NAME=\"761\"\u003e\u003c/A\u003eit is false that A belongs to no B. But though this is false, it does not \n\u003cA NAME=\"762\"\u003e\u003c/A\u003efollow that it is true that A belongs to all B.\n\u003cA NAME=\"763\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWhen A belongs to some B, suppose that A belongs to no B, and let \n\u003cA NAME=\"764\"\u003e\u003c/A\u003eA belong to all C. It is necessary then that C should belong to no B. Consequently, \n\u003cA NAME=\"765\"\u003e\u003c/A\u003eif this is impossible, A must belong to some B. But if it is supposed that \n\u003cA NAME=\"766\"\u003e\u003c/A\u003eA does not belong to some B, we shall have the same results as in the first \n\u003cA NAME=\"767\"\u003e\u003c/A\u003efigure.\n\u003cA NAME=\"768\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eAgain suppose that A belongs to some B, and let A belong to no \n\u003cA NAME=\"769\"\u003e\u003c/A\u003eC. It is necessary then that C should not belong to some B. But originally \n\u003cA NAME=\"770\"\u003e\u003c/A\u003eit belonged to all B, consequently the hypothesis is false: A then will \n\u003cA NAME=\"771\"\u003e\u003c/A\u003ebelong to no B.\n\u003cA NAME=\"772\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWhen A does not belong to an B, suppose it does belong to all B, \n\u003cA NAME=\"773\"\u003e\u003c/A\u003eand to no C. It is necessary then that C should belong to no B. But this \n\u003cA NAME=\"774\"\u003e\u003c/A\u003eis impossible: so that it is true that A does not belong to all B. It is \n\u003cA NAME=\"775\"\u003e\u003c/A\u003eclear then that all the syllogisms can be formed in the middle \n\u003cA NAME=\"776\"\u003e\u003c/A\u003efigure.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"777\"\u003e\u003c/A\u003e\u003cB\u003ePart 13\u003c/B\u003e\n\n\u003cA NAME=\"778\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eSimilarly they can all be formed in the last figure. Suppose that \n\u003cA NAME=\"779\"\u003e\u003c/A\u003eA does not belong to some B, but C belongs to all B: then A does not belong \n\u003cA NAME=\"780\"\u003e\u003c/A\u003eto some C. If then this is impossible, it is false that A does not belong \n\u003cA NAME=\"781\"\u003e\u003c/A\u003eto some B; so that it is true that A belongs to all B. But if it is supposed \n\u003cA NAME=\"782\"\u003e\u003c/A\u003ethat A belongs to no B, we shall have a syllogism and a conclusion which \n\u003cA NAME=\"783\"\u003e\u003c/A\u003eis impossible: but the problem in hand is not proved: for if the contrary \n\u003cA NAME=\"784\"\u003e\u003c/A\u003eis supposed, we shall have the same results as before.\n\u003cA NAME=\"785\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eBut to prove that A belongs to some B, this hypothesis must be \n\u003cA NAME=\"786\"\u003e\u003c/A\u003emade. If A belongs to no B, and C to some B, A will belong not to all C. \n\u003cA NAME=\"787\"\u003e\u003c/A\u003eIf then this is false, it is true that A belongs to some \n\u003cA NAME=\"788\"\u003e\u003c/A\u003eB.\n\u003cA NAME=\"789\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWhen A belongs to no B, suppose A belongs to some B, and let it \n\u003cA NAME=\"790\"\u003e\u003c/A\u003ehave been assumed that C belongs to all B. Then it is necessary that A \n\u003cA NAME=\"791\"\u003e\u003c/A\u003eshould belong to some C. But ex hypothesi it belongs to no C, so that it \n\u003cA NAME=\"792\"\u003e\u003c/A\u003eis false that A belongs to some B. But if it is supposed that A belongs \n\u003cA NAME=\"793\"\u003e\u003c/A\u003eto all B, the problem is not proved.\n\u003cA NAME=\"794\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eBut this hypothesis must be made if we are prove that A belongs \n\u003cA NAME=\"795\"\u003e\u003c/A\u003enot to all B. For if A belongs to all B and C to some B, then A belongs \n\u003cA NAME=\"796\"\u003e\u003c/A\u003eto some C. But this we assumed not to be so, so it is false that A belongs \n\u003cA NAME=\"797\"\u003e\u003c/A\u003eto all B. But in that case it is true that A belongs not to all B. If however \n\u003cA NAME=\"798\"\u003e\u003c/A\u003eit is assumed that A belongs to some B, we shall have the same result as \n\u003cA NAME=\"799\"\u003e\u003c/A\u003ebefore.\n\u003cA NAME=\"800\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is clear then that in all the syllogisms which proceed per impossibile \n\u003cA NAME=\"801\"\u003e\u003c/A\u003ethe contradictory must be assumed. And it is plain that in the middle figure \n\u003cA NAME=\"802\"\u003e\u003c/A\u003ean affirmative conclusion, and in the last figure a universal conclusion, \n\u003cA NAME=\"803\"\u003e\u003c/A\u003eare proved in a way.