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ARISTOTLE ON FALLACIES 
 
 OE THE 
 
 SOPHISTICI ELENCHI 
 
 WITH A 
 TRANSLATION AND NOTES 
 
 BT 
 
 EDWARD POSTE, M.A. 
 
 PELLOW OF OBIEL COLLEOE, OXFORD 
 
 
 ^wnbon 
 
 
 MACMILLAN AND 
 
 CO., __ • :^;, ./ 
 
 1866 
 
 9 
 
 />; f-^% 
 
 
 '""///(laino^^' 
 
OXFORD: 
 
 BT T. COUBE, M.A., E. PICEABD HALL, AND H. LATEAU, H.A. 
 PRINTERS TO THE UNIVERSITY. 
 
PREFACE. 
 
 Aristotle's explanation of the nature of Fallacies, 
 if not satisfactory, seems to be as complete and iatel- 
 ligible as any that has since been offered. As his doc- 
 trines, indeed, are the source and substance of those 
 of his successors, it appeared to the translator that 
 the student of this theory would prefer to resort for 
 instruction to the fountain-head, if it were made more 
 easy of access. 
 
 "Is not, however, the whole subject of Fallacies 
 somewhat trumpery, and one that may be suffered, 
 without much regret, to sink into oblivion 1" 
 
 Possibly : but besides the doctrine of Fallacies, 
 Aristotle offers either in this treatise, or in other pas- 
 sages quoted in. the commentary, various glances over 
 the world of science and opinion, various suggestions 
 on problems which are still agitated, and a vivid pic- 
 ture of the ancient system of dialectic, which it is 
 hoped may be found both interesting and instructive. 
 
 The text adopted is that of Bekker, except where emenda- 
 tion was absolutely necessary to the sense. Attention is 
 called in the Notes to all changes except mere changes of 
 punctuation. 
 
TABLE OF CONTENTS. 
 
 Chap. Pagb 
 
 1. Conception and existence of sophistry .... 2 
 
 2. Classification of reasoning 
 
 3. Five branches of sophistry ..... 
 
 4. First branch of sophistry. 
 
 Fallacies dependent on diction 
 
 5. Fallacies not dependent on diction .... 
 
 6. All the fallacies may be deduced from the definition of con- 
 
 futation ........ 
 
 7. All the fallacies arise from confusion, and must be solved by 
 distinction ........ 
 
 8. Difiierence of paralogism and sophistic proof 
 
 9. Difierence of pseudographema and sophistic proof 
 
 4 
 6 
 
 6 
 
 10 
 
 18 
 
 22 
 24 
 28 
 
 10. Examination of a division of proofs into proofs addressed to 
 
 the word and proofs addressed to the thought. 
 Distinction of dialectic and didactic . . . .30 
 
 11. Sophistic proof is simulated pirastic, or simulated scientific, 
 
 proof. 
 Distinction of sophistic and eristic, sophistic and pseudo- 
 graphic, scientific and pirastic, proof . . . .34 
 
 12. Second and third branches of sophistry. 
 
 Reduction to falsehood and paradox . . . .40 
 
 13. Fourth branch of sophistry. 
 
 Keduction to tautology or pleonasm . . . .42 
 
 14. Fifth branch of sophistry. 
 
 Reduction to solecism ...... 44 
 
vi TABLE OP CONTENTS. 
 
 „ Pagb 
 
 Chap. 
 
 15. Arrangement and tactics of the questioner 
 
 16. Utility of the study of sophistry . 
 
 19. Solution of the fallacies of homonymia and amphibolia . 
 
 20. Solution of the fallacies of composition and division 
 
 21. Solution of the fallacies of prosody . , . . 
 
 22. Solution of the fallacies of figura dictionis . 
 
 23. The solution of all fallacies dependent on diction contains an 
 
 antithesis . 
 
 46 
 50 
 
 17. Kules of answering. 
 
 The answerer must distinguish in all cases of ambiguity . 52 
 
 18. Three kinds of solution. 
 
 The solution of inconclusive reasoning is distinction : the 
 solution of conclusive reasoning is objection or counter- 
 proof 
 
 58 
 60 
 62 
 64 
 6^. 
 
 70 
 
 24. Solution of the fallacies of accidens. Examination and rejec- 
 
 tion of other solutions which refer the same examples to 
 ignioratid elenchi or homonymia . . . . .72 
 
 25. Solution of the fallacies a dicto secundum quid ad dictum 
 
 simpliciter *,....... 76 
 
 26. Solution of the fallacies of ignoratio elenchi . . . .80 
 
 27. Solution of the fallacies of petitio principii . . . .80 
 
 28. Solution of the fallacies of consequens . . . . .80 
 
 29. Solution of the fallacies of non causa pro causa . . .82 
 
 30. Solution of the fallacies of plures interrogationes . .82 
 
 31. Solution of reduction to tautology . . . .84 
 
 32. Solution of reduction to solecism . . . . .84 
 
 33. Degrees of ingenuity and difficulty of solution of fallacies . 88 
 
 34. Eecapitulatlon . 90 
 
 Notes • . . 97 
 
TABLE OF CONTENTS. vii 
 
 Pagb 
 Appendix A. 
 
 Petitio principii . . • 176 
 
 Appendix B. 
 
 Non causa pro causa 186 
 
 Appendix C. 
 
 Enstasis when a premiss is false . . . . . 192 
 
 Appendix D. 
 
 Kotrai 'Apxai, or metkod-founding principles . . . 203 
 
 § I. The dialectic maxims or loci are premisses of u,ni- 
 
 yersal, applicatioA 203 
 
 § 3. HofF far do the maxims of dialectic coincide with 
 the axioms ,of science 1 The axioms are indispens- 
 able to all reasoning, necessary^ and self-evident 
 truths r the maxims have not these characters . 207 
 
 § 3. Peculiar principles of science and dialectic. Examina- 
 tion of Mill's theory of definition . . .■ .209 
 
 § 4. The maxims are instrumental or auxiliary truths. 
 When dialectic is purely logical, the loci or topical 
 
 conceptions are the materials as well aff the instru- - 
 
 ments' of proof ". . '. . . . 210 
 
 § g. Examination of Whately's distinction of logical and 
 
 extra-logical fallacies 211 
 
 § 6. The maxims are metaphysical or ontological proposi- 
 tions 212 
 
 § 7. The loci or maxims may all be grouped under the 
 category of relation, or deduced from the definitions 
 of the predicables or from the definition of definition 214 
 
 § 8. Dialectic is based on two definitions : the definition of 
 proof supplies the loci of solution ; the definition of 
 definition supplies the loci of invention . . .217 
 
 § 9. An earlier system attempted to obtain the loci of in- 
 vention as well as the loci of solution from the 
 definition of proof 219 
 
viii TABLE OF CONTENTS. 
 
 Page 
 
 § lo. Dialectic like science is based on definitions, but on 
 definitions of a different order from those which are 
 the basis of science. Dialectic like art is based on 
 definitions of the final cause, and its maxims are 
 rather imperative than declaratory • • .221 
 
 § II. The definitions on which science is based are causal 
 propositions ; therefore the branch of dialectic em- 
 ployed to investigate the first principles of science 
 should be founded on the definition of causation . 223 
 
 § 12. Comparison of dialectic with the modern method of 
 
 scientific induction 227 
 
 § 13. Are definitions or the first principles of science sus- 
 ceptible of demonstration 1 232 
 
 § 14. Specimens of dialectic maxims formulated by the 
 
 schoolmen 236 
 
 Appendix E; 
 
 Limited competence of pirastic 239 
 
 Appendix F. 
 
 Quadrature of the circle by Hippocrates, Antipho, and 
 Bryso 245 
 
n EPi 
 
 50(DI5TIKnN EAErXQN. 
 
HEPI SOcDISTIKQN 
 
 I. Hepl 8e tZu a-o^KTTiKcav k\iy)((ii>v Kol t&u (paiuo/iivo)!/ jikv 
 fkiy)(a)u ovTcov Se irapaXoyia-fiwv aXX' ovk eXey^^eof Xeym/iev, 
 dp^dfievoi Karii cpijcni' diro tS>v rrpdiToov. 
 
 "On fikv ovv oi jikv eta-l a-v\Xoyi(r/j.oi, ol 8' ovk ovres SoKovm, 
 (pavepov Sanep ykp Kal eirl tS>v dXXaiv tovto yiuerai Sid tlvos 
 6/j,0i6t7]Tos, Kal evl rmv Xoymv dxravroos ex^'- ^*' Y^P '''V^ ^l"*^ 
 ol fiku e)(ova-iv eS ol Se ^aivovrai, </)vXeTiK&s^ ^varjcravTes Kal 
 ewiaKevdaavres airovs, Kal KaXol ol jikv Sid KdXXos ol Se <f)ai- 
 vovTai, KOfifjida-avTes * airovs. ' Eni re t&v dyfrij^cop wa-avras' 
 Kal ydp Tovrmv rd fiev dpyvpos rd Se \pv<r6i eariv dXTjOms, rd 
 S' ecTTi fiev ov, (j>aivetai Se Kard rfiv aia6rj(nv, otov rd jiev 
 XiOapyipiva Kal rd KaTTiripiva dpyvpd, rd Se y^oXo^dipiva 
 Xpvad. Tbv avTov Se Tp&irov Kal a-vXXoyi(Tfj.os Kal eXey)(oi 
 6 fiev ecTTiv, 6 S" ovk eari fiev, (fiaiperai Se Sid t^v dneipiav 
 ol ydp drreipoi mcnrep df direyovTes iroppmOev Oecepovcnv. '0 
 fiev ydp avXXoyi(r/j,os eK rivS>v earl reQevTwv more Xeyeiv 
 erepov ti k^ dvdyKrjs tS>v Keifievrnv Sid t&v Kei/ievcov eXey)(os 
 Se avXXoyicTfibs fier di/ricjidarems rov <Tv/i7repda-/j,aros. 01 Se 
 TOVTO noiovcri jiev oii, SoKovcri Se Sid TroXXds ainas' &v^ eis 
 T&iros evipvea-TaTos ea-Ti Kal Sr]fioaLa>TaTos 6 Sid tS>v ovofxaTOiv, 
 
 Eirel ydp oAk ea-Tiv avrd Td irpdy/iara SiaXeyeaOai ipipovras^, 
 aXXd ToTs ovofiaaiv dvrl twv Trpay/iaToov xpS/ieOa avfi^oXois, 
 TO crvfi^aTvov enl Tmv ovofidrmv Kal knl t&v Trpay/iaTotv riyov- 
 jieOa a-v/ifiaiveiv, KaQdnep eirl t5>v yjr'^^mv toTs Xoyi^oaevois. 
 
 To S OVK ecTTiv ojioiov. Td jiev ydp ovojiaTa ireirepavTai Kal 
 
EAErXnN. B/e^ho^^ 
 
 I. We propose to treat of Sophistical Confutations and those 
 seeming confutations which are not really confutations but para- 
 logisms^; and we thus begin, following the natural order of 
 inquiry. 
 
 The existence, over and above real proofs, of seeming but 
 unreal proofs is evident. As in other departments resemblance 
 generates semblance, so in reasoning. Bodily vigour is sometimes 
 genuine, sometimes, as in the tribal choruses, simulated by the 
 aid of dress : beauty is sometimes natural, sometimes counter- 
 feited by cosmetics. So in lifeless objects : some bodies are 
 genuine silver or gold, others are not silver or gold but 
 seem such to the sense; as litharge® and tin seem to be 
 silver, and yellow metal seems to be gold. So Proof and Con- 
 futation are either real or only seem to be such to the inex- 
 perienced. For the inexperienced resemble persons who view 
 from a distance. Proof is a tissue of propositions so related that 
 we of necessity assert some further proposition as their conse- 
 quence^. Confutation is a proof whose conclusion is the contra- 
 dictory of a given thesis. Some proofs and confutations have 
 not really these characters, but seem to have them from various 
 causes ; and one multitudinous and widespread division are those 
 that owe their semblance to names. For, not being able to 
 point to the things themselves that we reason about, we use 
 names instead of the realities as their symbols, and then the 
 consequences in the names appear to be consequences in the 
 realities, as the consequences in the counters appear to the cal- 
 culator to be consequences in the objects represented by the 
 counters. But it is not so. For names, whether simple or 
 
 B % 
 
4 HE PI IOf>IITIKiiN 
 
 TO tS,v Xoycop^ trXfjeos, to. 8e irpdyiiara rhv dpiO/iov dneipA 
 ea-TLV. 'AvayKoiov o5v irXem rhv airrov Xoyov koX Tovvofia 
 TO ty a-rj/iaiveiv. "Danep odv KUKeT ol fifj Seivol Tas fv^ovs \ 
 ^epetv iiTTO tS)v iirio'Trj/j.oveov irapaKpovovTai, tov avTov Tporirov 
 Kal eirl tS>v Xoycoy ol Tmv ovofidTcav ttjs Swafiecos aireipoi 
 irapaXoyt^ovTai. Kal avTol SiaXeyo/ifj/oi Kal dXXeov aKovovTes . 
 Aid [ikv ovv TavTijy ttjv aiTiav Kal Tds Xe)(_dr]croiJLevas earl Kai 
 (TvXXoyi.a-/ios Kal eXeyxoy (paiv6fj,evos [ikv ovk cav Se. 
 
 ' Eirel 8' ia-Ti Tieri [laXXov npo epyov to SoKeTv eivai. ao^oTs ^ 
 TO etvai Kal fir} SoKeTi/ {^ittl yap rj ao^iaTiK^ (paivofievi] ao^ia 
 ovaa S" oxj, Kal 6 o-o^iaTfjS ^rifiaTia-T^s dnb (f)aiyo/iivr)S ao(pias 
 aXX OVK o^a-rjs), SrjXoy oti dvayKoiov tovtols Kal to tov ao<pov 
 epyov SoKuv iToieiv /idXXou ^ woietv Kal ji-q SoKety. 'EaTi 8' 
 &s ev Trpbs ev elneiy epyov irepl eKacrTOv tov elS&ros d'^evSetv 
 /lev avTov rrepl &v oTSe, tov Se ^evSo/ievov eii(f>avi^eiv SvvacrOai. 
 Tavra 8' eaTi to fiev ev Tea SvvaaOai 8ovvai Xoyov, to 8' kv T^ 
 Xa^elv^^. 'AvdyKt] ovv tovs ^ovXo/ievovs a-o<f)i<TTeveiv to twv 
 eiprj/jLevcav Xoycov yevos ^rfTelv irpb epyov yap eariv 17 ydp 
 ToiavTT] Svva/iis ^^ iroiijaei (paiveadai ao^ov, oS Tvyydvovai. Trjv 
 TTpoaipecriv e^^ovres. 
 
 "Oti (lev ovv eari ti toiovtov Xoycov yevos, Kal oti ToiavTrjs 
 e^ievTai 8vvd/iems of>s KaXov/iev aoipLa-Tds, 8rjXov noaa 8' earlv 
 ei8rj tZv Xoycov toiv aocftia-TiK&v, Kal e/c iTocrcov tov dpiOjiov 
 rj 8{jvafiLS aijTr} avveaTrjKe, Kal irocra fiepr] Tvyydvei Trjs npay- 
 ftaTeias ovTa, Kal nepl t&v aXXcov tS>v avvTeXovvTCov els Trjv 
 Texfrjv Ta^TTjv ^Srj Xeyco/iev. 
 
 II. "EcTTi 8^ Twv ev tS 8iaXeye(rdai Xoycov Terrapa yevrj, 
 Si8aaKaXiKol Kal SiaXeKTiKol Kal veipacmKol Kal epia-TiKoi, 
 
 AiSaaKaXtKol jxkv ot eK Toav oUemv dp)(6ov eKaarov fiaBrj- 
 fiaTOS Kal oiiK eK Tcav tov dvoKpivo/ievov 8o^mv auXXoyi^o/ievoi 
 {Set ydp mcTTeveiv tov fiavOdvovra), 
 
 AiaXeKTiKol 8" 01 eK Tmv ev86^<ov crvXXoyicrTiKol dvTickd- 
 trecos, 
 
EAETXnN. 5 
 
 complex, are finite, realities infinite; so that a multiplicity of 
 things is signified by the same simple or complex name. As, 
 then, in calculation, those who are unskilled in manipulating 
 the counters are deceived by those who are skilled, so in reason- 
 ing, those who are unacquainted with the power of names are 
 deceived by paralogisms both when they are parties to the con- 
 troversy and when they form the audience. From this cause, 
 and others to be enumerated, there exist proofs and confutations 
 that are apparent but unreal. 
 
 Now it answers the purpose of some persons rather to seem 
 to be philosophers and not to be than to be and not to seem; 
 for Sophistry is seeming but unreal philosophy, and the Sophist 
 a person who makes money by the semblance of philosophy with- 
 out the reality ; and for his success it is requisite to seem to per- 
 form the function of the philosopher without performing it rather 
 than to perform it without seeming to do so. Now, if we define 
 by a single characteristic, the function of a man who knows 
 is to declare the truth and expose error respecting what he 
 knows. The former of these powers is ability to stand examina- 
 tion in a subject, the latter is ability to examine another who 
 professes to know it. Those, then, who wish to practise as 
 Sophists wiU aim at the kind of reasonings we have described, 
 for it suits their purpose, as the faculty of thus reasoning pro- 
 duces a semblance of philosophy, which is the end they propose. 
 
 The existence, then, of such a mode of reasoning, and the fact 
 that such a faculty is the aim of the persons we call Sophists i^, 
 is manifest. The various kinds of sophistical reasoning, the 
 branches of the sophistical faculty, the various elements of the 
 sophistical profession, and the other components of the art, 
 remain to be examined ^*. 
 
 II. Reasonings in the form of dialogue may be divided into 
 four orders. Didactic, Dialectic, Pirastic, and Eristic ^ 
 
 Didactic reasonings conclude from the scientific principles ap- 
 propriate to a subject, and not from the answerer's opinions, for 
 the learner is required to believe ^ : , 
 
 Dialectic employ as premisses probable propositions and con- 
 clude in contradiction to a thesis : 
 
6 HEPI IO<t>IITIKnN 
 
 PeipaaTiKol S' oi e/c tS>v Sokovvtw t£ diroKpivo/ievcp Kal 
 dvayKaiwv elSivai tS irpoo-TroLovixivc^ e)(eiy Tf]v em<rTr]fJ.riv ^ov 
 rp&irov 8i, SiwpicrTai kv iripois), 
 
 'EpiariKol 5* oi kn tS>v ^aivojxkvcov kvSo^mv fif] ovtwv Se 
 trvWoyiariKol i/j (paivo/ievoi avWoyiariKoi. 
 
 riepl fikv ovv tS>v dnoSuKTiKSiv kv rofy ' AvaKvTiKois dprjrai, 
 Trepl 8e rwy SiaKeKTiKcav Kal ireipaafiKcav kv TOis aWois' nepi 
 8e tS)v dycovKTTiKmv Kal kpiariKtov vvv Xiywfiev. 
 
 III. ripwTov St) XrjTrrkov iroaoDv crToya^ovTai oi kv rois 
 Xoyois dycavi^ojxevoi Kal Sia<pi\oveiKovvTes. "Ecrri 8e nkvTe 
 Tavra tov dpidftov, eXey^oy Kal ylrevSos Kal wapdSo^ov Kal 
 (ro\oiKL(rfibs Kal irk/iTTTov to TTOt^cat d8o\e<r\fj(rai rbv wpocr- 
 8ia\ey6/ievov (tovto S" ka-rl to iroWaKis dvayKa^eaOai TavTO 
 Xeyeiv)' ^ to fir} 6v, dWb, to (paLfOfMevov sKaarov etvai tovtcov. 
 MaXicTTa fiev yap irpoaipovvTai ipaivetrdai kXkyypvTis, SevTe- 
 pov 8e ■^evSop.evov tl SeiKvvvai, Tpvrov els irapaSo^ov dyuv, 
 TerapTov 8e croXoiKi^eiv ttoisTv (tovto 8' kaTl to Troiija-ai Trj 
 Xe^ei ^apPapi^eiv eK tov Xoyov tov dnoKpivojiivov), TfXev- 
 TaTov 8€ TO nXeovaKis TaiiTo Xeyeiv. 
 
 IV. TponoL 8" elal tov fiev kXey)(eiv Svo' oi fiev yap 
 eicTi Trapb, Trjv Xe^tv, ol S" e^m Trjs Ae^ews. " Eottl 8e tA fiev 
 ■jTapk TTjv Xe^LV kfiTTOiovvTa t^v ^vTacrtav %^ tov dpiBjioV 
 TavTa 8' karlv 6/j,a>vv/j.ia, dfKpi^oXia, avvdeais, SiaCpecris, 
 npoa^Sta, a^rj/ia Xi^ems. Tovtov 8e tticttis ^ T€ Sia Trjs 
 kirayoDyfjs Kal avXXoyia-fiSs, dv re Xri^Qfj tls dXXos, Kal 
 oTi ToaavTa'^ms av rots aiiToTs ovofiaai Kal Xoyois firi Tairrh 
 8r]XoocraLiiev. 
 