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"804\"\u003e\u003c/A\u003e\u003cB\u003ePart 14\u003c/B\u003e\n\n\u003cA NAME=\"805\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eDemonstration per impossibile differs from ostensive proof in that \n\u003cA NAME=\"806\"\u003e\u003c/A\u003eit posits what it wishes to refute by reduction to a statement admitted \n\u003cA NAME=\"807\"\u003e\u003c/A\u003eto be false; whereas ostensive proof starts from admitted positions. Both, \n\u003cA NAME=\"808\"\u003e\u003c/A\u003eindeed, take two premisses that are admitted, but the latter takes the \n\u003cA NAME=\"809\"\u003e\u003c/A\u003epremisses from which the syllogism starts, the former takes one of these, \n\u003cA NAME=\"810\"\u003e\u003c/A\u003ealong with the contradictory of the original conclusion. Also in the ostensive \n\u003cA NAME=\"811\"\u003e\u003c/A\u003eproof it is not necessary that the conclusion should be known, nor that \n\u003cA NAME=\"812\"\u003e\u003c/A\u003eone should suppose beforehand that it is true or not: in the other it is \n\u003cA NAME=\"813\"\u003e\u003c/A\u003enecessary to suppose beforehand that it is not true. It makes no difference \n\u003cA NAME=\"814\"\u003e\u003c/A\u003ewhether the conclusion is affirmative or negative; the method is the same \n\u003cA NAME=\"815\"\u003e\u003c/A\u003ein both cases. Everything which is concluded ostensively can be proved \n\u003cA NAME=\"816\"\u003e\u003c/A\u003eper impossibile, and that which is proved per impossibile can be proved \n\u003cA NAME=\"817\"\u003e\u003c/A\u003eostensively, through the same terms. Whenever the syllogism is formed in \n\u003cA NAME=\"818\"\u003e\u003c/A\u003ethe first figure, the truth will be found in the middle or the last figure, \n\u003cA NAME=\"819\"\u003e\u003c/A\u003eif negative in the middle, if affirmative in the last. Whenever the syllogism \n\u003cA NAME=\"820\"\u003e\u003c/A\u003eis formed in the middle figure, the truth will be found in the first, whatever \n\u003cA NAME=\"821\"\u003e\u003c/A\u003ethe problem may be. Whenever the syllogism is formed in the last figure, \n\u003cA NAME=\"822\"\u003e\u003c/A\u003ethe truth will be found in the first and middle figures, if affirmative \n\u003cA NAME=\"823\"\u003e\u003c/A\u003ein first, if negative in the middle. Suppose that A has been proved to \n\u003cA NAME=\"824\"\u003e\u003c/A\u003ebelong to no B, or not to all B, through the first figure. Then the hypothesis \n\u003cA NAME=\"825\"\u003e\u003c/A\u003emust have been that A belongs to some B, and the original premisses that \n\u003cA NAME=\"826\"\u003e\u003c/A\u003eC belongs to all A and to no B. For thus the syllogism was made and the \n\u003cA NAME=\"827\"\u003e\u003c/A\u003eimpossible conclusion reached. But this is the middle figure, if C belongs \n\u003cA NAME=\"828\"\u003e\u003c/A\u003eto all A and to no B. And it is clear from these premisses that A belongs \n\u003cA NAME=\"829\"\u003e\u003c/A\u003eto no B. Similarly if has been proved not to belong to all B. For the hypothesis \n\u003cA NAME=\"830\"\u003e\u003c/A\u003eis that A belongs to all B; and the original premisses are that C belongs \n\u003cA NAME=\"831\"\u003e\u003c/A\u003eto all A but not to all B. Similarly too, if the premiss CA should be negative: \n\u003cA NAME=\"832\"\u003e\u003c/A\u003efor thus also we have the middle figure. Again suppose it has been proved \n\u003cA NAME=\"833\"\u003e\u003c/A\u003ethat A belongs to some B. The hypothesis here is that is that A belongs \n\u003cA NAME=\"834\"\u003e\u003c/A\u003eto no B; and the original premisses that B belongs to all C, and A either \n\u003cA NAME=\"835\"\u003e\u003c/A\u003eto all or to some C: for in this way we shall get what is impossible. But \n\u003cA NAME=\"836\"\u003e\u003c/A\u003eif A and B belong to all C, we have the last figure. And it is clear from \n\u003cA NAME=\"837\"\u003e\u003c/A\u003ethese premisses that A must belong to some B. Similarly if B or A should \n\u003cA NAME=\"838\"\u003e\u003c/A\u003ebe assumed to belong to some C.\n\u003cA NAME=\"839\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eAgain suppose it has been proved in the middle figure that A belongs \n\u003cA NAME=\"840\"\u003e\u003c/A\u003eto all B. Then the hypothesis must have been that A belongs not to all \n\u003cA NAME=\"841\"\u003e\u003c/A\u003eB, and the original premisses that A belongs to all C, and C to all B: \n\u003cA NAME=\"842\"\u003e\u003c/A\u003efor thus we shall get what is impossible. But if A belongs to all C, and \n\u003cA NAME=\"843\"\u003e\u003c/A\u003eC to all B, we have the first figure. Similarly if it has been proved that \n\u003cA NAME=\"844\"\u003e\u003c/A\u003eA belongs to some B: for the hypothesis then must have been that A belongs \n\u003cA NAME=\"845\"\u003e\u003c/A\u003eto no B, and the original premisses that A belongs to all C, and C to some \n\u003cA NAME=\"846\"\u003e\u003c/A\u003eB. If the syllogism is negative, the hypothesis must have been that A belongs \n\u003cA NAME=\"847\"\u003e\u003c/A\u003eto some B, and the original premisses that A belongs to no C, and C to \n\u003cA NAME=\"848\"\u003e\u003c/A\u003eall B, so that the first figure results. If the syllogism is not universal, \n\u003cA NAME=\"849\"\u003e\u003c/A\u003ebut proof has been given that A does not belong to some B, we may infer \n\u003cA NAME=\"850\"\u003e\u003c/A\u003ein the same way. The hypothesis is that A belongs to all B, the original \n\u003cA NAME=\"851\"\u003e\u003c/A\u003epremisses that A belongs to no C, and C belongs to some B: for thus we \n\u003cA NAME=\"852\"\u003e\u003c/A\u003eget the first figure.