 Eicrl 8e irapk fiev t^v Sficovv/jiiav oi ToioiSe tcov Xoywv, olov 
 OTi ixavOdvovaiv ol knia-Td/jtevof tA yap dnoaTOfiaTi^ofieva ^ 
 p.av6dvovaiv ol ypap-fiaTiKoi. To yap fj.av6dveiv d/iwvv/jiov, to 
 re iwievai xP^t^^'^O" W kniaTrj/jiri Kal to Xa/i^dveiv km- 
 aTTj/iriv. < 
 
 Kal irdXiv otl to. Aca/ca dyaBd- to. yap SkovTa dyaOd tA 8e 
 KaKOL 8eovTa^, Aittov yctp Th 8eov, to t' dvayKaiov, h auu- 
 
EAErXQN. 7 
 
 Pirastic employ as premisses the opinions of the answerer on 
 points that ought to be known by th%pretender to science, with 
 the limitations elsewhere mentioned ^ : 
 
 Eristic conclude from premisses which seem but are not 
 probable, or only seem to conclude from probable premisses. 
 
 Demonstrative reasonings having been discussed in the Analyt- 
 ical, Dialectic and Pirastic elsewhere, contentious and Eristic 
 reasonings remain to be investigated. 
 
 III. Wb must first enumerate the objects aimed at when dis- 
 putants are contentious and fight for victory. They are five : 
 to confute the opponent, to drive him into false proposition, to 
 drive him into paradox, to reduce him to solecism, and to reduce 
 him to pleonasm, that is, to superfluous repetition : or the sem- 
 blance of any one of these achievements without the reality. 
 The end most desired is to confute the answerer, the next to 
 shew that he holds a false opinion, the third to lead him into 
 paradox, the fourth to land him in solecism, that is, to shew 
 that his expression involves a violation of the laws of grammar, 
 the fifth to force him to unmeaning repetition. 
 
 IV. Seeming confutations fall under two divisions; those 
 where the semblance depends on language, and those where it 
 is independent of language. Language produces a false sem- 
 blance of ratiocination from six causes ; the ambiguity of a term, 
 the ambiguity of a proposition, the possibility of wrong disjunc- 
 tion, the possibility of wrong conjunction, the possibility of 
 wrong accentuation, and similarity of termination. This classi- 
 fication may either be established by inspection of instances, or 
 may be deduced (not to exclude other modes of deduction) from 
 the fact that there are just so many ways by which a single 
 term or proposition may have a plurality of meanings. ' 
 
 Ambiguous terms may be found in the following instances : — 
 Those that learn are those that already know, for it is those that 
 know the use of the alphabet who learn (can write or spell) what 
 is dictated. " Learn" is ambiguous, signifying either to appre- 
 ciate, that is, to employ knowledge, or to acquire knowledge. 
 
 Again : — ^Evil is good, for what is necessary is good, and evil is 
 necessary. " Necessary" is ambiguous, meaning either the result 
 
8 HEP I IO<t>IITIKnN 
 
 ^aivec TToWaKis Kai enl tZv KaKmv {ivTi yap KaKov Ti avay- 
 KoiovS, Kal rdyaOit, 8e SiovToi ^afiev eivai. 
 
 "En Tov aiirhv Ka6fja-6ai Kal iardvai, Kal KafiviLV Kal vyi- 
 atveiv. "Otnrep yap dviaraTo, ea-rriKev, Kal ocrrrep iyid^ero, 
 iyiaivei- dviaraTO S' 6 KaOrmevos Kal iyid^ero 6 Kdjivmv^. 
 To yap TOV Kdjivovra otlovv ttoiuv ^ irda^eLv ovx e«' o''7/*a'»'e', 
 dX\' ori /iev 8ti 6 vvv Ka/ivcav ^ Ka6ijfi€vos, ore S" os eKa/ive 
 irpSrepov. HXrjv vyid^ero* jjikv Kal Kdfivmv Kal 6 Kd/iva>v 
 iyiaivei S' oii Kafivayv dW' 6 Kdfivmv ov vvv oKKa irp&repov. 
 
 fJapii, Se rriv d/i^t^oXiav oi ToioiSe, to ^o-uXeaBai Xa^eTv fif 
 Toiis iroXe/iiovs. 
 
 Kal dp' o Tis yivaxTKei, tovto yivdxTKei ; Kal yhp tov yivw- 
 (TKOvTa Kal to yivaxTKOfievov kvBi^erai my yivataKovTa arjjifjvai 
 TOVTO) Tffl X6ya>^. 
 
 Kal dpa 8 opa tis, tovto 6pa ; Spa Se tov klovu, &<tt€ Spa 6 
 Kimv ". 
 
 Kal dpa 8 (yii (f)^s eivai, tovto ai) ^^s eTvai ; ^^y Se XiOov 
 eivai, ai) dpa 0^y Xi6os eivai ''. 
 
 Kal dp e<TTi (riyrnvra Xeyeiv ; Sittov ydp Kal to aiyStvTa 
 XeyeLv, to re tov XeyovTa aiydv Kal to to, Xeyofieva ®. 
 
 EM Se TpeTs Tpoiroi t&v napd t^v oficovvfiiav Kal ttjv d/i^i- 
 PoXiav, ets (lev orav fj 6 Xoyos ^ ToiSvofia Kvpims (rrj/iaipri 
 irXeico, oiov aeroy Kal kvcov eis Se oTav etmOoTes &/iev ovt<o 
 Xeyeiv TpiTOS Se orav to crvvTedev wXeiw crrjfiaivri, KeywpKTjie- 
 vov Se anXw, oiov to eiriaTaTaL ypd/ifiaTa. ' EKo/repov fiev 
 yap, el eTvy^ev, ev Ti a-r]fj.aivei, to eirivTaTai Kal Td ypdfifiaTa- 
 d/j.(f)Ci> Se irXeim, ^ to tA ypd/ifiara avrd eiriaTrifirjv e)(etv ^ 
 T&v ypaiifidTcav dXXov. 
 
 n fiev ovv d/M^i^oXia Kal S/icowfiia napd tovtovs roils Tp6- 
 TTOvs ea-Tiv, napd Se Tr)v avvQemv Td ToidSe, oiov to SvvaaBai 
 KaOrJuevov ^aSi(eiv Kal jirf ypd<povTa ypdcpeiv. Ov ydp tovto 
 a-rifiaivei, &v SteXcov tls einr} Kal tnvdek, m Swutov tov 
 KaOrjfievov ^aSi^etv Kal fir) ypd^ftovTa ypdcpeiv Kal rovQ' dxr- 
 avTCos dv Tis a-vvBfj, tov nfj ypd^ovra ypdcpeiv a-ri/iaivei ydp 
 
EAErXDN. 9 
 
 of antecedent conditions^ and this may be evil, or the condition 
 of a desirable result, which is a good. * 
 
 Again : — ^The same person is standing and sitting, and is an 
 invalid and restored to health. For he who rose up is standing, 
 and he who was getting well is restored to health. But it was 
 the sitter who rose up, and the invalid who was getting well. 
 Invalid and sitter mean respectively more than one person, both 
 him who is now an invalid or sitting, and him who was formerly 
 an invalid or sitting. He who is getting well may be now an 
 invalid, but he who is restored to health can only have been 
 formerly an invalid. 
 
 Of ambiguous propositions the following are instances. I 
 hope that you the enemy may slay. 
 
 Whom one knows, he knows. Either the person knowing 
 or the person known is here affirmed to know. 
 
 What one sees, that one sees : one sees a pillar ; ergo, that 
 one pillar sees. 
 
 What you are holding, that you are : you are holding a stone : 
 ergo, a stone you are. 
 
 Is a speaking of the silent possible ? " The silent" denotes 
 either the speaker or the subject of speech. 
 
 There are three kinds of ambiguity of term or proposition. 
 The first is when there is an equal linguistic propriety in several 
 interpretations; the second when one is improper but customary; 
 the third when the ambiguity arises in the combination of ele- 
 ments that are themselves unambiguous, as in " knowing letters." 
 "Knowing" and "letters" are perhaps separately unambiguous, 
 but in combination may imply either that the letters are known 
 or that they themselves have, knowledge. Such are the modes 
 in which propositions and terms may be ambiguous. 
 
 Wrong conjunction is the source of fallacy in the following in- 
 stances. A man can walk when sitting or write when not writing. 
 The meaning is different according as " sitting" is joined with 
 
10 HEP I IO<l>IITlKnN 
 
 toy ex" Svvaniv rov fir) ypdipovra ypd<j>iiv^ ^'""' * /'v 
 avv6fj, oTi e^et Svvajiiv, ore ov ypd^ei, rov ypacpeiv. 
 
 Kal [lavOdvei vvv ypd/ifiara, einep kiidvOavev & km(TTaTai^^. 
 "En TO ev jiovov Swd/ievov ^epeiv noXXa SvvaaOai ^epeiv. 
 
 riapa Se Tr)V Siaipeaiv, on ra nevT earl Svo Kal rpia, Kal 
 wipiTrii Kal dpna. Kal rb /leT^ov i<rov Toaovrov yap Kal ert 
 Trpos. '0 yiip avTOS \6yos Sirjprjfievos Kal avyKeL/jLevos ovk 
 del ravTo ar/fiaiveiv av So^eiev, otov " eyd> a eOrjKa SovXov opt 
 eXevOepov ^^," Kal to " irevTriKovT dv8pS>v eKUTOP Xiire Sioi 
 'AxiXXevs." ' ,, 
 
 Papa 8e Tfjv irpoaaiSiav ev jiev tois avev ypa(f>fjs SiaXeKTi- 
 KoTs 01) paSiov iroirjcrai Xoyov, kv Se toTs yeypafi/jtevois Kal 
 TTOirjiiaai /laXXov, otov Kal Tov"Ofn}pov euioi SiopOovvTai irpos 
 Toiis eXeyypvTas eby droncos eiprjKOTa " to /lev o5 KaTairvOeTai 
 ofi^pm." Avovai yap airrb rfj TrpotrcoSca, Xeyovres rb oil o^v- 
 repov. Kal rb irepl rb kvmrviov rov ' Ayafie/ivovos, on ovk 
 aiirbs 6 Zeds einev " SiSofiev Si ot eu^oy dpeaOai" dXXa ra 
 kvvnvico evereXXero SiSSvat. T& jxev o5p roiavra Trapa rfjv 
 irpoamSiav ecrriv. i 
 
 01 Se wapa rb a-yrjjia rijs Xe^eoos (TVii^aivovaiu, orav rb nrj 
 ravrb ma-avrms epjxrjvevrirai., otov rb dppev 6fjXv ^ rb OrjXv 
 dppev, fj rb fiera^i) Odrepov rovTcov, irj ndXiv rb iroibv irotrbv 
 fj rb TToabv noiov, ^ rb iroiovv nd(T)(^ov ^ rb SiaKei/ievov noieiv, 
 Kal rdXXa S , wy Si^prjrai nporepov. "Eari yap rb fir] rwv 
 TToieTv ov d)S t5>v iroieiv ri rfj Xe^ei a-rj/iaiveiv. Otov rb vyiai- 
 veiv ofioims rm airman rrjs Xe^ems Xiyerai rm re/Jiveiv ^ oiko- 
 Sofieiv Kairoi rb jxev ttolov ri Kal SiaKeifievov irms SrjXoi, to 
 Se TTOieTv ri. Tbv aiirbv Se rpimov Kal kwl rwv dXXcov. 
 
 V. 01 fiev ovv Trapa Tfjv Xe^iv eAeyxot e/f tovtcov t5>v 
 ronwv ela-LV rmv S' e^co rfjs Xe|ea)y napaXoyia-fimv etS-q karlv 
 enrd, %v /lev Trapa rb a-Vfi^e^riKos, Sevrepov Se rb aTrXms V fifj 
 ajrXZs dXXa irfj rj ttov ^ nore ^ Trpos n Xkyea-Qai, rpirov Se rb 
 Trapa Tr)v rov kXiyxov dyvoiav, reraprov Se rb Trapa rb eTrS- 
 
EAErxnN. 11 
 
 " can^^ or with " walkj" and " not writing^' with "can" or with 
 "write." • 
 
 He knows the alphabet he had to learn. 
 
 The lesser weight if you can hardly lift the greater weight you 
 easily can lift. 
 
 Of wrong disjunction the following are instances. Five is 
 two and three : therefore five is even and odd ^^. The greater 
 is equal to the less, for the greater is as much as the less— 
 and something more. For the same words have different mean- 
 ings when joined and disjoined ; as, I made thee a slave origi- 
 nally free. Fifty warriors with Achilles fought a hundred of 
 them hit the dust. 
 
 Accentuation in unwritten discussion can hardly furnish a 
 fallacious reasoning, but only in written controversy and criti- 
 cism on the poets. Homer ^^, for instance, is emended against 
 those who condemn the expression, "part thereof is rotten by 
 the rain." Some meet the criticism by substituting an acute 
 accent for the circumflex, making him say, " nought thereof is 
 rotten by the rain." Again, in Agamemnon^s dream, instead 
 of making Jove say, " I grant him triumph o'er his foes,'''' they 
 make Jove command the dream to promise Agamemnon triumph 
 o'er his foes ^*- These arguments, then, turn on accentuation. 
 
 Similarity of termination produces fallacy when unlike things 
 have names with a like inflexion, a male object a feminine name, 
 a female object a masculine name, or a neuter a masculine or 
 feminine ; or when a quantity has a name with the termination 
 of a quality, or a quality a name with the termination of a 
 quantity, or an agent a name with the termination of a patient, 
 or a state a name with the termination of an action, and so 
 on throughout the categories before enumerated ^^. For the 
 name of what is not an action may terminate like a name of 
 action, as " ailing" resembles in inflexion " cutting" and " build- 
 ing,'" though it expresses a quality or state, while they express 
 actions, and so in the other categories. 
 
 V. Language, then, furnishes occasion for seeming confuta- 
 tions in the modes we have mentioned. Independent of lan- 
 guage, there are seven classes of paralogism arising from the 
 equation of subject and accident ; from the confusion of an 
 absolute statement with a statement limited in manner, place. 
 
12 nEPI 20<t>IITIKDN 
 
 fievop, nifiTTTov Si to irapbi rh kv dpxv Xaii^dveiv, ?ktou Sk rh 
 fifl airiov &s airiov rMvai, ^pSofiov Sk rh rh nXem tpcoT^iiara 
 if TTOieTv. 
 
 01 fiev ovv napdi. to avfi^ePriKos^ vapaXoyia-fioi eicnv, orav 
 ofioitos oTLovv d^LCoOrj TOO Trpdy/iaTi Kol ra crvfi^eprjKOTi tmap- 
 Xeir. 'Enel yap Tm avTm iroWa avfi^e^riKev, ovk dvdyKr\ 
 irdai Toty KaTtjyopovfievois, /cat Ka6' oS KaTrjyopeiTai, ravTh 
 ■ndvTa imdpyf.iv. Olov el 6 KopiaKos eTepov dvOpmrov, avTm 
 aiiTov sTepos' ecrTi yhp dvOpamos. *H el ZeoKpaTovs erepoi^ 
 6 Se ZcoKpdTTis dvOpcoTTOs, eTepov dvdpmrov ipaa-lv &fioXoyriKevat 
 Sia TO arvfjLpe^rjKevai., ov e(pr]a'ev eTepov eivai,- tovtov eivat 
 dvdpamov. 
 
 01 8e wapa to dnXms ToSe ^ nrj XeyeaBai Kal iifj Kvpim, 
 oTav TO kv fiepei Xey6fievov d>s awXas elprjftevov Xri<p6rj, oiov 
 el TO fji^ OV e<7Ti 8o§a(rT6v, on to /j,^ tv ea-Tiv oii yhp Tavrov 
 elvai re ti koI elvai anXms. *H irdXiv oti to hv ovk ecmv ov, 
 ei Tmv ovTCiv ti fir) k<TTiv, oTov el fifj dv6pmro9. Ov ydp Tavro 
 Hfj eivai ti Kal dnXms firj etvai.' ^atveTai Se Sih to Trdpeyyvs 
 TTJs Xe^eeos, Kal fiiKpov Si.a<f)ep€iv to elvai ti tov elvai Kal to jir) 
 elvai Ti TOV firi elvai. '0/j.oi(os Se Kal to irapb, to irrj Kal to 
 airXm. Oiov el 6 'IvSbs oXos /leXas av XevKos eari Tois 
 oSovTas' XevKos dpa Kal ov XevKos ko'Tiv, *H el d/i<pa> ttJ, 
 OTi afia Td kvavTia iwdpyei. To Se toiovtov kw kviwv fiev 
 TravTl Oecopjja-ai ^aSiov, olov el Xa^mv tov A lOiona elvai fieXava, 
 Tois oSovTas epoiT el XevK6s' el ovv TavTrj XevKos, on /leXas 
 Kal ov /leXas oi'oiTO SieiXeyOai, avXXoyia-TiK&s TeXeimaas t^v 
 ep&TTja-iv. Bit kvuov Se XavOdvei iroXXaKis, k<f)' oamv, OTav 
 TTTj XeyrjTai, k&v to dwXmi So^eiev aKoXovQelv, Kal kv oaois fifj 
 paoiov Oecopfjcrai norepov aiiToov Kvpims diroSoTeov. FiveTai 
 Se Tb TOIOVTOV kv oTs ofioicos inrdpxei Ta dvTiKeijxeva- SoKeT yap 
 fj d/j,^ fj fiTjSeTepov SoTeov dirXms elvai KaTtjyopeTv, olov el 
 TO fiev rj/iitrv XevKov to S" ij/jiiav jxeXav, woTepov XevKov fj 
 fieXav ; 
 
EAErXDN. 13 
 
 time, or relation ; from an inadequate notion of confutation ; from 
 a conversion of consequent and antecedent; from begging the 
 question; from taking what is not a cause for a cause; and, 
 lastly, from putting many questions as one. 
 
 The equation of suhject and accident occasions fallacy when 
 it is assumed that subject and accident have all their attributes 
 in common. For a subject has many accidents, and it is not 
 necessary that the accidents and the subject should have all their 
 attributes in common. For example, if a man is not Coriseus 
 it does not follow that Coriseus is not Coriseus because Coriseus 
 is a man ^ : nor, because Coriseus is not Socrates and Socrates 
 is a man, does it follow that Coriseus is not a man, because 
 Socrates, who is denied of Coriseus, is an accident of man ^, 
 
 Confusion of absolute, and qualified or limited, statements gives 
 rise tor fallacy when the mere copula is taken as affirming abso- 
 lute existence ; when, for instance, from the premiss, that what 
 is not, is believable, we infer that what is not, is ; for the copula 
 affirms merely a relation, not absolute existence : or, again, if 
 we infer that what is, is not, because it is not a man or some 
 particular thing; for not to be a particular thing is not the 
 same as absolutely not to be. The semblance of identity is 
 produced by the similarity of the expressions and the slightness 
 of the difference between the enunciation of existence and attri- 
 bution, or of non-existence and non-attribution, or between 
 restricted and unrestricted predication. If, for instance, the 
 Indian is black generally, but white in respect of his teeth, it 
 may be argued that he is white and not white ; or, if he has 
 both attributes in different respects, that contraries coexist. The 
 difference in some eases is easily perceive4 ; as, for instance, if 
 from the premisses that the Ethiopian is black, and that his 
 teeth are white, one should fancy he had proved that he is 
 black and not black, putting the propositions into syllogistic 
 form. But it is often difficult to detect, when a qualified pre- 
 miss is conceded but the unqualified proposition seems to 
 follow*, and when it is difficult to say which alternative is 
 properly affirmed; as happens when opposite qualities equally 
 exist ; for it seems as if either both or neither may be absolutely 
 affirmed. If,, for instance, half is white and half is black, which 
 is the whole to be called, white or black^ ? 
 
14 nEPI lO^IITIKDN 
 
 01 S'e irapii. rh /ifj di(opia-6ai ri kcrri avX\oyi<riJ.hs fj t[ 
 eXfyxos, dXX^ Ttaph t^v iXXei^Lv yivovTM rod Xoyov. "EXeyxoi 
 likv y&p dvTi^aa-is rod avrov koI evos, M ovofiaros dXX^ 
 rrpdy/j.aTos, Kal ovojiaros /xfj arvvtavv/iov dXXh tov avrov, (k tcov 
 SoOiVTCov, ei dvdyKTis, fJ.fi crvvapi6/j.ov/ievov rov kv dpxn, Karh- 
 ravTo Kal npos ravrb Kal axravTm^ Kal kv Tcp avTa> Xpova. 
 Tbv avrov Se rp&jTov Kal ro \freva-acr6ai irepi tlvos. Evtoi 
 Se aTToXtnovres ri ra>v Xex^evrmv ^aivovrai eXey^etj/, otov on 
 ravro SiwXdaiov Kal ov SirrXdcnov ra ycip Svo rov jikv ivh 
 8iirXd<ria, r&v Se rpiaiv ov SiirXdaia. *H el rb aiirb rov 
 avrov SinXdaiov Kal ov SiTrXdcriov, dXX ov Karai, ravror Kara 
 jiev yap rb firJKOs SirrXdcnov, Karh Se rb irXdros ov SiirXdariov. 
 *H el rov avrov Kal Kara ravrb Kal maavrms, aXX' ov^ dfiw 
 SioTrep ka-rl (paivo/ievos eXey^os. "EXkoi^ 8' dv ris rovrov Kal 
 eh rois irapa rfjv Xe^iv. \ 
 
 01 Se irapbi, rb kv dp^jj Xa/x^dveiv yivovrai fiev otjrm kuI 
 roaavray&i 6(rayS>S evSeyerai rb k^ dpyrjs alreiadai, (pai- 
 vovrai S kXeyx^iv Sia rb firj Svvacrdai avvopav rb ravrbv Kal 
 rb erepov. 
 
 Se wapd rb errojievov eXey^oy Sia rb oieaOai dvriarpecfteiv 
 rrjv dKoXovOrjatv. "Orav yccp rovSe ovros k^ avdyKr/s roSl 5, 
 Kal rovSe Svros olovrai Kal Qdrepov eivai k^ dvdyKtjS. "OOev 
 Kal at irepl rfjv So^av eK rfjs ala-OrjiTems dwdrai yivovrai. 
 UoXXdKii yap rfjv )(o^W )"^^' inriXa^ov Siii rb eweaBai rb 
 ^avObv XjOft'A'a tw fieXirr Kal krrel avfi^aivei rfjv yfjv vaavTOi 
 yivecrOai Sid^po^ov, k&v' ^ Sid^po^os, inroXafiPdvoiJiev Saai. 
 Tb S ovK dvayKaiov. Ev re roTs prjropiKoTs at Karit ro 
 <rri/ieTov diroSei^eis kK rcav kTro/iivmu elcriv. BovXofievoi, yhp 
 SeT^ai Sri fioi^os, rb kirofievov eXafiov, on KaXXamia-r'qs rj on 
 vvKrcop opdrai nXavSfievos. floXXoTs S^ ravra fiev indp-vei, 
 rb Se Kartjyopovfievov oiix ivdpxei. 'Ofioioos Se Kal kv roTs 
 avXXoyia-TiKoTs, otov 6 MeXia-a-ov Xoyos 8ri aireipov rb dirav 
 Xa^av TO /lev dvav dyevqrov {eK ydip fir) Svros ovSev Siv 
 yevea-Oai), rb Se yevo/ievov e| dp^Vf yeveaOai. El fifj qSv 
 
EAErxnN. 15 
 
 other fallacies arise from not defining proof or confutation, 
 and neglecting some element of the d^nition. To confute is 
 to contradict one and the same predicate, not only the name 
 but also the reality, and not only a synonymous name but the 
 identical name, as a necessary consequence of the premisses, not 
 including the point to be proved, in the identical respect, rela- 
 tion, manner, and time in which the predicate is affirmed by 
 the opponent. The same limitations are required in defining 
 false proposition. Sometimes a man omits one of the elements, 
 and then appears to confute, proving, for instance, that the 
 same thing is double and not double, because two is the double 
 of one and not the double of three j or that the same is double 
 and not double of the same correlative but not in the same 
 respect, double in length but not in breadth; or double of the 
 same correlative in the same respect and manner but not at 
 the same time, whereby the proof is vitiated. With some 
 violence we might put this class under the head of fallacies 
 dependent on language. 
 
 Fallacies from assuming the conclusion fall into as many 
 classes as there are modes of assuming the conclusion. The 
 semblance of proof arises from the difiiculty of deciding what 
 is dififerent or identical''. 
 
 A consequent gives rise to fallacy because the consecution 
 of consequent and antecedent seems reciprocal. If B follows 
 from A we imagine that A must follow from B. Hence mis- 
 taken perception in sensation, as when gall is mistaken for 
 honey because it is yellow ; and because rain wets the ground, 
 wetness of the ground is supposed a proof of rain. In rhetorical 
 argument proof by signs* is based on consequences, as a man is 
 proved to be an adulterer by the characteristics of the adulterer, 
 dressing elaborately or wandering at night, which facts may be 
 true while the accusation is false. So in dialectic reasoning. 
 Melissus in his proof of the infinite extension of the universe 
 assumes that the universe is not generated, because from nothing 
 nothing can be generated, and that what is generated has a 
 beginning (is finite in space), and concludes that the universe 
 has no beginning, and therefore is infinite in space. This does 
 not follow. Because whatever is generated has a beginning. 
 
16 HEPI IO<PIITIKnN 
 
 yiyoviv, ap^^v ovk ?x" to nav, &<tt direipov. Ovk dvdyKt, 
 Se TovTo o-v/M^aiveiv ov yap d to yevS/Jievov airav dpx^v eX", 
 Kal ei Ti dpxfiv exet, yiyovtv, wanep oiiS' €t o irvpfrrmv 
 Gepfios, Kal Tov depfibv dvdyKr) TTvperTeiv. 
 
 '0 Se irapa rh jirj atriov my aiTiov, orav TrpO(r\r]<j)6^ ri 
 dvairiov &s nap eKeivo yivofiivov tov iXeyxov. Zv/i^aivei Sk 
 TO ToiovTov kv TOLS els TO dSvvaTov avWoyiafioTs' kv To&roii 
 y&.p dvayKoiov dvaipeiv ti tZv Kei/iivcav. ' Eav odv eyKUTO^ 
 pid/ir]6f} kv To'is dvayKatoLS kpa)Ti]fiaai npos to av/i^aivoir 
 dSvvaTov, S6^ei napdi tovto yiveaOai noWaKis 6 eXeyxos, oiov 
 OTL OVK ecTTi '^frvxv Kal ^oafj TaiiTov el yoip ^6opa ykvtaii 
 kvavTiov, Kal Trj tivI <j>6opa eaTai tis yiuearis kvavTiov 6 Sk 
 BduaTOS (f)6opd Tis Kal kvavTLOv ^oarj, &<rTe yiueais rj ^mfj Kal 
 TO ^rji/ yiv€<r6ar tovto 5' dBvvaTov ovk apa TavTov i) '^vyj\ 
 Kal ■q (cari. Oil S^ ovWeXoyicrTar avfi^aivei yap, k&v H'q m 
 TOVTO (ftrj Ttjy ((ofjv Trj '^vxij, to dSvvaTOv, dWh jiovov kvavTiov 
 ^(ofju jiku OavdTW, 6vtl ^6opa, <p6opa Sk yivemv. ' A(rv\\6yiaroi; 
 fiey ovv airXSti ovk eialv ot tolovtoi Xoyoi, irpos Se Tb npoKei- 
 fievov davXXoyiaTOi. Kal XavBdvei iroXXdm ov^ ^ttov avrovs 
 Tois kpooTwvTas to toiovtov. 
 
 01 fiev ovv wapa to enofievov Kal irapa Th jii] aiTiov Xoyoi 
 ToiovTot e'uTiv 01 Sk napa to tu Sio kpoaT'qjiaTa %v TTOieTv, orav 
 Xav6dvri vXeico ovTa, Kal m evos Svtos dvoSoOjj dnSKpiais fiia. 
 En kvimv fikv ovv ^aSiov iSeiv 8ti nXeia>, Kal Sti oi Soreov 
 dnSKpia-iv, o?ov noTepov fj yfj OdXaTTa eariv fj 6 ovpavos^"; en 
 evUov S' ?JTTov, Kal, m ivbs Svtos, ^ 6/ioXoyova-i r^ fi^ dnoKpi- 
 ve<r6aL to kptoTco/ievov, Hj kXeyxea-Oai ^atvovTui, ofov dp' oStos 
 Kal o^iTos k<TTiv dvOpconos ; wot' dv tis t^ttj tovtov kuI toStov, 
 dvOpconov dXX' o{,k dv6pmnovs TvnT^aei. *H ndXiv, S>v Tb, /lev 
 kiTTiv dyaOd T& S' oiK dyadd, ndvTa dyaOd ^ o't5/c dyaOd ; 
 6n6Tepov ykp dv ,pg Uti fjikv &s tXeyxov ^ ^evSos <f>aiv6fievok 
 
EAErXDN. 17 
 
 it need not be that whatever has a beginning is generated, 
 i. e. that whatever is not generated ha^no beginning : just as, 
 because every man in a fever is hot, it does not follow that 
 every man who is hot is in a fever. 
 
 We mistake for a cause what is not a cause when an irre- 
 levant proposition has been foisted into an argument as if it 
 were one of the necessary premisses. This is practised in 
 reduetio ad impossibile, for it is here that the proposition con- 
 futed is one of the premisses. If, then, a foreign proposition 
 be introduced among the premisses required to famish an im- 
 possible consequence, it may be mistaken for the cause of that 
 impossible consequence. Thus, to prove that Life and the 
 Soul are not identical, a man assumes that the opposite of 
 destruction is generation, and therefore the opposite of a par- 
 ticular destruction is a particular generation. But Death is 
 a particular destruction and its opposite is Life. Life there- 
 fore is generation, and to live is to be generated. This is 
 absurd : therefore Life and the Soul are not identical. There 
 is no sequence here : for, independently of the identification of 
 Life and the Soul, the impossible conclusion follows from the 
 premisses that Life is the opposite of Death, that Death is 
 destruction, and that the opposite of destruction is generation. 
 Such an argument is not entirely inconclusive ; but it does not 
 bear on the point in dispute, and of this the confuter himself is 
 often unconscious''. 
 
 The conversion of consequent and antecedent and false impu- 
 tation of a residt to a cause gives rise to fallacies in the way we 
 have explained : the union of several questions in one occasions 
 a fallacy when the plurality of questions is not detected and no 
 single answer is true. It is sometimes easy to see that there 
 is more than one question, and that a single answer should not 
 be given ; for instance. Is the ocean surrounded by the earth, 
 and the earth by the sky? Sometimes it is not; and the 
 answerer, supposing that the question is single, either confesses 
 defeat by silence, or exposes himself to seeming confutation. 
 For instance. Is A and B a man ? Yes. Then if you strike A 
 and £ you strike not men but a man. Again ; if part is good 
 and part evil, is the whole good or evil ? Whichever you 
 answer you are open to a seeming confutation or conviction of 
 
 c 
 
18 HEP I IO<t>IITIKDN 
 
 Soieiev av noieiv rb yckp ^idvai t&v /Mfj dya6Zv ri eTuai dydr. 
 6hv ^ tS>v 6.ya6wv fi^ dyaShv ■^evSos. 'Ork 81 7rpoa-Xr,(j)6evrm 
 rivcov K&v eXeyxos yivoiro dXTjOLvos, otov d ris Soir] dfioias tv 
 Kal . TToXXcb Xiyea-dai XevKa Kol yv/iva. Kot TvfXd. El yap 
 Tv<})Xbu TO fifj exov oi^iv ve^vKos 8' exe.iv, Kal TV<f>Xa ecrrai 
 T& fi^ exovTo. o'^iv we^vKOTa 8' ex^iv. "Orav ovv to \ikv 
 exi} TO 8k firi exUt ''^ oififfxa ea-Tai ■^ opmvTa t] rvt^iXd' oirep 
 
 dStJi/aTov. 
 
 I 
 
 VI, *H Sfj oijToas SiaipiTiov tovs (paLvofiivovs avXXoyurjiLabi 
 Kal kXkyxovs, ^ irdi/ras dvaKTeov els Trjp tov eXeyxov dyvoiav, 
 dpxfjv TavTr]v TroLrjaafiii/ovs' e<TTi yap anavTas dvaXvarai tovs 
 XexOevras Tponovs els Tbv tov eXeyxov Siopia-fiov. np&rov 
 li\v ei davXXoyicTTOi' Sei yap eK tZv Keifievmv av/iPaiveiv to 
 cruinTepaaiia, &<TTe Xeyeiv k^ dvdyKTjs dXXa fi^ (paivecrOai. 
 "EireiTa Kal KaTo, refe iiepr] tov Siopiafiov. 
 
 4 
 
 Tmv fi\v yot,p ev Trj Xe|ei ol fiev elcri irapk to Svttov, otov rj 
 re oficavvfiia Kal 6 Xoyos Kal tj ojioioa-x'niJ^o'^vvri {crvvqOes ykp 
 Tb irdvTa as T68e ti cniiiaiveivY fj Se aivOea-is Kal Siaipeim 
 Kal irpo(T(p8ia too /i^ Tbv avTov etvai tov Xoyov fj Toifvojia 
 8ia<f)epov. "ESei 8e Kal tovto, KaOdwep Kal Tb irpdyfjia raiirov, 
 el jxeXXei eXeyxos ■/] crvXXoyia-fibs eaecrBai, oTov el Xmnov, ji^ 
 IfidTLOv ovXXoyia-aa-daL dXXa Xcottlov. AXr/Oes fiev yap KOr 
 KeTvo, aXX' ov avXXeXoyia-Tai, aXX' eTi epayrrjfiaTos Sei, on 
 TaiiTbv arj/jMivei, Trpbs Tbv ^rjTovvTa to 8ia ti. j 
 
 01 8k Trapb, Tb (rv/x.^e^i]Kbs 6pur6evTos tov (ruXXoyia-fiov 
 (j>avepol yivovTai. Tbv avTbv yap opia-fibv SeT Kal tov eXeyxov 
 yivea-6ai, nXfiv irpoa-KeTo-Qai t^v dvTi^aa-iv 6 yAp eXeyx"*, 
 auXXoyicr/ibs dvTi<pda-eas. El ovv fj.^ e<TTi (nXXoyuTfibs tov 
 (Tvii^e^rjKOTOs, ov yiveTai eXeyxos. Ov yap el tovtcdv ovrmv 
 dvdyKij t68' efvai, tovto 8' ea-Tl XevKov, dvdyKtj XevKbv etvai 
 8i& TOV a-vXXoyi(T/j.6v^. OvS' el 70 Tpiymvov 8voTv opBaTv t<ras 
 
EAErXDN. 19 
 
 false statement^ for the statement that good is evil, or evil is 
 good, is false. Sometimes indeed the addition of a premiss 
 would give room for a genuine eonfiitation : e. g. if you grant 
 that the same circumstances justify us in calling a single thing 
 and a number of things white, or naked, or blind, because if one 
 animal is bUnd when deprived of sight which it naturally has, 
 a nximber of animals are blind when deprived of sight which 
 they naturally have. If, then, one is blind and another sees, 
 both or neither will be blind or see : which is false''. 
 
 VI. We may either divide seeming proofs and confutations 
 into these classes, or reduce them all to a false conception of con- 
 futation, laying down the true conception as a basis. For all the 
 fallacies we enumerated may be resolved into offences against 
 the definition of confutation; for either the reasonings are 
 inconclusive ; whereas the premisses ought to involve the con- 
 clusion, of necessity and not merely in appearance ; or they fail 
 to satisfy the remaining elements of the definition. 
 
 Of those that depend on language some fail in the singleness 
 of the object signified, as those occasioned by the ambiguity of 
 term or proposition or similarity of termination; the last of 
 which classes contains many fallacies that depend on our custom 
 of speaking of attributes in the terms proper to substances^. 
 Those from conjunction, disjunction, and accentuation want 
 even that singleness of name or proposition which, as well as 
 singleness of the thing signified, is required in proof and con- 
 futation. If, for instance, the thesis speaks of cloaks, the 
 conclusion of the confutation must not speak of mantles but 
 of cloaks. The conclusion may be true of cloaks when the 
 other word is employed, but the reasoning is unfinished, and 
 requires a further proposition that the words are synonymous, 
 if the answerer demands to have it explained how he is 
 refuted 2. 
 
 The equation of subject and accident will be seen to offend 
 against the definition of proof, which is that of confutation 
 minus the condition of contradiction. For confutation is dis- 
 proof, or contradictory proof. If, then, in proof we cannot 
 identify subject and accident, no more can we conclude of the 
 subject whatever is true of the accident, or vice versa, in con- 
 futation. If the premiss states a fact of the subject A, and 
 
 c Q, 
 
20 HE PI 10<t>llTIKQN 
 
 exei, avfi^i^riKi S' avTw axw'^ri eiuai v ^P^V^ ^PXVi on 
 a-XVlJ-a fj apxr) ^ irp&rov tovto. Ov yap rj (rxnH'"' ov8 § 
 irpmTov, dW rj rpiycovov, 77 diroSeL^LS. 'Ofioiws Se Kal ktrl t&v 
 dWcov. "na-T ei 6 eXeyxos (rv\XoyL<rp,6s tls, ovk &v fftj 
 KuTct. axifi^ePrjKbs eXeyxos. 'AWii, vaph, tovto koi 01 TexvlTdli 
 Kal oXcos 01 eina-TTJfioves vno tS>v dvema-Trjiiovav kXeyxovTw 
 KaTh avjifie^riKos yii.p iroiovvTai Toiis avXXoyur/ji.ovs irpbs Toils 
 eiSoTas. Ol 8' oil Swd/ievoi SiaipeTv ^ epa/rmfievoi 8iS6aa-tv fj 
 ov Savres oiofTai 8e8eoKevai. 
 
 Ol Se trapa to nrj Kal anXSis, otl ov tov aitov r) KaTafoffH 
 Kal fi aTTOifyaa-is. Tov yap irrj XevKOV to vrj ov XevKov^'TOV S' 
 anXms XevKov to arrXms ov XevKw dno^aais. El ovv 86vtos 
 rrrj eivai XevKov my anX&s elprjfiivov Xafi^dpei, ov iroiu 
 iXeyxov, ^atviTai 8\ 8ia ttiv dyvoiav tov ti k<TTiv eXeyxof. 
 
 4>avepcaTaT0i 8e TrdvTceu ol trpoTepov Xex^^vTei iraph tov tov 
 iXiyxov Siopio'fJ.ov 810 Kal irpoarjyopeuQrja'av ovTCOS' irapa 
 yhp TOV X6yov ttjv iXXny^iv fj (pavTaa-ia ytveTai, Kal Siaipov- 
 /leuois ovTCOi KOLvhu kirl Train tovtois OeTiov Trfv tov Xoyov 
 eXXeii/ftj'^ J 
 
 Ol fe iraph rh Xafi^dvdv to kv dpxij xal to dvaiTiov &i 
 oLTiov TiOivai 8fjXoi Sth toC opLo-fiov. Ail yap to avfiirepacriili 
 Tm TavT eTvai avfi^alveiv'', Svep ovk rjv kv toTs dvaiTioir 
 Kal irdXiv fifj dpiO/iovfikvov tov k^ dpx^s, ovep ovk exovmv ol 
 traph Trfv a'iTy\(nv tov kv dpxi). 
 
 01 Se irapoi, to eTrofievov fiepos fieri Tov aVfi^e^rjKOTOf to 
 ySi.p knSiievov av/M^k^rjKe, SLa((>epei 8i tov (fV/Mpe^r]K6T0S, on to 
 fiev (TV/Ml3€^r]K09 Utiv k<f>' ivbs fiovov Xa^ecv, oTov ravrS etvai 
 TO iav6bv Kal ftkXi Kal Tb XevKbv Kal kvkvov, rb Sh napiirS- 
 ixevov del kv nXeioa-iv t& yb.p ivl TaiTw TavT&. Kal dXX^XoLS 
 
EAErXDN. 21 
 
 white is an accident of A, it does not follow that the fact is true 
 of all that is white. If a triangle contains angles equal to two 
 right angles, and figure, element, or principle is an accident 
 of triangle, it does not follow that every figure, element, or 
 principle contains angles equal to two right angles. For it is 
 not figure, element, or principle, but triangle, that is essentially- 
 connected with this property by the demonstratioti*. And 
 so in other cases. Wherefore, if confutation is a species of 
 proof, a reasoning that assumes the equivalence of subject and 
 accident cannot be a confutation. It is by this assumption that 
 artists and men of science are confuted by the unscientific. 
 The latter assume the subject and accident to be interchange- 
 able, and the men of science, knowing the essential subject 
 of a law and unready at distinction, either ackaowledge the 
 equivalence or imagine it has been acknowledged^. 
 
 Fallacies from not distinguishing absolute and limited state- 
 ments fail to deny the identical predicate that is affirmed in the 
 thesis. The true negation of partially white is, not partially 
 white; of totally white, not totally white. If, therefore, the 
 admission that an object is partially white is used as an ad- 
 mission that it is totally white, the confutation of the thesis 
 that it is not totally white is only apparent, and depends on 
 a false notion of confutation. 
 
 Most readily referrible to misconception of confutation are 
 the class which we mentioned as such before, and which hence 
 received their special denomination, for their semblance arises 
 from the want of a definition, though in making such a class 
 we must admit that its difierentia is a character common to 
 all the classes. 
 
 Assuming the point in issue, and treating as a cause what is 
 not a cause, are at pnee excluded by the definition of proof; 
 for the conclusion must be a consequence of the premisses, 
 which it is not when we mistake the cause ; and must not be 
 assumed among the premisses, as it is in begging the question. 
 