\n\u003cA NAME=\"853\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eAgain suppose it has been proved in the third figure that A belongs \n\u003cA NAME=\"854\"\u003e\u003c/A\u003eto all B. Then the hypothesis must have been that A belongs not to all \n\u003cA NAME=\"855\"\u003e\u003c/A\u003eB, and the original premisses that C belongs to all B, and A belongs to \n\u003cA NAME=\"856\"\u003e\u003c/A\u003eall C; for thus we shall get what is impossible. And the original premisses \n\u003cA NAME=\"857\"\u003e\u003c/A\u003eform the first figure. Similarly if the demonstration establishes a particular \n\u003cA NAME=\"858\"\u003e\u003c/A\u003eproposition: the hypothesis then must have been that A belongs to no B, \n\u003cA NAME=\"859\"\u003e\u003c/A\u003eand the original premisses that C belongs to some B, and A to all C. If \n\u003cA NAME=\"860\"\u003e\u003c/A\u003ethe syllogism is negative, the hypothesis must have been that A belongs \n\u003cA NAME=\"861\"\u003e\u003c/A\u003eto some B, and the original premisses that C belongs to no A and to all \n\u003cA NAME=\"862\"\u003e\u003c/A\u003eB, and this is the middle figure. Similarly if the demonstration is not \n\u003cA NAME=\"863\"\u003e\u003c/A\u003euniversal. The hypothesis will then be that A belongs to all B, the premisses \n\u003cA NAME=\"864\"\u003e\u003c/A\u003ethat C belongs to no A and to some B: and this is the middle \n\u003cA NAME=\"865\"\u003e\u003c/A\u003efigure.\n\u003cA NAME=\"866\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is clear then that it is possible through the same terms to \n\u003cA NAME=\"867\"\u003e\u003c/A\u003eprove each of the problems ostensively as well. Similarly it will be possible \n\u003cA NAME=\"868\"\u003e\u003c/A\u003eif the syllogisms are ostensive to reduce them ad impossibile in the terms \n\u003cA NAME=\"869\"\u003e\u003c/A\u003ewhich have been taken, whenever the contradictory of the conclusion of \n\u003cA NAME=\"870\"\u003e\u003c/A\u003ethe ostensive syllogism is taken as a premiss. For the syllogisms become \n\u003cA NAME=\"871\"\u003e\u003c/A\u003eidentical with those which are obtained by means of conversion, so that \n\u003cA NAME=\"872\"\u003e\u003c/A\u003ewe obtain immediately the figures through which each problem will be solved. \n\u003cA NAME=\"873\"\u003e\u003c/A\u003eIt is clear then that every thesis can be proved in both ways, i.e. per \n\u003cA NAME=\"874\"\u003e\u003c/A\u003eimpossibile and ostensively, and it is not possible to separate one method \n\u003cA NAME=\"875\"\u003e\u003c/A\u003efrom the other.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"876\"\u003e\u003c/A\u003e\u003cB\u003ePart 15\u003c/B\u003e\n\n\u003cA NAME=\"877\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIn what figure it is possible to draw a conclusion from premisses \n\u003cA NAME=\"878\"\u003e\u003c/A\u003ewhich are opposed, and in what figure this is not possible, will be made \n\u003cA NAME=\"879\"\u003e\u003c/A\u003eclear in this way. Verbally four kinds of opposition are possible, viz. \n\u003cA NAME=\"880\"\u003e\u003c/A\u003euniversal affirmative to universal negative, universal affirmative to particular \n\u003cA NAME=\"881\"\u003e\u003c/A\u003enegative, particular affirmative to universal negative, and particular \n\u003cA NAME=\"882\"\u003e\u003c/A\u003eaffirmative to particular negative: but really there are only three: for \n\u003cA NAME=\"883\"\u003e\u003c/A\u003ethe particular affirmative is only verbally opposed to the particular negative. \n\u003cA NAME=\"884\"\u003e\u003c/A\u003eOf the genuine opposites I call those which are universal contraries, the \n\u003cA NAME=\"885\"\u003e\u003c/A\u003euniversal affirmative and the universal negative, e.g. \u0027every science is \n\u003cA NAME=\"886\"\u003e\u003c/A\u003egood\u0027, \u0027no science is good\u0027; the others I call contradictories.