 Fallacies from the consequent are a species of those from the 
 accident, and difier from other fallacies from accident because 
 the latter identify the accident with a single subject, as, for 
 instance, yellow with honey, and white with swan; while 
 fallacies from a consequent connect the consequent with two 
 
22 HEPI ZO<PllTIKnN 
 
 d^iovjiev eivuL ravTa- Sib yiferai napa to iirofiivov eXeyxoy. 
 "Ea-Ti S' oil irdvTm dXriOes, olov &v ^ XevKov Kara «7u/i/3e^77«6y. 
 Kal yhp i) ximv Kal 6 kvkuos t^ \evKa ravrov. *H irdXiv, m 
 kv TO) MiXiaiTOV Xdyeo, to avTb ehai Xa/ipdveL to yeyovevai 
 Kal dpxfiv ^X^i-v, ^ "TO ia-OLS yivecrOai Kot rauTO fiiyedos 
 Xajj-^dviiv. "Oti yap to yeyovos e^ei dpx^f, 'f«' '''o eX"" 
 dpx^f yeyovevai d^ioT, cos afloat TavTo, ovTa Tcp cipXW ^X^"*! 
 TO re yeyovos Kal to ireTrepaa-fievov. 'Ofioicos Se Kal eni t&v 
 icrcov yivofievmv el to, to avTo jieyeOos Kal ev Xa/i^dvovTa lira 
 yiveTai, Kal to, la-a yivdjieva ev jieyeOos Xa/ifidvei. "Hare to 
 enofievov Xafi^dvei. ' Eirel ovv 6 Trapa to mjji^e^riKos eXeyxps 
 ev ft] dyvoia tov eXey^ov, (ftavepov oti Kal 6 napa to errojievov. 
 ' EwKTKevTeov Se toSto Kal dXXms. 
 
 01 8e irapa to Td nXeica epeoTrjfiaTa ev TTOieiv ev tw {ir\ 
 SiapOpovv Tjiids ^ nfj SiaipeTv tov ttjs irpoTdaem X6yov. 
 'H yap npoTaa-is eaTiv ev KaQ' evos. yap avTos opos 
 evbs fiovov Kal airX&s tov irpdyfiaTos, ofov dvOpmrov Kal evos 
 jxovov dvOpdmov ojioicos Se Kal ewl tcov dXXmv. Ei ovv fiia 
 TTpoTaa-is j) ev Ka6' evbs d^iovaa, Kal dnXm ea-Tai irpoTaa-is 17 
 roiavTT} epd>TTia-LS. 'Eirel S' 6 ovXXoyKTfibs eK irpoTda-ecou, 6 8 
 eXeyxos ovXXoyKTjios, Kal 6 eXey\os ea-Tai eK irpoTaaemv. El 
 oSv -fj npoTatTLS ev Ka& evos, ^avepbv oti Kal oStos ev Trj tov 
 eXeyxov dyvoia,' (f>aiveTai ydp elvai Ttporacns 17 ovk ov(ra 
 irpoTaa-is'. El jiev oSv SeScoKev drrSKpiaiv as irpbs fiMv 
 epdiTTjaiv, e<TTai eXey^os, el Se /ifj SeSmKev dXXd ^aiverai, 
 (paivofievos eXey^os. "DaTe wdvTes ol tottoi ttitttovctiv eis Trjv 
 TOV eXeyxov dyvoiav, ol fjiev ovv Trapd ttjv Xe^iv^, on <f>aivonevr] 
 avTitpaais, owep rjv i'Siov Tov eXey^ov, ol S' dXXoi napd tov tov 
 avXXoyicrfiov opov. 
 
 VII. H S' dndTT) ytverai tS>v /j.ev napd ttjv dfimwuiav Kal 
 TOV Xoyov Tffi fifj Svvaa-Oai SiaipeTv Tb noXXaxws Xeyo/xevov 
 
EAErXON. 23 
 
 antecedents. When two terms are identified with, a third, the 
 axiom identifies them with one another ; ^nd it is this identifica- 
 tion which gives rise to the fallacy from consequent. The axiom 
 is not true if the identity in the premisses is only of subject 
 and accident, else snow and swan, which have each an accidental 
 identity with white, would be identical. Again : — the argu- 
 ment of Melissus identifies what is generated with what has 
 a beginning, and equality with having received the same 
 magnitude. Because all that is generated has a beginning 
 he assumes that all that has a beginning is generated, and, 
 having identified what has a beginning^ with the finite in space, 
 infers that all the finite in space is generated. So with equality. 
 Because things which receive the same magnitude are equal, he 
 assumes that things which are equal have received the same 
 magnitude. That is to say, he converts two antecedents with 
 the same consequent and thereby identifies the two antecedents. 
 If, then, the fallacy from accident depends on a false idea of 
 confutation, so does that from consequent. This topic must be 
 handled again. 
 
 Fallacies from the union of several questions in one may be 
 shewn to be illegitimate by developing the definition of pro- 
 position. Propositions conjoin a single subject and single 
 predicate j_ for the definition of a class is the same as the 
 definition of a single thing, that of man, for instance, as that 
 of a single man, and so on. If, then, a single proposition 
 conjoins a single subject and predicate, so does the class of 
 proposition*. Now, as proof is composed of proposi^ons, and 
 confutation is proof, confutation must be composed of proposi- 
 tions. If, then, propositions ought to conjoin single subjects 
 and predicates, the fallacies that fail in this shew a false con- 
 ception of confutation, for they are composed of seeming but 
 not genuine propositions. If an answer was given to a single 
 question, there is a real confutation; if it only seemed to be 
 given, a seeming confutation. All fallacies, then, are resolvable 
 into a false conception of confatation; because some contain 
 no genuine contradiction, which is peculiar to confutation, and 
 others fail to satisfy the definition of proof. 
 
 VII. In fallacies by ambiguous terms and propositions the 
 deception arises from our inability to discriminate the differeht 
 
24 HEP I ZO<t>llTIXnN 
 
 {ivLa yap oi,K eiSvopov SieXdy, ohv to ev Kul to ^u Kcti rh 
 TairSv), tS>v Si irapb. a{,vBe<riv koX Sia(pe<yiy tS> iir^S^ oU<T6ai 
 Sia<j)ipeiv (rvvTidejievov ij Siaipo^iiivov tov Xoyoy, Ka6dwep otj 
 T&v irXeiareov. 'O/ioicos Se Kal twv jrapa TfjV npoa-epSiav . oi 
 yap dWo SoKei (rrjuaiveiv dvie/ievos Kal enLTeLVOfievos 6 \6yos, 
 en oiiSevbs ^ ovk enl TroXXmy. T&v Se Tcapa to ayji^a Slo. 
 TTjv ofjLoioTVTa TTJs Xi^ecos. XaXerrov yhp SieXeXv troia (ocravrm, 
 Kal irota ms irepoos XiyeTar a)(eSbv yhp 6 tovto Svvdfievos 
 TTOieTv eyyvs evTi tov OeoapeTv TaX-qQes. MaXiaTa S" kwioTaTai'' 
 crvveinveveLv, oti ndv to KaTrjyopov/ievov tivos inroXafi^dvoiiev 
 ToSe TL Kal d)s iv intaKovofiev too yap evl Kal Trj ovffia 
 jMaXiaTo, SoKet Trapinetrdai to ToSe ti Kal to 6v. Aio Kal Tm 
 irapd TTiv Xe^iv ovtos 6 Tpcmos OeTeos, irpStTov fiev oti /jluXKov 
 ■fj dirdTT} yiverai fieT dXXwv aKoirovjievois fj Ka6' avTOvs (ji 
 {lev yap fieT dXXov orKeyjns Sid Xoymv, ij Se KaO avTov oi^ 
 fjTTov Si avTov TOV TrpdyfiaTOs), eiTa Kal Ka6' aiiTov diraTOr- 
 <r6ai avji^aivei, orav kwl tov Xoyov TTOirJTaL Tr)v a-Ke'^iv en rj 
 fiev dTrdrr] e« Ttjs dfMOioTrjTOS, j) S' ofioioTrjs e/c ttjs Xe^ems. 
 TS)v Se irapd to avfi^e^rjKos Sid to jit] SvvaaOai SiaKpiveiv ro 
 TavTov Kal TO eTepov Kal ev Kal troXXd, /J-rjSe tois woiols twv 
 KaTrfyoprjjidTwv ndvTa TavTd Kal tw rrpdyfiaTi av/i^e^j]Kev. 
 'OfioLcos Se Kal t5>v irapd to enofievov /lepos yap ti tw, 
 xrv/i^e^Tj KOTOS to eirofievov. "Etc Kal eirl iroXXwv (^aiveTai Kai 
 d^iovTai ovTcos, el ToSe dirb TovSe p-ij ^oopi^eTai^ firjS' dirb 
 OaTepov )(copi^e(rOai OdTepov. TS>v Se irapd ttiv eXXei^jnv tov 
 Xoyov Kal tS>v irapd Tb irfj Kal dirXms ev Tm irapd /iiKpbv rj 
 diraTTj' ms ydp oiiSev irpocrcrrj/iawof to tI t/j nrj ^ nms fj Tb vvv 
 KaOoXov avyywpovfiev. O/ioims Se Kal eirl tcov Tb ev dp^jj 
 Xa/ij3av6vTcov Kal tS)v dvaiTicov, Kal o(roi ra irXe[a> epcoT^qfiaTa 
 (BS ev voLovaiv ev diraai ydp fj diraTrj Sid Tb irapd jiiKpbv- 
 ov ydp SiaKpi^ovfiev ovre ttjs irpoTaaecos o^Te tov avXXoyKTfiov 
 Tbv opov Sid TTjv elprjfievriv a'lTiav. 
 
 VIII. Enel S eyofiev irap' oaa yivovTai ot (f>aiv6fievoi a-vX- 
 Xoyia-fioi, exofiev Kal nap' onoo-a oi (to^io-tikoI yevoivT dv 
 
EAErXDN. 25 
 
 significations of an equivocal word, for it is sometimes no easy- 
 task to classify the meanings of an equivocal word ; for instance, 
 of Unity, Being, Identity. In fallacies of conjunction and 
 disjunction it arises from overlooking the difference produced 
 by the conjunction or disjunction, because in other cases it is 
 unimportant. So in fallacies of accentuation, because the tone 
 or pitch of the voice is generally indifferent to the sense ^- In 
 fallacies from similarity of termination the deception is due to 
 the similarity, for it is hard to define when similar forms of 
 expression indicate similar or dissimilar realities, and he who 
 can do it must be far advanced in the pursuit of truth. We are 
 seduced into error by our aptness to suppose that every pre- 
 dicate is determinate and single and that something single and 
 substantive is implied by determination and existence. This 
 class, then, must be reckoned among the fallacies from language : 
 firstly, because the deception is more common in reasoning with 
 others than in reasoning by ourselves; for in reasoning with 
 others we think the words, in reasoning by ourselves we think 
 the realities^ : secondly, because in our solitary reasonings we are 
 more likely to be deceived when we think by words : thirdly, 
 because the deception arises from resemblance, and this lies in 
 the words. In fallacies from accident the deception arises from 
 inability to discriminate what is identical and different, one and 
 plural, and what predicates and subjects have or have not all 
 attributes in common. So in fallacies from consequent ; for a 
 consequent is a species of accident, and in many cases it seems 
 to be true and is treated as an axiom that, if A never exists 
 without B, B never exists without A. In fallacies from not 
 defining confutation and from identifying absolute and limited 
 propositions the deception is due to the minuteness of the 
 difference*. We suppose the qualification of manner, mode, 
 relation, time, to be unimportant, and grant the unqualified 
 proposition. And so in begging the question, and misassigning 
 the cause, and uniting maijy propositions in one. In all these 
 the minuteness of the difference creates the deception, for it 
 makes us fail to entirely satisfy the definition of proposition and 
 proofs. 
 
 VIII. Possessing the sources of seeming proof we possess the 
 sources of sophistic proof and confutation'. By sophistic con- 
 
26 HEP I IO<PIITIKDN 
 
 avWoyia/iol kol eXeyxoi. Aeym 8\ (to^uttikov eXeyxov Kal 
 avWoyia-fibv ov fiovov rbv (piaivofievov avWoyia-fiov ^ eXeyxov,' 
 /J.^ ovTa Se, aXXck Kal rov ovra jiev, (ftaivojievov S\ o'lKeiov tov 
 irpdy/iaros^. Eial 8' oStoi ol ji^ Kark to Trpayjia eXeyxoirey's 
 Kal SeiKvvvTes dyvoovvras, OTtep rjv rfjs TrecpaaTLKrjs. Eari 5' 
 ■fj TTf.LpaaTi.Krj /lepos Trjs 8ia\eKTiKr]S' avTT] Se Svvarai avWoyi- 
 ^ea-6ai ■^evSos 8i' ayvoiav tov Si86utos tov \6yov. 01 Se a-o<pi- 
 (TTLKol eKeyyoi, &v Kal avXXoyi^covTai Trjv dvTi^aaiv, ov noiovai 
 SrjXov el dyvoer Kal yhp tov eiS&ra einroSi(av<n tovtois Toii 
 Xoyois. 
 
 "Oti 8' eypjJLev airroiis Ttj avTrj /leOoSm, SfjXov nap oaa yhp 
 (jiaiveTai toTs dKovovaiv ms rjpcoTrjfieva trvXXeXoyivOai, napa 
 Tavra k&v t£ diroKpLvo/ievo) So^eiev, mar eaovTai avXXoyia-iiol' 
 yjrevSeis Sia toIjtcov ^ navTcov ^ kvicav 8 yap /iri epayrrjOels 
 oteTai SeScoKevai, k&v epayrrjOels Oeir], HX^v eni ye tivcov djia 
 (rv/M^aivei irpoaepayrdv to evSees Kal to ^evSos efi^avt^eiv, ohv 
 ev roty irapb, ttjv Xe^iv Kal tov a-oXoiKia/iov. El ovv ol irapaXo- 
 yicTfiol TTJs dvTKpdaeoos iraph tov ff>aLv6iievov eXeyypv euri, 
 SrjXov OTi iraph TOcrama dv Kal tS>v ■^evSSiv etrjaav crvXXo- 
 yia/iol trap' oa-a Kal 6 ^aivofievos eXey)(os. 8e ^aivofievos^ , 
 irapa to, fiopia tov dXrjQivov eKaaTov yap eKXehrovTos (ftavevr\ 
 dv eXeyxps, oTov 6 naph. to [it] avfifiaivov Sid tov Xoyov, 6 et$ 
 TO dSiuvarov, Kal 6 ToiS 8vo epcoT'qaeis /iiav iroimv irapa ttjv irpa- 
 TacTLv, Kal dvTl tov KaQ' airrb 6 irapa to o-v/^jSe/ST/KOS, Kai to 
 tovtov fiopiov, 6 irapa to eirojievov eTi to p,r] kirl tov irpay[iar 
 Tos dXX' eirl tov Xoyov crv/jifiaLveiv eiT dvTl tov kuOoXov Trjv 
 dvTi^aa-iv Kal KaTd TavTo Kal irpbs TaiiTo Kal oKyavTcos irapa 
 Te TO eiri ti ^ irap' eKaarov tovtcov en irapa Tb jjjj evapiS- 
 fiov/ievov TOV ev dp-^y Xa/iPdveiv*. "Do-t eyoip-ev dv nap' otra 
 yivovrai ol napaXoyia-p.oi^- napd nXeico p.ev yap ovk dv etev, 
 napd Se Tcc elpij/xiva eaovTai ndvTes. 
 
EAErxnN. 27 
 
 futation, I mean not only proof or confutation which is seem- 
 ing but unreal, hut that which thou^ real is seemingly but 
 not really appropriate to the subject-matter. Such are those 
 which fail to confute and prove ignorance within the peculiar 
 sphere of the subjectj which is the function of Pirastic . Pirastic 
 is a branch of Dialectic, and arrives at a false conclusion owing 
 to the ignorance of the person examined . Sophistic confuta- 
 tions, even when they prove the contradictory of a thesis, do 
 not prove the ignorance of the respondent, for they may be 
 brought to bear against the scientific. 
 
 We know the sources of inappropriate proofs by the same 
 method as those of unreal proofs. For the same causes that 
 induce an audience to imagine the premisses admitted and the 
 conclusion proved, will induce the respondent to imagine so, 
 and wlU. furnish the premisses of a false proof; because, what 
 a man has not been asked but thinks he has granted, he 
 would grant if he were asked. Only sometimes we no sooner 
 ask for the wanting premiss than we unmask its falsehood, as 
 often occurs in verbal fallacies and in reductions to solecism. 
 If, then, the paralogisms of contradiction are equal in number 
 to the conditions of confutation that may be unfulfilled, the 
 modes of sophistic confutation will be equally numerous 3. 
 Paralogism arises from not fulfilling any of the elements into 
 which true confutation may be decomposed. Any one that 
 may be wanting will leave only a semblance of confutation. 
 For instance, when the cause is misassigned in reduction to 
 impossibility, there is no sequence : when two questions are 
 put as one, there is no genuine proposition : when we replace 
 a subject by its accident, we substitute for a term something 
 else than its whole essence : when we convert a consequent 
 we do the same, for this fallacy is a subdivision of the last : 
 when the diction is fallacious, the sequence is not in the 
 reality but in the words : when the conclusion is irrelevant, 
 or limitations are neglected, the contradiction instead of being 
 absolute and total is partial and restricted, or the terms are not 
 taken in the same respect, relation, manner : and when we beg 
 the question the premisses are not independent of the conclu- 
 sion. We know, then, how many causes of sophistic proof 
 there are; for there cannot be more than we have enumerated. 
 
28 HEP I lO^IITIKDN 
 
 "Ea-Ti S' 6 a-o(f>iaTi.Kos eXeyxoy ovx anX&s eXeyxos, aXU 
 Trpos Tiva- Kat 6 avXXoyia-fios dxravTcos. ^^^ jJ-ev yap /itj 
 Xd^H 6 re irapa to 6fia>vv/j.ov er (rrifiaiveiu, km 6 irapa t^v 
 ofj.oioa-xvH'Oa-vvr]]/ to fiovov ToSi'^, Kal ol dXXoi dxravTcos, oir' 
 eXeyxot ovTe avXXoyia-fiol ivovTai, ov6' AirXms oihe. irpbs tov 
 epcoTWfiei/ov e&v Se Xd^ooai, nphs fiiv tov kpoDTSjiivov ecrovTai, 
 dirXcos S' ovK ea-ovTar ov ydp %v ar]fiaTvov eiXrjtpaaiv, dXXii, 
 (paivofievov, Kal irapd TovSe. 
 
 IX. Hapd irocra 5' iXiyxovrai ol eXeyxofievoi, ov Sit tru- 
 pdaOai Xafi^dveip dvev Trjs Twv ovToav eiriaT'q/ir]S diravTCov. 
 TovTO S oiiSe/jLids ((ttI T^xyis' dweLpoi ydp fcrms at kirurTTJjuu, 
 &a-Te SfjXov oTi Kal at aTToSei^eis. "EXeyxoi S' eia-l Kal aXjj- 
 6eTs' oa-a ydp e<rTiv diroSei^ai, ea-ri Kal eXey^ai tov Bifievov Trjv 
 dvTi<pa(TLv TOV dXr}6ovs, ocov ei avfifieTpov Trjv Sid/ieTpov eOrjKev, 
 iXiy^eiev dv Tis rrj aTToSei^ei ori dav/jifieTpos. "Qa-Te ndvTwv 
 Serj(r€L enKTT'^fj.ovas eivar ol fiev ydp eaovrai irapd ray kv yfa>- 
 fiiTpia dpxds Kal Td tovtoov a-v/iirepda-fiara, ol Se irapd rAy kv 
 laTpiKfi, ol Se irapd Tcfcy tSiv dXXav kiria-Ttifiav. 'AXXd firjv Kal 
 ol ■^evSeis eXeyxoi 6fioi<os kv direipois' Ka$' eKaa-Trjv ydp Te^vriv 
 kaTl yfrevSr/s a-vXXoyicr(ji6s, oTov KaTd yem/ieTpiav 6 yewfieTpiKos 
 Kal KaTd laTpiKr]v 6 laTpiKos. AeycD Se to KaTd t^v Texvrjv to 
 KaTd Tds kKeivTjs dp^ds. AfjXov ovv ori ov irdvTtov twv kXey- 
 X<ov dXXd t5>v irapd ttjv SiaXeKTiK^v XrjiTTeov Toi>s toitovs' 
 oStoi ydp KOLvol irpos diracrav Teyvriv Kal Svvafuv. Kal tov 
 fiev KaO' eKd<TT7]v kina-Trjiiriv eXey^ov tov eiriaTri fiovov kari 
 defopeiv, eire //j) cdv ^aiveTai ei r ea-Ti, oia ti ecTTi' tov o tK 
 tS)v KOivaiv Kal virb firjSefiiav Texyqv twv SiaXeKTiKmv. Ei ydp 
 e^ofiev k^ S>v ol evSo^oi cniXXoyia-fiol irepl otiovv, e)(piiev e^ mv 
 01 eXeyxcn' 6 ydp eXey^os ecmv dvTi<f>da-ecos crnXXoyiafios, &(TT 
 Tj eis fj Svo a-vXXoyia-fiol dvTKpdaecos eXey^os kaTiv. "Expfiev 
 apa nap' diroaa irdvTes elalv ol tolovtol, ei Se tovt' exofiev, 
 Kal rds Xijcreis exofiev al ydp tovtcbv kva-Tdo-eis Xva-eis eicriv, , 
 €XoiJ.ev Se Trap' oirocra yivovTai*. Kal tovs (paivofievovs^, (bai- 
 vo/Mevovs Se ovx otwovv dXXd toTs ToioTaSe- dopiara ydp earcv. 
 