\n\u003cA NAME=\"887\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIn the first figure no syllogism whether affirmative or negative \n\u003cA NAME=\"888\"\u003e\u003c/A\u003ecan be made out of opposed premisses: no affirmative syllogism is possible \n\u003cA NAME=\"889\"\u003e\u003c/A\u003ebecause both premisses must be affirmative, but opposites are, the one \n\u003cA NAME=\"890\"\u003e\u003c/A\u003eaffirmative, the other negative: no negative syllogism is possible because \n\u003cA NAME=\"891\"\u003e\u003c/A\u003eopposites affirm and deny the same predicate of the same subject, and the \n\u003cA NAME=\"892\"\u003e\u003c/A\u003emiddle term in the first figure is not predicated of both extremes, but \n\u003cA NAME=\"893\"\u003e\u003c/A\u003eone thing is denied of it, and it is affirmed of something else: but such \n\u003cA NAME=\"894\"\u003e\u003c/A\u003epremisses are not opposed.\n\u003cA NAME=\"895\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIn the middle figure a syllogism can be made both oLcontradictories \n\u003cA NAME=\"896\"\u003e\u003c/A\u003eand of contraries. Let A stand for good, let B and C stand for science. \n\u003cA NAME=\"897\"\u003e\u003c/A\u003eIf then one assumes that every science is good, and no science is good, \n\u003cA NAME=\"898\"\u003e\u003c/A\u003eA belongs to all B and to no C, so that B belongs to no C: no science then \n\u003cA NAME=\"899\"\u003e\u003c/A\u003eis a science. Similarly if after taking \u0027every science is good\u0027 one took \n\u003cA NAME=\"900\"\u003e\u003c/A\u003e\u0027the science of medicine is not good\u0027; for A belongs to all B but to no \n\u003cA NAME=\"901\"\u003e\u003c/A\u003eC, so that a particular science will not be a science. Again, a particular \n\u003cA NAME=\"902\"\u003e\u003c/A\u003escience will not be a science if A belongs to all C but to no B, and B \n\u003cA NAME=\"903\"\u003e\u003c/A\u003eis science, C medicine, and A supposition: for after taking \u0027no science \n\u003cA NAME=\"904\"\u003e\u003c/A\u003eis supposition\u0027, one has assumed that a particular science is supposition. \n\u003cA NAME=\"905\"\u003e\u003c/A\u003eThis syllogism differs from the preceding because the relations between \n\u003cA NAME=\"906\"\u003e\u003c/A\u003ethe terms are reversed: before, the affirmative statement concerned B, \n\u003cA NAME=\"907\"\u003e\u003c/A\u003enow it concerns C. Similarly if one premiss is not universal: for the middle \n\u003cA NAME=\"908\"\u003e\u003c/A\u003eterm is always that which is stated negatively of one extreme, and affirmatively \n\u003cA NAME=\"909\"\u003e\u003c/A\u003eof the other. Consequently it is possible that contradictories may lead \n\u003cA NAME=\"910\"\u003e\u003c/A\u003eto a conclusion, though not always or in every mood, but only if the terms \n\u003cA NAME=\"911\"\u003e\u003c/A\u003esubordinate to the middle are such that they are either identical or related \n\u003cA NAME=\"912\"\u003e\u003c/A\u003eas whole to part. Otherwise it is impossible: for the premisses cannot \n\u003cA NAME=\"913\"\u003e\u003c/A\u003eanyhow be either contraries or contradictories.\n\u003cA NAME=\"914\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIn the third figure an affirmative syllogism can never be made \n\u003cA NAME=\"915\"\u003e\u003c/A\u003eout of opposite premisses, for the reason given in reference to the first \n\u003cA NAME=\"916\"\u003e\u003c/A\u003efigure; but a negative syllogism is possible whether the terms are universal \n\u003cA NAME=\"917\"\u003e\u003c/A\u003eor not. Let B and C stand for science, A for medicine. If then one should \n\u003cA NAME=\"918\"\u003e\u003c/A\u003eassume that all medicine is science and that no medicine is science, he \n\u003cA NAME=\"919\"\u003e\u003c/A\u003ehas assumed that B belongs to all A and C to no A, so that a particular \n\u003cA NAME=\"920\"\u003e\u003c/A\u003escience will not be a science. Similarly if the premiss BA is not assumed \n\u003cA NAME=\"921\"\u003e\u003c/A\u003euniversally. For if some medicine is science and again no medicine is science, \n\u003cA NAME=\"922\"\u003e\u003c/A\u003eit results that some science is not science, The premisses are contrary \n\u003cA NAME=\"923\"\u003e\u003c/A\u003eif the terms are taken universally; if one is particular, they are \n\u003cA NAME=\"924\"\u003e\u003c/A\u003econtradictory.\n\u003cA NAME=\"925\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eWe must recognize that it is possible to take opposites in the \n\u003cA NAME=\"926\"\u003e\u003c/A\u003eway we said, viz. \u0027all science is good\u0027 and \u0027no science is good\u0027 or \u0027some \n\u003cA NAME=\"927\"\u003e\u003c/A\u003escience is not good\u0027. This does not usually escape notice. But it is possible \n\u003cA NAME=\"928\"\u003e\u003c/A\u003eto establish one part of a contradiction through other premisses, or to \n\u003cA NAME=\"929\"\u003e\u003c/A\u003eassume it in the way suggested in the Topics. Since there are three oppositions \n\u003cA NAME=\"930\"\u003e\u003c/A\u003eto affirmative statements, it follows that opposite statements may be assumed \n\u003cA NAME=\"931\"\u003e\u003c/A\u003eas