EAErXDN. 29 
 
 A sophistic confutation is not an absolute confutation or a 
 confutation of the thesis, hut only wlative to the answerer; 
 and so of sophistic proof. Unless it is granted that the am- 
 biguous term has a single meaning, and that the similar termi- 
 nation expresses a similar reality, and so on, there is no confu- 
 tation or proof either absolute or relative to the answerer. If it 
 is granted, there is relatiTC proof, but not absolute, for the 
 meaning is not single, but only seemingly so, and none but this 
 respondent would admit it to be so?. 
 
 IX. All the sources of confutation could not be enumerated 
 without universal knowledge, which belongs to no single art. 
 Sciences and demonstrations are possibly infinite, and confuta- 
 tions may be valid, for every demonstration confutes the con- 
 tradictory thesis. The thesis, for instance, that the diagonal 
 and side of the square are commensurate is confuted by the 
 demonstration that they are incommensurate. To enumerate, 
 then, all true confutations would require omniscience : for some 
 confutations will be composed of principles and theorems of 
 geometry, others of medicine, others of other sciences. More- 
 over false confutations are infinite ; for every art has false proofs 
 peculiar to it', geometry, geometrical proofs; physiology, phy- 
 siological proofs. By peculiar I mean, moving exclusively in 
 the sphere of its characteristic principles. Our present task, 
 then, is to trace the sources not of all confutations but of all 
 dialectical confutations ; for these are limited in number, though 
 common to every art and faculty. Scientific confutations 
 whether seeming or real, and if real, the reasons why they are 
 real, must be investigated by the man of science-. The dialec- 
 tician must investigate the common confutations, that belong 
 exclusively to no particular sphere. If we know the sources of 
 probable proofs that are common to every sphere, we know the 
 sources of the common confutations. For confutation is con- 
 tradictory proof, and one or two proofs with a contradictory 
 conclusion are confutation. We have enumerated the sources 
 of all these^, and, if so, we have enumerated the solutions; for 
 the objections to these principles are the solutions, and we have 
 explained the forms of objection. The dialectician must also 
 enumerate the sources of apparent proofs, apparent, that is, not 
 
30 HEP I I0<PIITIKON 
 
 kdv TLS aKOirrj irap dirocra ^aivovrai toTs rvyovaiv. 'Ware 
 ^avepov on toC SiaXeKTiKov eaTi to Svvaa-Qai. Xa^eiy Trap Sera 
 yivirai Siol rmv Koivmv ^ mv eXeyxoy ^ ^aifo/xevos eXeyxoy, 
 Kal ^ SiaXeKTiKos rj ^aivo/ievos SiaXeKTiKos rj weipaaTiKOS. 
 
 X. OvK ea-Ti Se Sia^oph tZv Xoycov ijv \iyova-i Tives, to 
 iiuai Toiis likv irpos Toiivofia Xoyovs, irepovs 8e npbs ttjv Sid- 
 voiav aToirov ycLp to {moXaji^dveLv aXXovs /lev eu/ai npos 
 Tovvofia Xoyovs, iripovs Se irpbs ttjv Sidvoiav, dXX' ov Toh 
 avToiJS. Ti ydp eari to fi^ Trpos Tfjv Sidvoiav dXX' ^ oTav /iri 
 \pfJTaL t£ ovofiaTL, etp' a oiofiet/os epmrdaOai^ 6 epcoTconevck 
 eSwKev ; to S aiiTO tovto kaTi Kal Trpbs To^vo/ia. To Sf npos 
 T^v Sidvoiav, OTav e(f> m eScoKev 8iavorj$eis. El Srj th irXdm 
 (Tr]jiaivovTos Tov ovofiaTOS ocoito ev (rrjiiaiviiv Kal 6 ipooTwv Kal 
 6 epcoTWfJLevos, oiov t(7cos to hv rj to ev voXXa (rr]fiaii>ei, dWh 
 Kal 6 aTTOKpivofievos Kal 6 kpcoT&v Zrjvoov ev oiojievos etvai rjpw- 
 TT/a-e, Kal ecrTiv 6 Xoyos oti ev irdvra, oStos npbs Tovvojia 
 earai ^ npbs Trjv Sidvoiav tov epayrcofj.ei'ov SieiXeyfiivos ; Ei 
 8e ye tis iroXXa oieTai crj/jiaiveiv^, SfjXov oti ov npbs Trjv 8td- 
 voiav. flpcaTOv jiev yap nepl Toi)s tolovtovs ea-Tl Xoyovs Tb 
 npbs Toijvofia Kal npbs Tr]v 8idvoiav oaoi nXeiw a-rj/iacvova-iv, 
 eiTa nepl ovTivovv ecrTiv ov yap ev tw Xoyo) eo-xi Tb npbs Tr\v 
 Sidvoiav elvai, dXX' ev t£ tov dnoKpivofievov ^X^"' "''"^ ""P"^ 
 TO, 8e8o/j.eva. 
 
 EiTa npbs To-Svojia ndvTas ev8e)(^eTai airrovs elvai. Tb yap 
 npbs Toilvo/ia Tb jir} npbs t^iv 8idvoiav elvai eaTiv evTavOa. Ei 
 ydp fifj ndvTes, eaovTai Tives eTepoi oxhe npbs Tovvofia ovT( 
 npbs T^v Sidvoiav ol Si <pa(Ti ndvTas, Kal SiaipovvTai ^ npbs 
 Toilvofia ■^ npbs ttjv Sidvoiav efvai ndvTas, dXXovs 8' ov. 
 AXXd fifjv oa-oi <rvXXoyi(r/ioi elai napd to nXeova)(S>S, tovtcov 
 elcri Tives oi napd Toilvofia. 'AToncos fiev ydp Kal eiprjTai to 
 napd Tovvofia (pdvai ndvTas Tods napd Tf)v Xe^iv dXX' oSv 
 flat Tives napaXoyia-fxol ov Tm Tbv dnoKpivo/ievov npbs tovtovs 
 
EAErXDN. 31 
 
 to any idiot, but to people of average intelligence : for it would 
 be an endless work to inquire into tbe'sources of every idiotic 
 belief. The dialecticiaUj then, has to discover what in the 
 principles common to all spheres of thought are the sources of 
 confutation whether real or apparent, that is, whether dialectic or 
 seemingly dialectic, and whether pirastic or seemingly pirastic. 
 
 X. Reasonings cannot be divided, as some propose, into 
 reasonings addressed to the word and reasonings addressed to 
 the thoughts It is a strange error to suppose that reasonings 
 addressed to the word and reasonings addressed to the thought 
 form distinct classes and are not the same reasonings under 
 different circumstances. For not to address the thought is not 
 to apply a name to the object which the respondent thought he 
 was asked about when he made a concession, and is equivalent 
 to addressing the word. To address the thought is to apply 
 the name to the object which the respondent thought about 
 when he granted the premiss. If, then, a name is ambiguous, 
 but supposed to be unambiguous by the questioner as well as 
 the answerer : as, for instance. Being and Unity are ambiguous, 
 but were supposed to be unambiguous both by the answerer and 
 by Zeno the questioner in the argument to prove the unity of all 
 Being : was this argument addressed to the word, or was it not 
 rather addressed to the thought ? If, on the contrary, the re- 
 spondent thinks a term ambiguous when it is unambiguous 
 the reasoning is clearly not addressed to his thought. For the 
 possibility of being addressed to the word, or addressed to the 
 thought, though it belongs primarily to fallacies of ambiguous 
 term, belongs secondarily to aU reasonings ; because it does not 
 depend on the nature of the reasoning but on the state of the 
 respondent's mind. 
 
 It follows that all reasonings, valid and invalid, may belong 
 to the class addressed to the word ; for in this doctrine all those 
 reasonings are addressed to the word which are not , addressed 
 to the thought. Else there would be a third class, neither 
 addressed to the word nor addressed to the thought ; but we are 
 told that there is not, and that the division is exhaustive. But 
 in truth reasonings addressed to the word are properly confined 
 to fallacies of ambiguous term; and it is an abuse of language 
 to extend the name even to all fallacies in diction. We hold. 
 
32 nEPI IO<f>IITIKnN 
 
 exeiv TTCos, dXXoi. tZ toiovSI epSrrina top \6yov aiirbv exeiv, o 
 TrXeico (rrj/iaivei. 
 
 "OXrns re cltottov to irepi kXiyypv SiaXeyea-Bai, dXXii fir) 
 nporepov Trepl <rvXXoyi<7fioD, 6 yoLp eXeyxps avXXoyur/ios kariv. 
 "Da-re \p)} Koi irepl (niXXoyiafiov irporepou ^ wepl ■y^evSovs 
 eXiyy^ov ecm ydtp 6 tolovtos eXeyxoy (paivo/ieuos avWoyia-fihi 
 dj/TKpdcrems. Alo ^ ev tw cruXXoyt<r//(B eo-rat 70 ahiov fj kv 
 rrj dvTt,<f)d<TU [irpoaKeia-Qai' yhp SeT Trjj/ dvTL^acriv), ore 8' kv 
 dfKJiOLv, &v 27 <l>ai.v6fievos eXey)(os. "Ecrri 8e 6 /lev tov criywvTa 
 Xeytiv kv rrj dvTKpdareL, ovk kv tco avXXoyurfiw, 6 Se, a jir) iyoi 
 Tis, Sovvai, kv d/i(j)oTv, 6 Se on rj Ofirjpov noirjiris a^rjua Stii 
 TOV kvkXov kv TW avXXoyKTjim. "0 8' kv fJ.r]8eTepa> dXrjBrjf 
 avXXoyi(T/J,6s. 
 
 AXXa Sri, 86ev 6 Xoyoy ^X^e, irorepov 01 kv toTs fiad-q/iaai. 
 Xoyoi irpos ttjv 8idvoidv eicnv, fj oij ; koi ei Tivi 8oKeL woXXa 
 a-rj/xaivfiv to rpiymvov, Kol eScoKe /Mrj coy tovto to (T^rjlia, e^*^ ' 
 o5 (TvveTrepdvaTo on Sijo 6p6ai, irorepov wpos rrfv 8idvoiav 
 oSros SieiXeKTai rf/v kKeivov, fj oil; 
 
 "En ei iroXXd /lev a-rj/iatvei Tovvo/j,a, 6 Se /j.fi voet firjS 
 oierai, nms oSros ov irpbs Tr)v 8idvoiav 8ieiXeKTai ; *H irm Set 
 kpmrdv TrXfjv Si86vai 8iaipe<riv ; Eir' kpayrrjaeii ns'' ei eari 
 ariyStvra Xeyeiv ^ oi, fj eari fiev coy oil, ean 8' a>s vai, el Srj 
 ns Soirj fj.r]8a/juos 6 8k 8iaXe-)(6eir], dp' ov irpos Tfjv Sidvoiav 
 SieiXeKTai ; Kairoi 6 Xoyoy 8oKec rmv irapd Toijvojia etvai. 
 
 Ovk &pa ka-rl yivos n Xoycov to TTpoy rf/v Sidvoiav. 'AXX' 
 01 fiev irpos ToUvofid eicn- Kal roiovrot ov irdvres, ov^ on oi 
 eXeyxoi, aXX' ov8' ol ^aivofievoi eXeyxoi. Elal ytip Kal fii) 
 irapk T^v Xe^Lv ^aivo/ievoi eXeyxoi, oiov ol irapd rb av/JL^e^ 
 ^rjKbs Kal erepoL. 
 
EAErXDN. 33 
 
 therij that there are certain paralogisms of equivocation which 
 do not depend on the state of the respofdent's mind, but on the 
 reasoning itself containing a term that is ambiguous. 
 
 Again : we ought not to examine confutation before we have 
 examined proof; for confutation is a species of proof. We 
 ought a fortiori to examine proof before we examine false con- 
 futation, which is the seeming proof of a contradictory. Its 
 fault must be either in the proof, or in the contradiction, or in 
 both, if the confutation is not genuine. In the argument that 
 the outspoken may be silent, it lies in the contradiction, not in 
 the proof. In the argument that a man can give away what he 
 has not got, it lies in both. In the argument that the Homeric 
 poems are a figure because they are a circle, it lies in the proof. 
 Where there is no fault in either, the confutation is genuine*. 
 
 But to resume * ; is it true that mathematical reasonings are 
 always addressed to the thought ? If the respondent thought 
 triangle ambiguous, and granted the premiss in a difierent 
 acceptation from that in which it was afterwards proved to eon- 
 tain angles equal to two right angles ; surely it cannot be said 
 that the reasoning was addressed to his thought ? 
 
 If, on the other hand^, a name is ambiguous, and the re- 
 spondent thinks it unambiguous, is not the reasoning addressed 
 to his thought ? If not, how ought the question to be framed 
 in order that the reasoning may be addressed to the thought, 
 if it is not enough to suggest to the answerer that he may 
 draw a distinction ? If the opponent puts the question : Is it 
 possible or impossible for the silent to be outspoken, or pos- 
 sible in one sense, impossible in another ? and the respondent 
 answers, It is not possible in any sense, whereupon the op- 
 ponent proves it is : surely his reasoning is addressed to the 
 thought of the respondent? This argument, however, -they 
 class among those addressed to the word. 
 
 We conclude that there is no distinct class of reasonings 
 addressed to the thought as opposed to reasonings addressed to 
 the word. There is a class of reasonings addressed to the word, 
 but it does not include all confutations, nor even all fallacious 
 confutations ^ • for some are independent of language, those, for 
 instance, among others, that depend on the identification of 
 subject and accident 9. 
 
34 nEPI 20^1271 KQN 
 
 El Si ris diwT Siaipuu, Sri \iy<o 8k aiyBvra \iyeiv ri 
 fi'ey d>Sl TCI. 8' d>8r dX\a tovto y earl np&rov fiev drmov 
 TO diiovv {eviore y&p ov SoksT to kpayrmfievov noWax&S ix^w, 
 dSvyarov Se Siaipetv o /ifi oierai)- eireira to SiSdaKHv Ti dXXo 
 ea-Tui ; 'Pavepov yap iroiriaei coy ex^' ■"■? /*'?'"' eo"f «/'/'«»'?> /"jr' 
 elSoTi firjO' imoXan^dvovTi otl dWcos XeyeTai. Enfl Kal kv 
 Tois p-f] SnrXoTs tl KcoXvei tovto noieTv^^ ; ^Apa laai at fioudSes 
 rais Svdaiv kv rols TeTTapaiv ; Elo'l Se SvdSes at fi\v aSl 
 evovcrai al Se mSi, Kal S.pa Tmv kvavTimv fiia kirivTrjiir) f) 
 oxj ; "Ea-Ti S' kvavria to, fiev yvaxTTO, to. S" dyvwara. "flor 
 eoiKev dyvoeiv 6 tovto d^imv otl eTepov to SiSdaKeiv tov 8ia- 
 Xiyea-dai, Kal OTi Set top fiei/ SiSdaKovTa fir} kpcurav dX\' 
 aiitov SfjXa noielv, tov S' kpandv. 
 
 XI. "Eti to (pdvai ^ dwo(f)dvai d^iovv ov SeiKvvvTOS kariv, 
 dXXa TreTpav Xaji^dvovTos. ' H yhp ireipaaTiKJ] kaTi StaXeKTiKri 
 Tis Kal deoapei ov tov elSoTa dXXb, tov dyvoovvTa Kal irpoa- 
 iroLovjievov. 'O jiev ovv KaTo, to vpdyfia Beapmv to. koivo, 
 SiaXeKTiKos, 6 Se tovto (fyaivofieyms iroiwv (ro<pi<mK6i. 
 
 Kal avXXoyia-fibs epia-TiKos Kal a-otfua-TiKOS kcrTiv eis fiev o 
 <f>aLv6/ievos avXXoyia/i6s nepl mv^ 17 SiaXeKTLKri neipaaTiKT] eort, 
 kSLv dXj]6es TO av/nrepaa-fia rj- tov yiip Sid ri dwaTrfTiKos kern' 
 Kal oa-oi fiT] ovTes Kara ttjv eKaarov /lidoSov vapaXoyiffjiol'^ 
 SoKOva-iv eivai Kara Tfjv Texyrjv. Td ydp \lrevSoypa^rjfiaTa 
 ovK kpia-TiKd {Kard ydp rd vno Tfjv Texvrfv 01 vapaXoyuTHoi)^ 
 ovSe y ei ti kcrTi ^evSoypd^ri/j.a wepl dXriOes^, ohv to ' Ittito- 
 KpaTOVs ^ 6 reTpaycovia/ibs 6 Sid twv /irjvia-Koav. '/IXX' m 
 Bpva-mv kreTpaymviCe Thv k^kXov, ei Kal TeTpaycovi^erai 
 kvkXos, dXX' oTi ov KaTd rb Trpdy/xa^ Sid tovto o-o^iaTiKot, 
 
EAErXnN. 35 
 
 If, in order that the reasoning: may be addressed to the 
 thought, the questioner is required to drtw the distinction him- 
 self, and say, for instance, that the silence of the outspoken may 
 either mean this, or it may mean that ; the requirement cannot 
 be enforced, for the questioner does not always suspect the 
 ambiguity himself, and he cannot distinguish what he thinks 
 unambiguous. Secondly, would not this be didactic reasoning ? 
 For it discloses the truth to an answerer who has neither pre- 
 viously considered nor discovered nor formed any belief about 
 the ambiguity. And why not equally in the reasonings where 
 no ambiguity is involved give him similar information? As 
 thus : " Are the units in four equal to the twos ? Bear in mind 
 that the twos may be taken either distributively or collec- 
 tively." — " Is there one science of contraries ? Bear in mind 
 that some contraries are knowable, others unknowable." This 
 requirement, then, implies an ignorance of the difference be- 
 tween didactic and dialectic reasoning, and of the principle 
 that, while the teacher does not ask but informs, the dialectician 
 asks ^1. 
 
 XI. Again: — to challenge the respondent to affirm or deny 
 is not the part of Didactic or the teacher, but the part of 
 Pirastic or the examiner. For Pirastic is a species of Dialectic, 
 and probes, not knowledge but, ignorance and false pretensions 
 to knowledge. To do this by applying universal principles 
 within a special sphere is dialectic : to do it in semblance only 
 is sophistic. 
 
 Accordingly, one kind of eristic or sophistic proof is proof 
 which seems appropriate, though really inappropriate, to the 
 problem which Dialectic undertakes under the form of Piras'tic, 
 whether or not it has il true conclusion ; for even then it is 
 iUusive as to the reason. A second are those proofs which are 
 not confined to the special method of a science, though they 
 pretend to be scientific. For the Pseudographema, or the mis- 
 application of peculiar scientific principles, is not eristic, because 
 confined to a special sphere, whether of art or science ; e. g. the 
 reasoning of Hippocrates, or the squaring of the circle by 
 lunules. But Bryso's method of squaring the circle, even if 
 successful, is not mathematical, and is therefore not a pseudo- 
 graphema but a sophism. Proof, then, that falsely pretends to 
 
 D a 
 
36 nEPI lOtPIITlKDN 
 
 "Dare 6 re Trepl rwvSe ^awofieuos avWoyKT/ios epia-TLKos \6yos, 
 Kal 6 Kark to wpdy/ia ^aiv6/j.evos crv\\oyLa-fi6s, kS.v ^ arvWo- 
 yia-/j.6s, epLo-TiKos Xoyos- (f)aiv6fievos yap ea-ri Kara to irpdyjia, 
 wcTT aTraTTiTiKos Kal dSiKos. 
 
 "Dcnrep yap ij ei/ dymui dStKia eiSos ti e^^* f*' i<TTLv 
 d8iK0fia-)(ia Tis, ovtcos kv dyTiXoyia dSiKOjxayia rj ipi(TTiKrj 
 ka-Tiv eKe? re yap ol navTcos viKoiv npoaLpovjievoL navTrnv 
 awTOVTai Kal evTavOa ol kpicrrLKOi. Ol /lev ovv rfjs viKtjs 
 avTTJs X'^P"' '''oi-ovTOL epicTTiKol dvOpamoi Kal (piXepiSes Sokov- 
 ariv eivaL, ol Se So^rjs xdptv ttjs els \p7]fiaTi<Tiiov <TO<f)UTTiKo'f 
 ■f] yap a-0(f)L<TTLKri kcmv, cfxrirep eiTrofiev, )(pri/iaTia-TiKi] tis diro 
 a-ocptas (paivofiiuTjs, Slo fjiaivojievTjs diroSei^ems ktpUvTai. Kal 
 Twu Xoycov tS>v avTmv fikv elcriv ol (fiiXkpiSes Kal ao^iarai, 
 aXX' ov tS>v avT&v evsKev. Kal Xoyos 6 aiiTos fiev earai 
 ao^KTTiKos Kal kpia-TiKos, dXX' oii KaTb. tovtov, aXX' fj (lev 
 viKTjs (f>aivo/j,evris, kpLaTiKos, rj Se <TO<pias, aocpKTTiKOS' Kal yap 
 ■fj aro(pi(TTiKrj k<TTi (paivofievr] cro^ia tis dXX ovk ovcra. 
 