premisses in six ways; we may have either universal affirmative and \n\u003cA NAME=\"932\"\u003e\u003c/A\u003enegative, or universal affirmative and particular negative, or particular \n\u003cA NAME=\"933\"\u003e\u003c/A\u003eaffirmative and universal negative, and the relations between the terms \n\u003cA NAME=\"934\"\u003e\u003c/A\u003emay be reversed; e.g. A may belong to all B and to no C, or to all C and \n\u003cA NAME=\"935\"\u003e\u003c/A\u003eto no B, or to all of the one, not to all of the other; here too the relation \n\u003cA NAME=\"936\"\u003e\u003c/A\u003ebetween the terms may be reversed. Similarly in the third figure. So it \n\u003cA NAME=\"937\"\u003e\u003c/A\u003eis clear in how many ways and in what figures a syllogism can be made by \n\u003cA NAME=\"938\"\u003e\u003c/A\u003emeans of premisses which are opposed.\n\u003cA NAME=\"939\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is clear too that from false premisses it is possible to draw \n\u003cA NAME=\"940\"\u003e\u003c/A\u003ea true conclusion, as has been said before, but it is not possible if the \n\u003cA NAME=\"941\"\u003e\u003c/A\u003epremisses are opposed. For the syllogism is always contrary to the fact, \n\u003cA NAME=\"942\"\u003e\u003c/A\u003ee.g. if a thing is good, it is proved that it is not good, if an animal, \n\u003cA NAME=\"943\"\u003e\u003c/A\u003ethat it is not an animal because the syllogism springs out of a contradiction \n\u003cA NAME=\"944\"\u003e\u003c/A\u003eand the terms presupposed are either identical or related as whole and \n\u003cA NAME=\"945\"\u003e\u003c/A\u003epart. It is evident also that in fallacious reasonings nothing prevents \n\u003cA NAME=\"946\"\u003e\u003c/A\u003ea contradiction to the hypothesis from resulting, e.g. if something is \n\u003cA NAME=\"947\"\u003e\u003c/A\u003eodd, it is not odd. For the syllogism owed its contrariety to its contradictory \n\u003cA NAME=\"948\"\u003e\u003c/A\u003epremisses; if we assume such premisses we shall get a result that contradicts \n\u003cA NAME=\"949\"\u003e\u003c/A\u003eour hypothesis. But we must recognize that contraries cannot be inferred \n\u003cA NAME=\"950\"\u003e\u003c/A\u003efrom a single syllogism in such a way that we conclude that what is not \n\u003cA NAME=\"951\"\u003e\u003c/A\u003egood is good, or anything of that sort unless a self-contradictory premiss \n\u003cA NAME=\"952\"\u003e\u003c/A\u003eis at once assumed, e.g. \u0027every animal is white and not white\u0027, and we \n\u003cA NAME=\"953\"\u003e\u003c/A\u003eproceed \u0027man is an animal\u0027. Either we must introduce the contradiction \n\u003cA NAME=\"954\"\u003e\u003c/A\u003eby an additional assumption, assuming, e.g., that every science is supposition, \n\u003cA NAME=\"955\"\u003e\u003c/A\u003eand then assuming \u0027Medicine is a science, but none of it is supposition\u0027 \n\u003cA NAME=\"956\"\u003e\u003c/A\u003e(which is the mode in which refutations are made), or we must argue from \n\u003cA NAME=\"957\"\u003e\u003c/A\u003etwo syllogisms. In no other way than this, as was said before, is it possible \n\u003cA NAME=\"958\"\u003e\u003c/A\u003ethat the premisses should be really contrary.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"959\"\u003e\u003c/A\u003e\u003cB\u003ePart 16\u003c/B\u003e\n\n\u003cA NAME=\"960\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eTo beg and assume the original question is a species of failure \n\u003cA NAME=\"961\"\u003e\u003c/A\u003eto demonstrate the problem proposed; but this happens in many ways. A man \n\u003cA NAME=\"962\"\u003e\u003c/A\u003emay not reason syllogistically at all, or he may argue from premisses which \n\u003cA NAME=\"963\"\u003e\u003c/A\u003eare less known or equally unknown, or he may establish the antecedent by \n\u003cA NAME=\"964\"\u003e\u003c/A\u003emeans of its consequents; for demonstration proceeds from what is more \n\u003cA NAME=\"965\"\u003e\u003c/A\u003ecertain and is prior. Now begging the question is none of these: but since \n\u003cA NAME=\"966\"\u003e\u003c/A\u003ewe get to know some things naturally through themselves, and other things \n\u003cA NAME=\"967\"\u003e\u003c/A\u003eby means of something else (the first principles through themselves, what \n\u003cA NAME=\"968\"\u003e\u003c/A\u003eis subordinate to them through something else), whenever a man tries to \n\u003cA NAME=\"969\"\u003e\u003c/A\u003eprove what is not self-evident by means of itself, then he begs the original \n\u003cA NAME=\"970\"\u003e\u003c/A\u003equestion. This may be done by assuming what is in question at once; it \n\u003cA NAME=\"971\"\u003e\u003c/A\u003eis also possible to make a transition to other things which would naturally \n\u003cA NAME=\"972\"\u003e\u003c/A\u003ebe proved through the thesis proposed, and demonstrate it through them, \n\u003cA NAME=\"973\"\u003e\u003c/A\u003ee.g. if A should be proved through B, and B through C, though it was natural \n\u003cA NAME=\"974\"\u003e\u003c/A\u003ethat C should be proved through A: for it turns out that those who reason \n\u003cA NAME=\"975\"\u003e\u003c/A\u003ethus are proving A by means of itself. This is what those persons do who \n\u003cA NAME=\"976\"\u003e\u003c/A\u003esuppose that they are constructing parallel straight lines: for they fail \n\u003cA NAME=\"977\"\u003e\u003c/A\u003eto see that they are assuming facts which it is impossible to demonstrate \n\u003cA NAME=\"978\"\u003e\u003c/A\u003eunless the parallels exist. So it turns out that those who reason thus \n\u003cA NAME=\"979\"\u003e\u003c/A\u003emerely say a particular thing is, if it is: in this way everything will \n\u003cA NAME=\"980\"\u003e\u003c/A\u003ebe self-evident. But that is impossible.\n\u003cA NAME=\"981\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIf then it is uncertain whether A belongs to C, and also whether \n\u003cA NAME=\"982\"\u003e\u003c/A\u003eA belongs to B, and if one should assume that A does belong to B, it is \n\u003cA NAME=\"983\"\u003e\u003c/A\u003enot yet clear whether he begs the original question, but it is evident \n\u003cA NAME=\"984\"\u003e\u003c/A\u003ethat he is not demonstrating: for what is as uncertain as the question \n\u003cA NAME=\"985\"\u003e\u003c/A\u003eto be answered cannot be a principle of a demonstration. If however B is \n\u003cA NAME=\"986\"\u003e\u003c/A\u003eso related to C that they are identical, or if they are plainly convertible, \n\u003cA NAME=\"987\"\u003e\u003c/A\u003eor the one belongs to the other, the original question is begged. For one \n\u003cA NAME=\"988\"\u003e\u003c/A\u003emight equally well prove that A belongs to B through those terms if they \n\u003cA NAME=\"989\"\u003e\u003c/A\u003eare convertible. But if they are not convertible, it is the fact that they \n\u003cA NAME=\"990\"\u003e\u003c/A\u003eare not that prevents such a demonstration, not the method of demonstrating. \n\u003cA NAME=\"991\"\u003e\u003c/A\u003eBut if one were to make the conversion, then he would be doing what we \n\u003cA NAME=\"992\"\u003e\u003c/A\u003ehave described and effecting a reciprocal proof with three \n\u003cA NAME=\"993\"\u003e\u003c/A\u003epropositions.\n\u003cA NAME=\"994\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eSimilarly if he should assume that B belongs to C, this being as \n\u003cA NAME=\"995\"\u003e\u003c/A\u003euncertain as the question whether A belongs to C, the question is not yet \n\u003cA NAME=\"996\"\u003e\u003c/A\u003ebegged, but no demonstration is made. If however A and B are identical \n\u003cA NAME=\"997\"\u003e\u003c/A\u003eeither because they are convertible or because A follows B, then the question \n\u003cA NAME=\"998\"\u003e\u003c/A\u003eis begged for the same reason as before. For we have explained the meaning \n\u003cA NAME=\"999\"\u003e\u003c/A\u003eof begging the question, viz. proving that which is not self-evident by \n\u003cA NAME=\"1000\"\u003e\u003c/A\u003emeans of itself.\n\u003cA NAME=\"1001\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIf then begging the question is proving what is not self-evident \n\u003cA NAME=\"1002\"\u003e\u003c/A\u003eby means of itself, in other words failing to prove when the failure is \n\u003cA NAME=\"1003\"\u003e\u003c/A\u003edue to the thesis to be proved and the premiss through which it is proved \n\u003cA NAME=\"1004\"\u003e\u003c/A\u003ebeing equally uncertain, either because predicates which are identical \n\u003cA NAME=\"1005\"\u003e\u003c/A\u003ebelong to the same subject, or because the same predicate belongs to subjects \n\u003cA NAME=\"1006\"\u003e\u003c/A\u003ewhich are identical, the question may be begged in the middle and third \n\u003cA NAME=\"1007\"\u003e\u003c/A\u003efigures in both ways, though, if the syllogism is affirmative, only in \n\u003cA NAME=\"1008\"\u003e\u003c/A\u003ethe third and first figures. If the syllogism is negative, the question \n\u003cA NAME=\"1009\"\u003e\u003c/A\u003eis begged when identical predicates are denied of the same subject; and \n\u003cA NAME=\"1010\"\u003e\u003c/A\u003eboth premisses do not beg the question indifferently (in a similar way \n\u003cA NAME=\"1011\"\u003e\u003c/A\u003ethe question may be begged in the middle figure), because the terms in \n\u003cA NAME=\"1012\"\u003e\u003c/A\u003enegative syllogisms are not convertible. In scientific demonstrations the \n\u003cA NAME=\"1013\"\u003e\u003c/A\u003equestion is begged when the terms are really related in the manner described, \n\u003cA NAME=\"1014\"\u003e\u003c/A\u003ein dialectical arguments when they are according to common opinion so \n\u003cA NAME=\"1015\"\u003e\u003c/A\u003erelated.