 O S kpi<TTiK6s ka-Ti TTCos ovTOiS eymv irpos tov SiaXeKTiKov &i 
 6 i^evSoypd^os irpos tov yemfieTpiKov kK yap twv avTmv tj 
 SLaXeKTLKTf wapaXoyt^eTai Kal 6 ■^evSoypd(f)OS tw yemjieTpn^, 
 AXX 6 fiey OVK kpiaTLKOs, otl eK tS>v dpy(mv Kal avfirrepor 
 anaTcav tS>v inrb ttjv Teyyrjv ■^evSoypa<per 6 S' inb Trjv 
 SLoXeKTiKTjv nepl jiev TdXXa oti kpia-TiKos kcrri SfjXov^. Ofov 
 6 TeTpaymvia-fibs o jiev 8ia tcou jirivia-Kwv ovk kpLtrriKos, o 8e 
 Bpva-cuvos kpia-TiKos' Kal tov fiev ovk ea-ri fiereveyKeiv aAX' 
 ^ TTpbs yemfieTpiav fiovov Siic rb e/c t&v iSiwv eivai dp)(SiV, 
 TOV Se TTpbs iroXXoiJs, octol fif) fa-aai Tb Svvarbv kx eKaarf 
 Kal Tb dSlJvaTOV ap/i6aei yap''. *H a>s 'AvTKp&v eTeTpayoh 
 vi^ev. *H et Tis /ifj ^aiij ^eXTiov elvai dirb Seiirvov nepi- 
 iraTeTv Sia Tbv Z-qvmvos Xoyov, ovk laTpiKos- Koivbs yap. 
 
 Ei /lev ovv wdvTri dfioicos eixev 6 kpiariKbs vpbs Tbv Sior 
 
EAErxnN. 37 
 
 be pirastic, or relevant to the problem^ is eristic, and so is 
 proof that falsely pretends to be scientific, even though it be 
 conclusive ; for, pretending to proceed from scientific know- 
 ledge, it is deceptive and illegitimate. 
 
 Trials of force or skill are sometimes the occasions of unfair 
 play and illegitimate fighting : and Eristic is illegitimate fight- 
 ing in disputation. The competitor who is bent on victory at 
 all hazards sticks at no artifice; no more does the eristic 
 reasoner. If victory is his final motive, he is called contentious 
 and eristic ; if professional reputation and lucre, sophistic. 
 For Sophistic is, as I said before, a money- making art, that 
 trades on the semblance of philosophy, and therefore aims at 
 producing the semblance of demonstration. The contentious 
 disputant and the sophist use the same kind of arguments, but 
 not from the same motive; and the same kind of argument 
 is sophistic and eristic in difierent aspects. If semblance of 
 victory is the motive, it is eristic j if the semblance of wisdom, 
 sophistic; for sophistry is the semblance of philosophy without 
 the reality. 
 
 The eristic reasoner to a certain extent bears the same rela- 
 tion to the dialectician as the false geometer bears to the true 
 geometer : for he draws his principles from the same source 
 as the dialectician, and the false geometer from the same source 
 as the true geometer. The false geometer is not eristic, be- 
 cause his premisses are exclusively drawn from the principles 
 and theorems of a science, while Eristic constructs syllogisms 
 from the principles of Dialectic. They may, however, handle 
 the same problem. The mode of squaring the circle by lunules, 
 for instance, is not eristic, but Bryso's is eristic. The one 
 cannot be applied beyond the sphere of geometry, because it 
 is based on geometrical principles ; the other can be employed 
 against all disputants who do not know what is possible or 
 impossible in their respective spheres, for it applies to subjects 
 different in kind. The same may be said of Antipho's method 
 of squaring the circle. If, again, a person controverted the 
 expediency of walking after dinner by Zeno^s proof of the im- 
 possibility of motion, such an argument would not be medical, 
 because it has a catholic apphcation. 
 
 If the relation of Eristic and Dialectic was exactly similar 
 
38 nEPI IO<f>IITIKnN 
 
 XeKTLKw Tffl ^evSoypd^m npos tov yeoo/ierpvv, ovk av rjv nepl 
 (Keivcov epia-TiKos. Nvv 8' ovK eariv 6 SiaXeKTiKos irepl yevos 
 Ti a>pLa-/J.evov, oiiSe SeiKTiKos ovSevos, ovSe toiovtos o?os 6 /ca- 
 66\ov^. O^re yap eariv atravra kv evi Tivi yevei, oiSre d 
 f.17], oiov Ti vTTo Tus avTois dpx&s uvai TO. ovTa. "iidT ovSifiia 
 re\yrj tS>v SeLKvvovcraii' nvb. (pva-iv epayrrjriKrj^'-' eariv oii yhp 
 e^eariv onoTtpovovv rS>v fiopicov Sovvar ovWoyKr/jibs yap ov 
 yiverai e^ d/KpoTu. 'H _Se SiaXeKTiK^ epayrriTiKrj eariv. El 
 3' eSeiKvvev, el Kal fir] irdvra, dWa rd ye npcora Kal t^j 
 oUeias dp^as ovk Slv ripwra. Mfj SiSovros yh.p ovk dv en 
 ei)(ev k^ &v eri SiaKe^eTai irpos Tfjv evaraaiv. 
 
 ' H 5" avT^ Kal TreipaaTiKTJ. OvSe yap r) neLpaariKT} Toiavrri 
 earrlv oia i] yemfierpia, aXX' fju av e)^OL Kal fifi elSois ns, 
 "E^ecTTi yap weTpav Xa^eTv Kal tov fifj elSoTa to irpayfia tov 
 fii) elSoTos, ehrep Kal ScSaxriv ovk e^ &v oTSev ovS' eK twv ' 
 iSicov, d\\ eK t&v eno/ievrnv, o<ra TOiavTd eariv & elSorra fiev 
 ovSev KwXvei jiii elSevai ttjv Te-)(yrjv, fi^ elSoTa S' dvdyKri 
 dyvoeiv. "Qare ^avepov on ovSevos mpia/ievov rj ireipaariicrl^, 
 emcrTriiirj eaTiv. Aio Kal irepl irdvrmv ecrTi' irdcrai yhp al 
 Te\vai ypStvTai Kal KoivoTs Tia-iv. Aio iravres Kal ot ISiwrai 
 TpoTTOV TLvd xpmvTai Trj SiaXeKTiKrj Kal 7reipa<TTiKfj- irdvTei 
 yhp fiexpi Tivbs eyxeipovaiv dvuKpiveiv Toi>s ewayyeXXofievovi. ' 
 TavTa S' eaTl rA Koivd- Taura yap ovSev fJTTov iiraaiv avroi, 
 Kav SoKma-i Xiav e^a> Xeyeiv. 'EXeyxovaiv odv anavTer dTe^vw! 
 yap /leTexova-i tovtov o5 evTexvm i) SiaXeKTiKr) ecTTi, Kal 6 
 Texvv avXXoyia-TiKfj ireipaaTiKos SiaXeKTiKos. 'Eirel 5' earl 
 iroXXd fxh TavTa Kal KaTd ndvrmv, ov ToiavTa S" mtrTe (f)V(TCV^* 
 Tiva eTvai Kal yevos, dXX' oiov al dwo^da-eis, Th S' oil roiavra 
 dXXii, iSia, iaTiv eK Totrrav irepl andvTwv neipav Xa/i^dveiv,- 
 
EAErXDN. 39 
 
 to that of the false and the true geometerj there could not be 
 eristic arguments on geometrical problems. But the fact is 
 that Dialectic has no definite spherCj and demonstrates nothing 
 categorically, and investigates no essential theorems. For there 
 is no genus that embraces all Being, and, if there were, there 
 could be no common principles of all Being '. No science that 
 demonstrates categorically any positive theorem can interrogate 
 or oflFer to accept either alternative, for either alternative would 
 not furnish a proof. Dialectic interrogates. If it had to de- 
 monstrate any theorems, it could not trust, at least for the 
 elements and special principles of the proof, to interrogation : 
 for . if they were denied by the respondent, it could have no 
 weapons to oppose to his objection. 
 
 Pirastic is a Dialectic : for it is not a speciality like geometry, 
 but a faculty that may be possessed by the unscientific. He 
 who does not know may examine the pretensions of another who 
 does not know : for the theses and premisses granted by the re- 
 spondent are not scientific truths nor theorems from which the 
 primary laws may be obtained by analysis ^^, but consequences 
 or derivative facts, which are such that, while to know them does 
 not prove knowledge of the primary laws, not to know them 
 proves ignorance. Pirastic, then, is not knowledge of any definite 
 sphere, and therefore is conversant with every sphere : for all 
 sciences have certain common elements or catholic principles. 
 Accordingly, even the unscientific employ Dialectic and Pirastic, 
 for all persons to a certain extent assume to test pretensions 
 to knowledge. Pirastic and Dialectic are the application of 
 those catholic principles, and these the unscientific possess as 
 well as the scientific, though their expression of them may be 
 very defective in precision. Accordingly, all practise confuta- 
 tion. Unmethodically they perform the work which Dialectic 
 performs methodically, and the examination of false pretensions 
 by methodical reasoning is Dialectic. Such principles are nume- 
 rous, and applicable to every province, but have no positive 
 nature, and form no determinate genus, resembling, in this 
 respect, negations : others, on the contrary, are limited to 
 special spheres. The former enable us to examine pretensions 
 in any province, and compose what is a kind of art, though 
 
40 HEP I 10<t>IITIKnN 
 
 Kal ilvai T^yvrjv rivd, Kal jirj ToiavTrjv elvai oiai at S(iKv6- 
 ovcrai. Aioirep 6 epia-TiKos ovk ea-riv oiircos eycov iravTrj ay 
 6 -JrevSoypadiOS' ov yap ecrrai irapaXoyiariKos £^ wpia/ievm 
 Tivbs yifovs dp-)(S)V, dWii irf.pl irav yeuos icrrai 6 epiariKos. 
 
 TpoTTOi p-kf ovv elalv oStol tS)v cro(j)icrTLK&v kXkyywv on 
 S' ia-Ti Tov SiaXeKTiKov to deeopfjcrai nepl tovtcdv Kal Svvaadai 
 ravra iroieTv, ov )(^a\eTrbv ISeiv rj yhp nepl rdis TrpordcrHS 
 fiedoSos anaaav e)(et ravTrjv Tr}v 6ea>piav. 
 
 XII. Kal Trepl /lep tS>v e\iy)(a)v eiprjrai tSiv ^aivofiivcov wepl 
 Se TOV '^evSo/j.evov ti SeT^ai Kal tov \6yov els dSo^ov dyayeiv 
 (tovto yap rji/ SevTepov Trjs crotpuTTiKrjs Trpoaipia-ems) irpmov 
 p.\v ovv eK TOV TTVvOdvicrdai irms Kal 8id Trjs epcoTrja-tms (tvji- 
 ^aivei fidXia-Ta. To ykp irpos (MrfSlv opicravTa Kiip.evov epcordv 
 6r]pevTiK6v kcrTi tovtcov eiK^ yap XiyovTes dpapTdvovai /iSX- 
 Xov sIk^ Se XiyovcTLv, oTav p.T]Sev eyoaai TrpoKetpevov. To re 
 ipoDT&v iroXXd, Koiv dtpia-fievov fj irpos h SiaXeyerai, Kal to rh 
 SoKovvTa Xeyeiv d^iovv Troiei tiv eimoptav tov els dSo^ov 
 dyayeiv ^ ■^evSos' edv re epcoTcofievos <f>TJ ^ diro^^ tovtodv n, 
 dyeiv TTpos St etnyeiprjp.aTOS einropei. AvvaTov Se vvv ?jttov 
 KaKovpyeTv Sid tovtcov ^ irpoTepov diraiTovvTai yap ti tovto 
 Trpbs TO ev dpyrj. ZT0i)(^eLov Se tov TV)(^eTv fj '^evSovs Tivos 
 rj dSo^ov TO firjSefiiav evdvs epeoTav deariv, dXXd (pda-Keiv 
 epcoTav jJLaOeiv ^ovXofievov y(a>pav yap eTTi^eip'^fiaTos fj a-Keyjns 
 TToieT. npos Se to -^evSo/ievov SeT^ai iSios toitos 6 orocpicrTiKos, 
 TO dyeiv Trpbs Toiavra vpbs St. evwopei Xoycav. "EcTTai Se Kal 
 kuXms Kal n^i KoXm tovto iroteiv, KaOdirep eXe-^^Or} vpoTepov. 
 
 fldXiv Trpbs Tb napdSo^a Xeyeiv aKorreiv eK Tivos yevovs 
 6 SiaXey6/ievos, eiT eirepcoTav 8 toTs ttoXXoTs oStoi Xeyovai 
 TrapdSo^ov eaTi yap eKdaTois ti toiovtov. ZTOiveTov Se tov- 
 T(ov Tb Tas eKda-Tcev elXtj^evai dea-eis ev Tais wpoTdaemv^. 
 Ava-is Se Kal toiutcov ■q wpoa-rJKOva-a (jiipeTai Tb efKpavi^etv 
 Sti oil Sid Tbv Xoyov avf^lSaivei Tb dSo^ov del Se tovto Kal 
 fiovXeTai 6 dymvi^o/xevos. 
 
 "Eti S' eK tS)v ^ovXijcrecov Kal t5>v ^avepmv So^mv. Oi 
 
EAErXDN. 41 
 
 very unlike the sciences that demonstrate. Eristic reasoning, 
 then, is not exactly similar to false geometry; for it does not' 
 consist of paralogisms drawn from a limited sphere of principles^ 
 but of proofs drawn from catholic principles applicable to every 
 sphere ^°. 
 
 Such are the modes of sophistic confutation. The investiga- 
 tion of them and power to apply them belong to Dialectic : for 
 all these matters belong to the method of Proposition. 
 
 XII. Unreal confutation has been examined. False or 
 paradoxical statement, the second aim of the Sophist, is obtained 
 by the mode of questioning and interrogating ; by questioning, 
 for instance, without previous definition of the problem. For 
 random answers are more likely to be wrong, and answers are 
 made at random when there is no point in issue. If there is a 
 definite point in issue, it is useful to multiply questions and 
 request the respondent to give his genuine opinion, and if he 
 states candidly his beliefs and disbeliefs, to lead him on to 
 controversial ground^. This fraud is less practicable now, for 
 the answerer will demand. What has this to do with the 
 question? Another rule for obtaining a false or paradoxical 
 statement is not to put a proposition with confidence, but to 
 pretend to ask from a desire to learn : for consultation gives an 
 opening to attack. Another artifice for proving error is to lead 
 the discussion on to debatable ground. This may be done 
 fairly in some cases, as we have already mentioned. 
 
 Again : — paradox may be elicited by considering to what school 
 the respondent belongs, and proposing some tenet of the school 
 that the world pronounces to be a paradox ; for there are such 
 tenets in every school. For this purpose it is useful to have 
 made a collection of paradoxes. The proper solution is to shew 
 that the paradox has no connexion with the thesis, as the dis- 
 putant pretends. 
 
 Another source of paradox is the opposition of secret wishes 
 
42 HEPI I04>IITIKnN 
 
 yitp raxna ^oiXovrai re koL ^acriV, aXKh. Xiyovai jih 
 rovs ^vayrfjioveaTdrovi tS>v Xoyoov, PoUXovTat 8e rh ^aivo/iem 
 \va-iTe\eTv, oiov re$pdvai Ka\m /idWov rj {fjp fiSims (f>a(rl Seiv 
 Kal Trivsa-dai SiKaioas /idWov fj TrXovreTv aityyjiSas, ^ovXovtcu Se 
 TavavTia. Tbv fikv ovv Xiyovra Kardi ras PovXrja-eii els ris 
 ^avepd,s So^as aKriov, rov Se Karb, ravrai eU t^ls airoKiKpvfh^' 
 /levas' d/i<}>0Tep<us ydp dvayKoiov irapdSo^a Xeyeif ^ yap 
 wpoy T^y (pavepiis fj npos ras dtpavels So^as kpovaiv kvavria. 
 
 nXetoTos Se tottos ea-rl rov woieTv napdSo^a Xeyeiv, Mcnrep 
 Kal 6 KaXXiKXrjs kv rm ropyia yeypawTai Xeyaoi/, Kal ot dp)(aioi 
 Se irdvTes wovro av/i^aiveiv, irapdi to Karh <pv<nv Kal Kara rbv 
 vofiov evavTia yap etvai <pA<nv Kal vojiov, Kal tt\v SiKaioavvrjv 
 Karh vofiov plkv eivai koXov Karh ^vaiv S" ov koXov. Aeiv ovv 
 npos fiev Tov einovTa Karii, <fxvaiv Korh vojiov diravrav, wpbs Si 
 rbv Kara vojiov errl rfjv <f>v<nv dyeiv d/i<j)OTepcos yhp ehai 
 Xeyeiv irapdSo^a. ''Hv Se to fiev KaTo, ^ijo-iv avTois to aAj/fley, 
 TO Se KUTo, vofjLOv TO ToTi iroXXoTs Sokovv. "Da-re SfjXov on 
 KdKeTvoi, KaBdirep Kal oi vvv, ^ eXey^ai rj irapdSo^a Xeyeiv tw 
 dTTOKpivofievov ene^eipovv noieiv. 
 
 "Evia Se twv epayrrj/idTeov €j(6t dfKJyOTepcos dSo^ov ehai rfiv 
 dnoKpitTiv, oTov TTorepov rois <TO<j>ois rj tw iraTpl Set neiOecrOai, 
 Kal rd avfi^epovTa wpaTTeiv ^ rd SiKaia, Kal dSiKei<r6ai 
 atperdyrepov fj ^XdiTTeiv. AeT S dyeiv eh Ta toTs iroXXoh 
 Kal ToTs ao^oTs evavTia, edv jiev Xeyt) ris (if ot irepl roii 
 Xoyovs, ei9 Td toTs ttoXXoTs, edv S" d>s oi iroXXoi, eirl rd rois 
 kv Xoyw. <l>aa-l ydp ol fiev e^ dvdyKrjs tov eiSaifiova S'lKaiov 
 eivar toTs Se ttoXXoTs dSo^ov to ^aa-iXea fi^ evSaLjiovetv. 
 "EcTTi Se Tb eis Td ovtods dSo^a avvdyeiv ro aiyrb raJ eh t^v 
 KUTd (pvaiv Kai KaTd vop-ov imevavTicaaiv dyeiv 6 uev yap 
 vo/jios So^a T&v noXXmv, ol Se ao^ol KaTd <f>6(riv Kal Kar 
 dXriQeiav Xeyovaiv. 
 
 XII r. Kal Td /lev TrapdSo^a Ik rovrmv Sei {riTeiv tS>v TmrmV 
 irepl Se rov noifjaai dSoXeaxeiv, 8 fi'ev Xeyofiev Tb dSoXe<rxeiv, 
 elpriKanev vSr/. HdvTes Se oi roioiSe XSyoi tovto ^ovXovtm 
 
EAErXON. 43 
 
 and open professions. Men profess all that is noble while their 
 wishes are set on their material interelfcs. They profess that 
 a glorious death is better than a pleasurable life, and honour- 
 able poverty than sordid opulence ; but their wishes are not in 
 harmony with their words. If the thesis is in accordance with 
 their real desires, the respondent should be confronted with 
 their public professions j if it is in accordance with these, he 
 should be confronted with their real desires. In either case he 
 must fall into paradox and contradict their public or private 
 opinions. 
 
 An abundant source of paradox is what Callicles in the 
 Gorgias is represented as pointing out, and which was 
 familiar to all the ancient disputants, the discrepancy of nature 
 and law. They considered the two to be opposite, and justice, 
 for instance, to be beautiful by law, but not by nature : so that 
 if the thesis conforms to nature, it must be confronted with 
 law J if conformable to law, with nature. In either case the 
 respondent must fall into paradox. The ancients meant by 
 nature, truth; by law, public opinion. Thus, like modern 
 disputants, they aimed either to confute the respondent or to 
 land him in paradox. 
 
 Some questions involve a paradox whichever way they are 
 answered. Ought a man to obey the wise or his father ? Ought 
 he to do what is expedient or what is just ? Is it better to be 
 wronged or to wrong ? We must lead the respondent on into 
 the questions where the world and philosophy are at variance, 
 and if he agrees with the philosophers, confront him with the 
 opinions of the many; if he agrees with the many, with the 
 judgment of the speculators. The one think that there is no 
 happiness without virtue ; the others think that happiness is 
 the lot of every king. This method is the same as that which 
 employs the discrepancies of nature and law : for law is current 
 opinion ; nature and truth the creed of the wise. 
 
 XIII. Paradoxes, then, are to be obtained from the sources 
 enumerated. Pleonasm, as we have already stated, means 
 superfluous iteration. Reduction to pleonasm is as follows. 
 