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"1016\"\u003e\u003c/A\u003e\u003cB\u003ePart 17\u003c/B\u003e\n\n\u003cA NAME=\"1017\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThe objection that \u0027this is not the reason why the result is false\u0027, \n\u003cA NAME=\"1018\"\u003e\u003c/A\u003ewhich we frequently make in argument, is made primarily in the case of \n\u003cA NAME=\"1019\"\u003e\u003c/A\u003ea reductio ad impossibile, to rebut the proposition which was being proved \n\u003cA NAME=\"1020\"\u003e\u003c/A\u003eby the reduction. For unless a man has contradicted this proposition he \n\u003cA NAME=\"1021\"\u003e\u003c/A\u003ewill not say, \u0027False cause\u0027, but urge that something false has been assumed \n\u003cA NAME=\"1022\"\u003e\u003c/A\u003ein the earlier parts of the argument; nor will he use the formula in the \n\u003cA NAME=\"1023\"\u003e\u003c/A\u003ecase of an ostensive proof; for here what one denies is not assumed as \n\u003cA NAME=\"1024\"\u003e\u003c/A\u003ea premiss. Further when anything is refuted ostensively by the terms ABC, \n\u003cA NAME=\"1025\"\u003e\u003c/A\u003eit cannot be objected that the syllogism does not depend on the assumption \n\u003cA NAME=\"1026\"\u003e\u003c/A\u003elaid down. For we use the expression \u0027false cause\u0027, when the syllogism \n\u003cA NAME=\"1027\"\u003e\u003c/A\u003eis concluded in spite of the refutation of this position; but that is not \n\u003cA NAME=\"1028\"\u003e\u003c/A\u003epossible in ostensive proofs: since if an assumption is refuted, a syllogism \n\u003cA NAME=\"1029\"\u003e\u003c/A\u003ecan no longer be drawn in reference to it. It is clear then that the expression \n\u003cA NAME=\"1030\"\u003e\u003c/A\u003e\u0027false cause\u0027 can only be used in the case of a reductio ad impossibile, \n\u003cA NAME=\"1031\"\u003e\u003c/A\u003eand when the original hypothesis is so related to the impossible conclusion, \n\u003cA NAME=\"1032\"\u003e\u003c/A\u003ethat the conclusion results indifferently whether the hypothesis is made \n\u003cA NAME=\"1033\"\u003e\u003c/A\u003eor not. The most obvious case of the irrelevance of an assumption to a \n\u003cA NAME=\"1034\"\u003e\u003c/A\u003econclusion which is false is when a syllogism drawn from middle terms to \n\u003cA NAME=\"1035\"\u003e\u003c/A\u003ean impossible conclusion is independent of the hypothesis, as we have explained \n\u003cA NAME=\"1036\"\u003e\u003c/A\u003ein the Topics. For to put that which is not the cause as the cause, is \n\u003cA NAME=\"1037\"\u003e\u003c/A\u003ejust this: e.g. if a man, wishing to prove that the diagonal of the square \n\u003cA NAME=\"1038\"\u003e\u003c/A\u003eis incommensurate with the side, should try to prove Zeno\u0027s theorem that \n\u003cA NAME=\"1039\"\u003e\u003c/A\u003emotion is impossible, and so establish a reductio ad impossibile: for Zeno\u0027s \n\u003cA NAME=\"1040\"\u003e\u003c/A\u003efalse theorem has no connexion at all with the original assumption. Another \n\u003cA NAME=\"1041\"\u003e\u003c/A\u003ecase is where the impossible conclusion is connected with the hypothesis, \n\u003cA NAME=\"1042\"\u003e\u003c/A\u003ebut does not result from it. This may happen whether one traces the connexion \n\u003cA NAME=\"1043\"\u003e\u003c/A\u003eupwards or downwards, e.g. if it is laid down that A belongs to B, B to \n\u003cA NAME=\"1044\"\u003e\u003c/A\u003eC, and C to D, and it should be false that B belongs to D: for if we eliminated \n\u003cA NAME=\"1045\"\u003e\u003c/A\u003eA and assumed all the same that B belongs to C and C to D, the false conclusion \n\u003cA NAME=\"1046\"\u003e\u003c/A\u003ewould not depend on the original hypothesis. Or again trace the connexion \n\u003cA NAME=\"1047\"\u003e\u003c/A\u003eupwards; e.g. suppose that A belongs to B, E to A and F to E, it being \n\u003cA NAME=\"1048\"\u003e\u003c/A\u003efalse that F belongs to A. In this way too the impossible conclusion would \n\u003cA NAME=\"1049\"\u003e\u003c/A\u003eresult, though the original hypothesis were eliminated. But the impossible \n\u003cA NAME=\"1050\"\u003e\u003c/A\u003econclusion ought to be connected with the original terms: in this way it \n\u003cA NAME=\"1051\"\u003e\u003c/A\u003ewill depend on the hypothesis, e.g. when one traces the connexion downwards, \n\u003cA NAME=\"1052\"\u003e\u003c/A\u003ethe impossible conclusion must be connected with that term which is predicate \n\u003cA NAME=\"1053\"\u003e\u003c/A\u003ein the hypothesis: for if it is impossible that A should belong to D, the \n\u003cA NAME=\"1054\"\u003e\u003c/A\u003efalse conclusion will no longer result after A has been eliminated. If \n\u003cA NAME=\"1055\"\u003e\u003c/A\u003eone traces the connexion upwards, the impossible conclusion must be connected \n\u003cA NAME=\"1056\"\u003e\u003c/A\u003ewith that term which is subject in the hypothesis: for if it is impossible \n\u003cA NAME=\"1057\"\u003e\u003c/A\u003ethat F should belong to B, the impossible conclusion will disappear if \n\u003cA NAME=\"1058\"\u003e\u003c/A\u003eB is eliminated. Similarly when the syllogisms are negative.