44 HEP I IO<t>IITIKDN 
 
 TTouiv ei fiTjSy Sia<pepei rh Svoixa ^ rbv \6yov eineiv, SiirXd- 
 aiov 8e Kal 8nrXd<riov ^/iia-eos Tair6, el dpa karh ijfiicTeos 
 SivXaa-iov, icrrai ^fMiaeos rifiia-eos SiTrXdcrLov. Kal irdXiv h 
 dvrl rod SinXdaiov SiirXdcnov rjfjiia-eos reBfj, rpis earai ilprj- 
 liivov, ^fiiaeos ruiiaeos fi/iia-eos SmXaa-iov. Kal S.pd etrnv tj 
 eTTiOv/Mia -qSeos ; tovto S' ea-rlv Spe^is -qSeos' eanv Spa ij 
 f7n6v/j.ia ope^is fiSios '^Sios. 
 
 Eial Se ndvTis ol toioDtoi t5>v Xoyoov iv re rois npos n, 
 oaa firj fiopop t& yevq dXXa Kal aiiTa npos tl Xeyerai, Kal 
 Trpbs TO avTo Kal tv diroSiSorai. Oiov f] re ope^is tivos ope^i^ 
 Kal f) kmOvfita tivos emdv/iia, Kal to SivXdaiov tlvos SinXd<nov 
 Kal SmXdaiov ■fjp.iaios. Kal oaa>v 17 ovaia^ ovk ovtoov irpos n 
 oXcos, S)v elalp e^eis ^ ndQrj f] tl tolovtov, kv rm Xoyco airrm 
 TTpocrSriXovTai, KaTriyopovjikvoiv knl tovtois. Oiop to irepirrov 
 dpiOfihs jiktrov e)((ov eari 8' dpi6fios rrepiTTos' ecrriv apa 
 dpc6/ibs fiiaov e)(a>u dpi6fx,6s. Kal ei to aijiov KoiXoTrjs ^ivos 
 kcTTLv, ecTTi 8e pis (njirj, ecrriu dpa pis pis KOiXrj. 4>aivovTai 
 Se TTOieTv ov iroiovvTes kviore Sih, to fir] npooTrvvOdveaOai a 
 arjuaiveL ti Ka& avrb Xe^Oev Tb SiwXdcriov fj ovSev, Kal ei n 
 arjfiaivei, norepov to airrb ^ erepov, dXXh Tb crvfnrepaap,a XkyiLv 
 ev6vs. 'AXX&, (j>aiveTai 8ia to to 6vojj.a ravrb etvai Tairro Kal 
 arijiaiveiv. 
 
 XIV. ZoXoLKUTjibs S" oiov fiev ka-riv eiprjTai irpoTepov. "Ean 
 8e TOVTO Kal TroieTv Kal jir] iroiovvTa (ftaiveadai Kal noiovvra iifi 
 8oKeiv, KaOdirep 6 flpayrayopas eXeyev, el 6 /jirjvis Kal 6 nrjXrj^ 
 dppev kcTTiv d fiev ydp Xiymv ovXofievrjv (roXoiKi^ei jiev Kar 
 eKeivov, ov ^aiveTai Se roTs dXXois, 6 Se oiXo/ievov (paiveTai 
 p-ev dXX oil aoXoiKi^ei, AfjXov ovv otl koLv re^vrj tls tovto 
 SvvaiTo TToieTv Sib ttoXXoI tS>v Xoymv ov avXXoyi^o/ievoi aoXoi- 
 Kia-fibv (j>aivovTai avXXoyi^eaQai, KaOdirep kv toTs eXey)(ois. 
 
 Eia-L Se irdvTes a-)(€Sbv ol ^aivo/ievoi aoXoiKiajiol irapa to 
 ToSe, Kal orav ■^ Trrma-is^ firJTe dppev fi^re QrjXv Sj]XoT dXXa 
 Tb fieTa^v. To /lev oStos dppev arffiaivei, to S' a&TT] OfjXv to 
 Se tovto 6iXei fiev to /leraiv a-qnatveiv, iroXXdKis Se a-rjuaivH 
 
EAErXQN. 45 
 
 Let us assume that an equivalent expression may always be 
 substituted for a term. If, then, the double is double of its 
 half, and double is equivalent to double of its half, it follows 
 by substitution, that the double is double of its half of its half, 
 and, by further substitution, double of its half of its half of 
 its half. Again, if appetite is appetite of pleasure and appetite 
 is equivalent to desire of pleasure, appetite is desire of pleasure 
 of pleasure. 
 
 All these reasonings turn on relatives where both the genus 
 and the species^ is a relative and has the same correlative : as 
 desire and appetite are both relatives and have the same 
 correlative, pleasure; and double and double of half are both 
 relatives and have the same correlative, half. Or they turn 
 on terms which are not properly relatives but whose definition 
 expresses the subject of which they are states, affections, or 
 other attributes. E. g. if odd is equivalent to number that 
 has a middle unit, odd number is number number that has a 
 middle unit ; and if aquiline is equivalent to hooked nose, an 
 aquiline nose is a hooked nose nose. The reduction to pleonasm 
 is not genuine when the premiss has not been granted that the 
 relative has a meaning by itself and means the same when 
 joined with the correlative^. The conclusion is drawn without 
 this premiss : because the term being the same, it is assumed 
 to have the same meaning in both cases. 
 
 XIV. Solecism we explained before to be barbarism in 
 language. It may be either real and apparent, or real and 
 unapparent, or apparent and unreal, as Protagoras said. If 
 wrath and helmet are masculine nouns, he who gives them 
 a feminine concord commits a real but unapparent solecism; 
 he who gives them a masculine concord commits an apparent 
 but unreal solecism. This appearance can be methodically pro- 
 duced ; and there are methods which apparently but not really 
 convict of solecism, as there are methods of apparent but not 
 real confutation. 
 
 Almost all seeming solecisms depend on the neuter pronoun 
 That, and the masculine or feminine names of objects that are 
 not really male or female but neuter. He denotes a male. She 
 a female. That properly denotes a neuter, but often really 
 
46 HEP I IO0IITIKDN 
 
 KOLKiivmv eKdrepov, oTou rl tovto ; KaWiorrr), iiiXov, KopurKO?, 
 Tov iikv ovv dppevos Kai tov di^Xeos Siafepovaiv at nTwrm 
 atraaai, tov Se /leraid at fiev al S' otf. AodevTOS S^ woXXaKLS 
 TOVTO tTvWoyi(ovTai coy eiprj/iepov tovtov ofiotass 81 Kal dWr/v 
 iTTma-iv dvT dX\r]S. '0 Se irapaKoyurnos yiveTai Sia to koivov 
 etvai to tovto wXeioucav irTaxreeov to y&p tovto a'TfjiaivH h\ 
 fikv oStos oTe Se tovtov. AeT S' evaXXdt^ arjfiaiveiv, p-eTci fiev 
 tov eoTi TO oStos, fieTk Se tov eivai to tovtov, olov eari Kopt- 
 (TKos, eivai KopiaKov. Kal errl t&v BrjXeoov ovofiaTcav dxrairwi^ 
 Kal eiri tcov Xeyojievoav jAv <rKevS>v, ey(pvT<iDv Se 6r]Xeias 7 
 dppevos kXtjo-iv. "Oaa yhp els to o Kal to v TeXevTa, Tavra 
 (lova (TKevovs e)(€i kXtjo-iv, ofov ^vXov, aypiviov, Tb. Se (if) oirmi 
 dppevos Tj OrjXeos, mv evia (pepofiev eirl Tii a-Kevr), ofov d<TKoi 
 liev dppev Toi/vo/ia, kXivt) Se 6r}Xv. Aiofirep Kal eirl tcov toiov- 
 Twv maavToas to ecrTi Kal to eivai Sioiaei. Kal Tporrov nva 
 o/ioios eoTTiv 6 (ToXoiKiafibs toTs napa to to. p.ri ofioia bjioiwi 
 Xeyo/JLevois^ eXey)(ois. "Oawep yhp eKeivois eirl t&v irpay/iA- 
 rmv, TovTOis eirl t&v ovojidTcav avfiiriiTTei <roXoiKi^eiv dvdpmros 
 yap Kal XevKov Kal irpdy/ia Kal Svofid eaTiv. *t>avepov oSv on 
 TOV <roXoiKi<rfibv neipareov e/c twv ecpijftevav irTwaemv uvXXo' 
 yi^ea-Bai. 
 
 EiSri jiev oSv TavTa tS>v dycaviariKcav Xoymv Kal jieprf Tmv 
 eiScav Kal Tp&iroi ol eiptj/ievoi. Aiatpepei 5* ov jiLKpov, eav 
 Ta)(6r] TTO)? TO. irepl ttjv epmTrjaiv irpbs to Xav6dveiv, &<nrep kv 
 ToTs SiaXeKTiKoTs. Etpe^rjs ovv toTs eipij/ievois Tavra irpSerov 
 XeKTeov. 
 
 XV. "Ea-Ti S^ irpbs to eXeyy^eiv^ tv ftev /ifJKOs' \aXeiTov 
 ydp d/ia iroXXa avvopav els Se Tb nfjKos tois irpoeiprjfievois 
 oToixeiois Xpria-Teov. *Ev Se Ta^os' iia-Tepc^ovTes ydp ^ttov 
 vpoopSxriv. Eti S opyfi Kal ^iXoveiKia' TapaTTojievoi yap 
 rJTTOV SiuvavTai ^vXdTTeaOai irdvTes- aroLxeta Se ttjs opyfjs 
 TO Te <f>avepbv eavrbv iroieTv ^ovX6/ievov dSiKew Kal Tb irapdirap 
 dvaitrxvvTeiv. 'Eti Tb evaXXd^ to, epayrrj/iaTa TiOevai, edv Tt 
 irpbs Tavrb-irXeiovs tis exD Xoyovs, edv re Kal oti ovtcos koI 
 
EAErxnN. 47 
 
 denotes a male or female. What is that ? That is Calliope : 
 That is wood : That is Coriscus. The Cases of masculine and 
 feminine nouns are always distinguishable j not so those of 
 neuters. When That in the premiss represents He, we may 
 argue as if it represented Him, and vice versa : and a fallacy 
 will arise from this variety of representation. It alternately 
 represents He or Him, according as it accompanies the infini- 
 tive or indicative mood. So it either represents She or Her, 
 and either the nominative or the accusative of neuter objects 
 which have masculine or feminine nam.es. For neuter objects 
 ^ught to have names ending in On, and the other terminations 
 ought to denote the male or female sex, but are sometimes applied 
 to neuters, as askos (wine-skin) has a masculine termination, 
 kline (bed) a feminine. The names of these objects, just like 
 proper masculines and feminines, change their inflexion accord- 
 ing as they accompany the indicative or infinitive, that is, dis- 
 tinguish the nominative and accusative cases. Reduction to 
 solecism resembles the fallacies that arise from similarity of 
 termination or Figura dictionis. There we are cheated in the 
 category of the things, here in the cases of their names ^, for 
 man and white are both names and things. Solecism, then, is 
 proved under the circumstances we have indicated. 
 
 We have now enumerated the branches of sophistic disputa- 
 tion and their subdivisions and methods. For concealment of 
 his purpose. Arrangement is important to the sophist as to the 
 dialectician. We therefore proceed to treat of Arrangement*. 
 
 XV. Length is favourable to concealment; for it is hard to 
 see the mutual relations of a long series of propositions. Length 
 is to be produced by the methods abeady mentioned^. Quick- 
 ness facilitates concealment, for the answerer has not time to 
 foresee consequences. So, too, anger and the heat of dispute ; 
 for any mental discomposure puts us off our guard. Anger may 
 be produced by efirontery and open attempts to cheat. So, too, 
 alternately proposing the premisses either of different arguments 
 for the same conclusion, or of arguments to prove opposite con- 
 clusions, for the answerer has to guard against different and 
 
48 HEP I IO<t>IITIKnN 
 
 OTL ovx oiirms- a/ia ycLp avu^aivei ^ irpbs TrXew) ^ npos rdvav'- 
 ria iroieTa$ai t^v ^vXaKriv. "OXm Se ndvTa rh. npos rfiv 
 Kpiijyjnv \e-)(6kvTa vporepov xp'qcrifia /cat npos Toi)s dymvKTn- 
 Koi)s Xoyovs' ^ yap Kp^yjns earl rod XaQeiv xoipiv, to Sk Xa6uv 
 rfjs dndTrjs. 
 
 flpos Se Tovs dvavevovras &tt' av ohfOooaiv etvai npos top 
 Xoyov, e^ dno<pd(re<os epcoTTjTeov, ws TOvvavTiov fiovXofievov, fj 
 Kat e^ laov noiovvTa ttjv kpwTTjaiv dSrjXov yap ovtos tov tI 
 PovXeTui Xa^eiv tJttov Sva-KoXaivovaiv. "Otuv r knl twv 
 fiepmv SiSm tls to Ka6' eKaaTov, kndyovTa to KadoXov^noX- 
 XaKis ovK epayrriTeov, dXX' dts SeSofiivm ■^(prjaTeov kvioTi yap 
 oiovTai Kal avTol SeSaxivai Kat tois aKoijova-i <f>aivovTai Si& 
 Trjv T^s knayayyfjs /ivetav, d>s ovk av rjpayrrfukva /idrriv. Ev 
 ots Te fir) ovofiaTi (rr/fiaipeTai to KaOoXov, dXXa Trj d/iotorijn 
 XP'tJo'Tiov npos TO avfitpepov XavOdvei yap tj d/ioiorris noX- 
 XaKis. flpos re to Xa^eTv Tfjv npoTaviv TOvvavTiov napapdX- 
 XovTa XP^ TTwddfea-Oar oiov, el Seoi XaPeTv oti Set ndvra 
 Tcp naTpl n€i6e<r6ai, nonpov &navTa Set neideixdai toTs yov&i- 
 (TLv fj ndvT dneiOitv ; Kal Tb. oXiydKis oXtya^ norepov noXKa. 
 (rvy\<opr]Teov rj oXiya ; MaXXop yap, einep dvdyKt], So^eiev av 
 eivaL noXXd' napaTiOe/iivmu yap kyyiis tS>v kvavTicov, Kal jiu^i^ 
 Kal fieydXa ^aiveTai Kal X^^P"'' 'f*' jSeXTto) Tory dvOpwnois. 
 
 Z<j)6Spa Se Kal noXXaKis noiei SoKeTv kXrjXeyxOai to iidXurra 
 ao^iaTiKoi' a-vKO(pdi/Trj/j.a twv kpmTwvToav, to firjSev crvXXoyuyw- 
 fievovs /i^ kpwTrjfia noieiv to TeXevTaTov, dXXii. crv/inepavnKm 
 elneiv, ms avXXeXoyi<r/Jievovs, ovk &pa to Kal to. 
 
 Zo<piaTiKov Se Kal to, Kei/ievov irapaSo^ov, to (ftaivojievoi 
 d^iovv dnoKpivea-Qai, npoKei/ievov tov Sokovvtos k^ dpxvs, Kal 
 T^v epwTr](riv twv toiovtohv oirrm noiecaOai, noTepov aoi SoKti; 
 AvdyKT] yap, &v ^ to kpcoTrj/ia k^ wv 6 (TvXXoyuriids, fj eXeyxov 
 ^ napdSo^ov yiveadai, Sovtos fiev eXeyxov, fitj Sovtos Se jiriSk 
 SoKeTv (fidaKovTos dSo^ov, fif) Sovtos Se SoKeTv S" o/ioXoyovvroi 
 kXeyxoeiSes. 
 
 "Eti Kaddnep Kal ev toTs ^riTopiKoTs, Kal ev toTs kXeyKTiKOiS 
 
EAErXDN. 49 
 
 opposite dangers. Generally all the dialectic methods of con- 
 cealment ^ are available in contentious rea#ning, for concealment 
 is a means of fraud. 
 
 When the answerer denies whatever he fancies helps the 
 argument, you must ask the negative, as if you wanted the 
 opposite of what you really do, or affect indifference. When 
 doubtful what you want to obtain he has less scope for mere 
 obstruction. Often when the particulars of an induction are 
 granted, the universal should not be asked but employed as if 
 granted : for the answerer will fancy he has granted it and so 
 will the audience, as they wiU recollect the induction and 
 assume the particulars were not asked without a purpose. 
 The absence of a single name for the subject of the generaliza- 
 tion is advantageous to the questioner, for the similarity will 
 often be undetected*. To obtain a proposition you should con- 
 trast it with the opposite. If, for instance, you want to obtain 
 the premiss, that a man should obey his father in all things, 
 you should ask. Should a man obey or disobey his parents in all 
 things ; and if you want the premiss that a small number mul- 
 tiplied by a small number is a large number, you should ask 
 whether it is a small number or a large number; for if com- 
 pelled to elect, one would rather pronounce it a large number. 
 For the juxtaposition of contraries increases their apparent 
 quantity and value. 
 
 An appearance of confutation is often produced by a sophistic 
 fraud, when the questioner, without having proved any thing, 
 instead of asking the final proposition, asserts it in the form of 
 a conclusion, as if he had disproved the- thesis^. 
 
 It is sophistic, too, when the thesis is a paradox?, to ask in 
 proposing the premisses for the respondent^'s genuine opinion, 
 as if the thesis was his genuine opinion, and to put all the 
 questions in this shape : Is it your real opinion, et cetera. If 
 the question is a premiss of the proof, the answerer must either 
 be confuted or led into paradox: if he grants the premiss, he 
 must be confuted : if he says it is not his real opinion, he utters 
 a paradox : if he refuses to grant the premiss, though he allows 
 it to be his opinion, it looks as if he were confuted. 
 
 Again, as in Rhetoric so in Dialectic, discrepancies should 
 
 E 
 
50 HEP I I0<PI2TIKDN 
 
 o/jLoicos ra evavriSfiara SecoprjTeov ^ npbs rb. {)(f>' eavTOV Xeyi. 
 fieva, ^ npos ot>s o/xoXoye? KaXSis Xeyeiv fj irpdrTeiv, in npos 
 Toiis SoKovvras toiovtovs, ■n irpos tovs o/iolovs, ^ irpos Toiis nXei- 
 (TTovs, rj vpbs irdvTai. "Do'irep re Kal diroKpivojievoL ttoXXAkk, 
 orav eXeyxcovrai, iroiova-L Sittov, &v fieXXrj avfi^aii/eiv eXey^S^, 
 &ecr6ai, Kal epcoTavras Xprja-Teov TTore rovTcp Trpbs Toiis kvuTTCt- 
 fiivovs, dv mSl fikv av/i^aii/tj caSl Se /irj, on ovtcos eiXrj^fv, otov 
 Q KXeocpav iroieT kv rm MavSpo^ovXcp. Ae? Se Kal dipiarank- 
 vovs Tov Xoyov rb. Xoiird t&v e7ri)(eipr]fidTcov erriTe/jLveiv^j Kal 
 Tov diroKptvofievov, dv irpoaicrOdvqTaL, irpoevicrTaa-OaL Kal trpo- 
 ayopeveiv. EtriyeLprjTeov S' kviore Kal irpos dXXa tov dpi\- 
 fievov, kKeivo kKXa^ovras, kdv fifj irpos to Kei/ievov e^?? "S 
 eTn)(eLpeiV oirep 6 AvKoc^pcov kiroirjcye irpo^Xrjdii/Tos Xvpav 
 kyKco/jLid^eLv. Flpos Se Toi)s drraiTovuTas irpos n emxeipeP",: 
 kireiSrj SoKeT Seiy diroSiSovai Trjv ainav, Xey6evT<ov S" kv'im 
 eiKpvXaKTOTepov to KaQoXov avfi^aivov kv tols kXeyypis, Xeyew 
 TTjv dvTi(f)acnv, 6 tl e<pr](Tev dirocfifjcrai, fj o direcjyrjo-e (f)fj(Tcu, 
 dXXd jir) OTL tS)v kvavTLCOV 17 avT-rj eiriOT'qfirj fj oii^ rj avTrj. Oi 
 Sei Se TO avfJ.Trepa<rp,a irpoTaTiK&s kpmTav evia S" ovl^ kparrtj-i 
 reov, dXX coy dfioXoyov/ieuco )(^pricrTeov. 
 
 XVI. ' E^ a)v fiev ovv at kpanrjaeis, Kal irms kpeoTrjTeov kv 
 Tais dywvLo-TLKaTs SiaTpi^aTs, ei'prjTaf irepl Se diroKpiaem, Koi 
 irSts XP^ Xijeiv, Kal ti Kal irpos nva ^rjaiv ol toiovtoi t&v 
 Xoycov dxpeXifioi, fieTa Tavra XeKTeov. 
 