\n\u003cA NAME=\"1059\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIt is clear then that when the impossibility is not related to \n\u003cA NAME=\"1060\"\u003e\u003c/A\u003ethe original terms, the false conclusion does not result on account of \n\u003cA NAME=\"1061\"\u003e\u003c/A\u003ethe assumption. Or perhaps even so it may sometimes be independent. For \n\u003cA NAME=\"1062\"\u003e\u003c/A\u003eif it were laid down that A belongs not to B but to K, and that K belongs \n\u003cA NAME=\"1063\"\u003e\u003c/A\u003eto C and C to D, the impossible conclusion would still stand. Similarly \n\u003cA NAME=\"1064\"\u003e\u003c/A\u003eif one takes the terms in an ascending series. Consequently since the impossibility \n\u003cA NAME=\"1065\"\u003e\u003c/A\u003eresults whether the first assumption is suppressed or not, it would appear \n\u003cA NAME=\"1066\"\u003e\u003c/A\u003eto be independent of that assumption. Or perhaps we ought not to understand \n\u003cA NAME=\"1067\"\u003e\u003c/A\u003ethe statement that the false conclusion results independently of the assumption, \n\u003cA NAME=\"1068\"\u003e\u003c/A\u003ein the sense that if something else were supposed the impossibility would \n\u003cA NAME=\"1069\"\u003e\u003c/A\u003eresult; but rather we mean that when the first assumption is eliminated, \n\u003cA NAME=\"1070\"\u003e\u003c/A\u003ethe same impossibility results through the remaining premisses; since it \n\u003cA NAME=\"1071\"\u003e\u003c/A\u003eis not perhaps absurd that the same false result should follow from several \n\u003cA NAME=\"1072\"\u003e\u003c/A\u003ehypotheses, e.g. that parallels meet, both on the assumption that the interior \n\u003cA NAME=\"1073\"\u003e\u003c/A\u003eangle is greater than the exterior and on the assumption that a triangle \n\u003cA NAME=\"1074\"\u003e\u003c/A\u003econtains more than two right angles.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"1075\"\u003e\u003c/A\u003e\u003cB\u003ePart 18\u003c/B\u003e\n\n\u003cA NAME=\"1076\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eA false argument depends on the first false statement in it. Every \n\u003cA NAME=\"1077\"\u003e\u003c/A\u003esyllogism is made out of two or more premisses. If then the false conclusion \n\u003cA NAME=\"1078\"\u003e\u003c/A\u003eis drawn from two premisses, one or both of them must be false: for (as \n\u003cA NAME=\"1079\"\u003e\u003c/A\u003ewe proved) a false syllogism cannot be drawn from two premisses. But if \n\u003cA NAME=\"1080\"\u003e\u003c/A\u003ethe premisses are more than two, e.g. if C is established through A and \n\u003cA NAME=\"1081\"\u003e\u003c/A\u003eB, and these through D, E, F, and G, one of these higher propositions must \n\u003cA NAME=\"1082\"\u003e\u003c/A\u003ebe false, and on this the argument depends: for A and B are inferred by \n\u003cA NAME=\"1083\"\u003e\u003c/A\u003emeans of D, E, F, and G. Therefore the conclusion and the error results \n\u003cA NAME=\"1084\"\u003e\u003c/A\u003efrom one of them.\n\u003cBR\u003e\u003cBR\u003e\n\u003cA NAME=\"1085\"\u003e\u003c/A\u003e\u003cB\u003ePart 19\u003c/B\u003e\n\n\u003cA NAME=\"1086\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eIn order to avoid having a syllogism drawn against us we must take \n\u003cA NAME=\"1087\"\u003e\u003c/A\u003ecare, whenever an opponent asks us to admit the reason without the conclusions, \n\u003cA NAME=\"1088\"\u003e\u003c/A\u003enot to grant him the same term twice over in his premisses, since we know \n\u003cA NAME=\"1089\"\u003e\u003c/A\u003ethat a syllogism cannot be drawn without a middle term, and that term which \n\u003cA NAME=\"1090\"\u003e\u003c/A\u003eis stated more than once is the middle. How we ought to watch the middle \n\u003cA NAME=\"1091\"\u003e\u003c/A\u003ein reference to each conclusion, is evident from our knowing what kind \n\u003cA NAME=\"1092\"\u003e\u003c/A\u003eof thesis is proved in each figure. This will not escape us since we know \n\u003cA NAME=\"1093\"\u003e\u003c/A\u003ehow we are maintaining the argument.\n\u003cA NAME=\"1094\"\u003e\u003c/A\u003e\u003cBR\u003e\u003cBR\u003eThat which we urge men to beware of in their admissions, they ought \n\u003cA NAME=\"1095\"\u003e\u003c/A\u003ein attack to try to conceal. This will be possible first, if, instead of \n\u003cA NAME=\"1096\"\u003e\u003c/A\u003edrawing the conclusions of preliminary syllogisms, they take the necessary \n\u003cA NAME=\"1097\"\u003e\u003c/A\u003epremisses and leave the conclusions in the dark; secondly if instea\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}}