 Xprja-ifioi /lev ovv eicrl rrpbs fiev <piXoao<piav Sih Svo. HpSh 
 TOV jiev yap a>s eirl Tb iroXij yivojievoi irapii, t^v Xi^iv d/ieivov 
 exetj/ iroLovcri irpbs to iroaaySis eKaaTov Xeyerat, Kal iroia 
 ofioims Kal iroia eTepcos kiri re t&v irpayfiaToav (TVfij3aivei, km 
 kirl Twv ovofidTcav. AevTepov Se irpbs ray Kaff aiiTbv ^■qTrjo'eiS' 
 6 yap {icf> eTepov fiaSims irapaXoyi^ofievos Kal tovto fifj aitrdor 
 vojxevos Kdv airrbs i>(p' aiiTov tovto irdOoi iroXXdKis. TpiToii 
 Se Kal Tb XoiTTov eTi irpbs So^av, Tb irepl irdvra yeyvjivaffdm 
 SoKelv Kal nr)Sevbs dneipcos exeiv to yap KoivwvovvTa Xoywv 
 ylreyeiv Xoyovs, firjSev exovTa Siopi^eiv irepl ttjs (pavXorriTOt 
 
EAErXDN. 51 
 
 be developed between the thesis and the tenets either of the 
 answerer or of those whom he aeknowleiges to be high autho- 
 rities, or of those who are generally so acknowledged, or of 
 those of his own school, or of those of the majority of people, or 
 of those of all mankind s. And as the answerer avoids imminent 
 confutation by drawing distinctions, so the questioner who fore- 
 sees an objection that applies in one sense and not in another, 
 should explain that he means the proposition in the unobjection* 
 able sense, like Cleophon in the Mandrobulus. And digressing 
 from the argument in hand he should by anticipation restrict 
 the bearing of his other arguments, and the answerer similarly 
 should meet his other arguments by anticipatory protestation 
 and objection. Sometimes the questioner must attack a propo- 
 sition diflFerent from the thesis, by means of misinterpretation, 
 if he cannot attack the thesis, as Lyeophron did when required 
 to deliver an encomium on the lyre. If the answerer demands 
 what is the drift of a question, as the law is that the object of 
 a question must be assigned on demand, and a definite answer 
 might put him on his 'guard against the intended confutation, 
 he should be told that the object is to prove the contradictory of 
 his thesis, the affirmative of his negative, or the negative of his 
 affirmative ; not that the object is to prove, say, that contraries 
 fall under the same science, or that they fall under diffijrent 
 sciences. The conclusion should not be asked as a proposi- 
 tion. Some premisses should not be asked but assumed as 
 granted. 
 
 XVI. We have expounded the sources of questions and the 
 modes of questioning in contentious disputation. We have 
 now to discuss answers and solution and the use of this 
 theory. 
 
 It is useful to the lover of truth for two reasons. As it 
 chiefly turns on language, it teaches us the various signification 
 of words and the different sequences in the world of words and 
 the world of realities. Again, it corrects our solitary reason- 
 ings ; for he who is easily led by an opponent into undetected 
 paralogisms, will often fall of himself into similar errors. 
 Thirdly, it is useful to save us from the imputation of want of 
 culture. For if we censure a mode of disputation without being 
 
 E 2, 
 
52 HEPI r04>IITIKnN 
 
 avToav, vwoi^iav SiSma-i tov SoksTu Svcryepaivuv ov 5i& raXij^ey 
 dXXii. Sl diTfipiav. 
 
 ' AiroKpivo/iiuois Se ttqjs mravrrjTiov vpos rovs tolovtov? 
 Xoyovs, (fiavepov, einep 6pdS>s elprJKafiev trporepov k^ mv dalv ol 
 napa\oyicr/jLoi, kol tols kv r^ nvvOdvecrOaL nXeove^ias Uavm 
 SieiXofiev. Ov ravrov S ka-Ti Xa^ovra re tov Xoyov ISeTv Kal 
 XvcraL Tr)v fio)(drip(av, Kal kpcoratfieuoy OLTravTciv SwaaOac ra-. 
 )(kcos. *0 y^p lafj-ev, ttoXXukis fieTaTidifievov dyvoovfiev. 'En 
 8 , wanep kv toTs dXXois to OoLttov Kal to ^paSvrepov eK rov 
 yiyvfivdaOai yiveTai /laXXov, o'lrrca Kal knl twv Xoycov e^ft^ 
 aiTTe, &v SrjXov fiev rjjuv f, dfieXiTr]TOi 8' a/iev, vaTepovjiiv 
 t5>v Kaipcov TToXXaKis. Zv/i^aivei 8k voTe KaOdirep kv tok 
 8iaypd/j.fia(Tiv Kal yccp fKec dvaXvaavTes kviore avvQiivai 
 irdXiv d8vvaTovft.€v ofjTco Kal kv toTs kXiy)(ois e/Sorey Trap' 8 o 
 Xoyos avfi^aivei avveipaL, SiaXvcrai^ tov Xoyov dtropovfiev. 
 
 XVII. flpmrov jjLiv ovv, axrirep <rvXXoyi^i<r6ai ^a/iev kvSo^m 
 iroTe /laXXov ^ dXT]6a)S npoaipeia-Qai 8eTv, ovtod Kal Xvrkoy 
 iroTe jjLaXXov kv86^<os rj KaTo, rdXtjdesi "OXeos ydtp irpos Toiis 
 epicrriKovs fiay^eriov ov^ &s kXky)(ovTas dXX ms <paivofj.kvovr 
 ov yap <j)a/iev avXXoyi(e<r6ai ye avToiJs, airre irpos to jiji 
 SoKeTv SiopOooTeov. El yap kaTiv 6 eXey^oy dvTi^ams fifi 
 o/imw/jLos €K Tiveov, ov8ev &v Seoi 8iaipet(r6aL irpos rdfitpiPoXa 
 Kal Tr)v ofimw/jiiav ov yap Trout avXXoyia/iov. 'AXX' oiiSevos 
 dXXov \dpiv 7rpoa-8iaipeTeov dXX' 17 oti to <TVfj,irepaa-fia ^aiverai 
 kX€y\oei8ks. 0(jkovv to kXfy^Ofjvai dXXa to 8okuv ejJAor 
 ^rjTeov, kirel to y kp<OTav d/KpifioXa Kal ri napa ttjv ojumv- 
 fiiav, oaai t dXXai TOiavrai irapaKpovaeis, Kal tov dXrj&ivhv 
 eXey)(ov d^avi^ei Kal tov kXey^ofievov Kal [ifj kXeyxo/ievov 
 a8r]Xov TTOiet. 'Eirel y^p e^ecrriv kirl rlAei avfi7repava/ievoti:£: 
 /ij) Srrfp e<f)r]crev dno^fja-ai. Xiyeiv, dXX ofKovvfims, el Kal on 
 fidXia-T eTvxev knl Tavrov (f>ep<ov, &8r]Xov el kXrjXeyKTaf 
 S8r)Xov yhp el dXr)6rj Xeyei vvv. El 8e 8ieXobv ijpeTO to 
 ofiSwfiov f) Tb d/i<f,l^oXov, oiK &v d8r,Xos vv 6 eXeyxos. "0 t 
 emCvrova-i vvv fiev ^ttov Trpfrrepov Se /xaXXov ol kpio-riKoi, to ij 
 
EAErXDN. 53 
 
 able to specify its vices, our censure may be suspected of pro- 
 ceeding not from insight but from prejuiice. 
 
 The manner in which the answerer should encounter this 
 kind of argumentation is plain, if we have rightly enumerated 
 the sources of paralogism and the frauds of the questioner. 
 But it is not the same thing to be able on examination to see 
 through an argument and correct its error, and to be able under 
 interrogation to oppose it with promptitude. What we know 
 has often only to change its position to become unknown to us. 
 Here, too, as elsewhere, quickness and slowness depend on prac- 
 tice : and if we understand a sophism but want practice, wp 
 shall often be too late to apply our knowledge. And the same 
 occurs as in geometrical reasoning : here we sometimes accom- 
 plish an analysis but cannot succeed in the synthesis : so in 
 disputation we may know the principle of a sophism, and yet 
 be unable to arrest it in the process of formation. 
 
 XVII. To begin : — as the show instead of the reality of proof 
 may sometimes, in my opinion, be properly intended, so may 
 the show instead of the reality of solution. For eristic con- 
 futation is not genuine but only apparent. There is no genuine 
 proof but only the appearance of proof to be dissipated. If 
 confutation is the evolution of an unequivocal contradiction from 
 certain premisses, to avoid confutation there is no need of dis- 
 tinction when a term is equivocal, because it leads to no genuine 
 contradiction, and the sole motive for distinguishing when we 
 answer is to avoid the appearance. It is the shadow not the 
 substance of disproof that has to be repelled. Indeed equivocal 
 propositions and terms and the other fraudulent artifices may 
 mask genuine confutation and make it uncertain whether a man 
 is confuted when he really is. For as the answerer may say 
 when the questioner has constructed his proof, that the thesis 
 is only contradicted by means of an equivocation, even though . 
 he really used a word in the same signification as the questioner, 
 it is not certain whether he is confuted, for it is not certain that 
 his averment is false. Whereas if the questioner had drawn a 
 distinction when he put the equivocal question, there would have 
 been no uncertainty about the confutation, and the requirement, 
 less insisted on now than formerly in eristic, that the answer 
 
54 HEP I IOt>IITIKnN 
 
 vai fj ov oTTOKpivfcrOai rbv epcorwfievov, eyiver' dv. Nvv Sk iih, 
 TO /J.fj KaXms kpayrdv Toijs irvvOavofjiivovs dvaynr] irpoaatroKpi-- 
 vetrdai ri tov epoorSfievov, SiopOovvra rfiv fioyfirjpiav rrjs 
 TTpoTcia-eccs, €7re2 SieXofievov ye iKaySis rj vai -q ov dvdyKT] \kyuv 
 TOV diroKpivofievov. 
 
 El Si Tis vnoXri^^eTai tov Kara dfieovv/j.Lav e\ey)(ov e'cai, 
 Tponov Tivdi oiiK ecrTai 8ia<f)vyiTv to kXiy^eaOai tov diroKpi- 
 vofievov sttI yap t&v opaT&v^ dvayKaiov S e^ijcrev dnocftrja-ai 
 ovojia, Kal S diricfirjae <pfjarai. Ds yap SiopBovvTai Tives, ovSev 
 o^eXos. Ov yccp KopiCTKOv (paalv eivai /lOvaiKov Kal d/jLovcov, 
 aXXa TOVTOV tov KopicrKov fjuovcnuov Kal tovtov tov Kopia-Kov 
 djiovaov. yap aiiTos eaTai Xoyos to tovtov tov KopicrKOv^ tw 
 TOVTOV TOP KoptaKOv d/iOVCTOv elvai ^ fiovcriKov onep afia (prjai 
 re Kal dTr6<f>r]aiv. AXX 'iams ov tovto a~rjfiaiver ovSe ykp 
 kKii ToiSvo/xa. "DcTTe tl Siatpipei ; Ei 8e t£ jikv to airXm 
 Xiyeiv KopicrKov dvoSwa-ei, tw Se TrpoaO'qaei to tivol fj TovSe, 
 aTOTTOv ovSev yap fidXXov 6aTep(p- mroTtpa yap dv, ovSev 
 Sia^epei. 
 
 Ov /J.fjv aXX' eireiSfj dSrjXos fJ.iv kaTiv 6 fif] SiopKra/ievos ttjv 
 dfKpifioXiav TTorepov kXrjXfyKTai rj ovk eXrjXeyKTai, SiSoTM 
 ■S' kv ToTs Xoyois to SieXeTv, (pavepov oti to fir) SiopicravTa 
 Sovvai TTjv epdoTTjaiv dXX' aTrXms d/xapT-qfid eaTiv, wcm Kav 
 el /if) aiiTos, dXX' o ye Xoyos eXrjXeyfieveo ofioios eaTiv. Ivji- 
 fiaivei fievTOL iroXXaKis dpmvras Tfjv diJ.(j)L^oXiav oKveTv Siaipei- 
 aOai Sid rfjv TrvKvorrjra tS>v to, roiavTa TrpoTeivovTcov, onws fii] 
 jrpbs dnav SoKmai SvaKoXaiveiv eiT ovk dv oirjOevTcov irapa 
 TOVTO yevecrQai tov Xoyov, noXXaKi? dn'^VTrjcj-e wapdSo^ov. 
 "D<tt' eneiSf) SeSoTai SiaipeTv, ovk oKvqTeov, KaBdirep eXe\6r) 
 TTpoTepov. 
 
 El Se Ta Svo epoDTtjuaTa jif] ev noiei Tis* epmTrjfia, ovo av 
 6 napd TTjv oficovv/jiiav Kal Trjv dfi<f)i^oXiav eyivero trapaXo- 
 yi<Tp.6s, dXX' 7] eXeyxo? ^ ov. Ti ydp Sia^epei epmrfja-ai el 
 KaXXias Kal Oe/ua-TOKXfjs fiovcriKoi elaiv rj el dfi^oTepois <>' 
 ovO/J,a rjv erepois ovaiv ; ei yap TrXeKO Sr^Xol evos, nXeia 
 
EAErxnN. 55 
 
 must be simply Yes or Noj would then be practicable. As it is, 
 the unfairness of the questions compels ^s to add something to 
 them in our answer to correct their vices : though, if the 
 distinction was properly made by the questioner, the answer 
 should be simply Yes or No. 
 
 If it is held that equivocal terms lead to genuine confutation, 
 it is impossible for the answerer to avoid confutation. Where 
 the same proper name denotes several individuals, he must 
 perforce nominally deny what he affirmed, and affirm what he 
 denied. The correction that some have proposed is ineffectual. 
 Not Coriscus, they say, is musical and unmusical, but this 
 Coriseus is musical and this Coriscus is unmusical. Here " this 
 Coriscus" and " this Coriscus" are the same terms, and have 
 contradictory predicates. " But they do not mean the same 
 person." No more did the simple name : so that nothing is 
 gained. To call one of them simply Coriscus, and the other, 
 this or that Coriscus, is unjustifiable j for why should one rather 
 than the other have the distinctive addition, when their right 
 to it is equal ? 
 
 As it is uncertain when we have not drawn the distinction 
 whether we are confuted or no, and we have the right to draw 
 distinctions, to grant a premiss absolutely and without distinc- 
 tion is an error, and makes the answerer, or at least his answer, 
 appear to be confuted. It often happens that we see an 
 ambiguity but hesitate to distinguish, because the occasions are 
 so numerous, for fear of seeming to be perversely obstructive. 
 Then, never having suspected that a given point would be the 
 hinge of the argument, we are surprised into paradox. As, 
 then, we have the right 'of distinguishing, we must use it 
 unhesitatingly, as I said before^ 
 
 iS 
 
 In equivocation if two questions were not put as one, there 
 would be no paralogism, but either a genuine confutation or not 
 even a seeming one. What is the difference between asking 
 whether Callias and Themistocles are musical, and asking the 
 same question about two different persons of the same name ? 
 
56 HEPI 104>IITIKnN 
 
 ■npayr-qcTiv. El ovv fifj 6p6ov npbs Svo kprnTrjans /Mtau dir'o^ 
 Kpiaiv d^Lovv Xafi^dviiv &n\m, (pavepoy on ovSevl irpov'^m 
 tS>v 6fieovv/i(ov dnoKpivea-daL UTrXm, ovS" el Karci irdvT<ov dXtj- 
 Oes, &(Tnep d^Lovai Tives. OvSei/ yhp tovto Sia^ipei Ij ei 
 rjpero, KopicrKos Kul KaWias noTepov olkoi dalv rj ovk oikoi, 
 eire irapovTcov d/i(j)ou' eiVe p-fi irapovTCov d/KporipcDS yap 
 nXeiovs al npoTaa-ecr ov y&p el dXrjOes elireiv, Sia tovto fiia 
 T] epa>Ti]cns. ' Eyyatpel yap Koi /ivpia eTepa eprnT-qOevTa epcDTTJ- 
 /Mara dtravTa fj vat fj ov dXrjOes eivai Xeyeiv dXX o/ims ovk 
 dwoKpneov fiiS. diroKpicrev dvaipeiTai yap to SiaXeyea-Oai. 
 Tovto S ojjloiov As el Kal to avro ovojia Tedeiij tois eTepois. 
 El ovv fifj Sec wpbs Svo epcoTrjaeis [iiav diroKpiaiv SiSovai, 
 ^avepov oTi oiiS enl twv djioivviJimv to vai 7} oxi XeKTeov. OvSk 
 yap 6 elirmv dtroKeKpiTai dXX' eiprjKev. 'AXX' d^iovvrai ira>s 
 ev T0L9 8iaXeyofj.evoLS Siii, to XavOdveiv to ov/i^aTvov. 
 
 "Dcnrep ovv einonev, evetSijirep ovS' eXeyypi Tives ovTts 
 SoKovcriv eivai, KaTO. tov aiiTOV Tpowov Kal Xvcreii So^ovciv 
 elvai Tives ovk ovaai XvtreiS" &s Stj (pafiev kvioTe jiaXXov Seiv 
 <f>epeiv ^ Tas dXrjOels ev toTs dycavicTTiKoTs Xoyots Kal Trj npos 
 TO SiTTov dnavTYiaei. AwoKpiTeov 8' eirl fiev t5>v Sokovvtcov 
 TO eaTCo XeyovTa- Kal yap ovtcos ■^Kicrra yivoiT dv nape^e- 
 Xey)(^os- dv Se ti irapdSo^ov dvayKa^rjTai Xeyeiv, evTavda 
 HdXicTTa irpoadeTeov to SoKeTv oHitoi yap dv oUt eXey)(os ovre 
 napdSo^ov yiveadai So^eiev. 
 
 Ewel Se n&s alTedrai to ev dpyjj SfjXov, oiovTai Se ndvTei, 
 av fi (Tvveyyvs, dvaipeTeov Kal fir) (TvyyonpTfTeov eivai evia c»y 
 TO ev dpyrj aiTovvTos, OTav re * tolovtov d^ioi tcs o dvayKoiov 
 fj,ev (rv/jL^aiveiv eK Trjs 6ecre(os, rj Se yjrevSos rj dSo^ov, tovto 
 XeKTeov TO, yap e^ dvdyKijs avfi^aivovTa Trjs avTrjs eivai 
 SoKei Oeerems. "Eti OTav to KaBoXov fir/ ovojiaTi Xr](f)6ri dXXh 
 irapa^oXfj, XeKTeov oti ovx cor eSodrj ovS" toy irpovTeive Xaji^dvev 
 Kai yap wapd tovto yiveTai voXXaKis eXey^os. ' E^eipyofievov 
 Se TovTCov eirl to /ifj KaXm SeSeTxOai rropevTeov, dnavTrnvra 
 KUTd TOV elprjfievov Siopicr/j.6v. 
 
EAErXfiN. 57 
 
 If the persons are two j the question is two. If, then^ it is 
 wrong to give a single answer to two (questions, it is wrong to 
 give a simple answer to an equivocal question, even when it is 
 true in every signification, as some say you ought. It is just 
 the same as asking, are Coriscus and Callias at home ? In either 
 case, whether both are at home or neither, there are two ques- 
 tions. The truth of a single predicate to several subjects does 
 not make the questions one. Ten thousand questions might all 
 be answerable by one single Yes or No, and yet it would not be 
 a single answer : else there could be no dialectic. And the same 
 is true if many subjects have one name. If, then, a plurality of 
 questions must not receive a single answer, no more must an 
 ambiguous proposition be answered Yes or No. This is not 
 really an answer but a speech. It is made sometimes from not 
 foreseeing the consequences. 
 
 As there are unreal but seeming confutations, so, as we said 
 before, there are unreal but seeming solutions, which must some- 
 times be employed in preference to the true^ in contentious 
 disputation and replying to arguments based on equivocation. 
 When we admit premisses which we believe, we should use the 
 formula, Granted, for this will preclude accessory confutation. 
 When to save our thesis from confutation we must maintain a 
 paradox, we should profess it to be our genuine opinion ; thus 
 we avoid confutation and efface the character of paradox. 
 
 We have explained what begging the question means, and it 
 is allowed that when assumptions are closely connected with the 
 issue we may deny them and refuse to concede them as pre- 
 misses on the plea that they beg the question : similarly, if a 
 necessary consequence of the thesis is false and improbable, we 
 should use the same plea, for a necessary consequence seems to 
 be part of the thesis. Again, if the subject of a premiss obtained 
 by generalization is nameless, and only indicated by comparison, 
 we must say that what was propounded and granted was not 
 the principle now employed, for this is often the case?. Ex- 
 cluded from these courses we must attempt to shew that the 
 proof fails in some of the elements which we enumerated. 
 
58 HEPI IO<t>IITIKnN 
 
 'El/ /lev oSv ToTs Kvpims Xeyo/ievois ovofiaa-iv dvayKr} diro- 
 Kpivea-Bai ^ dirXms ^ Siaipov/ievov. *>l 8e avwrroi/oovvTeh 
 riOiHiv, ohv Sera firj aa<pS>s dWa koXo^Sis kpcoTdrai, irapk 
 TOVTO avfi^aivii 6 eXeyxoy, oioy dp' b &y ^ AQrjvaiaiv, KTTJfid 
 kvTLv' A6rjvaL<ov ; Nai. 'O/iolms Se Kat eirl tSiv dWmv. ' AXKit, 
 fifju 6 dudpanros kari t&v C^cc" ', ^«'' Krfjfia dpa 6 dvOpamos 
 tS>v ^fflcoi'. Tbv yap dvQpamov tSiv ^ma>v Xiyop-ev, ori ^mov eari, 
 Kal AvaavSpov rmv AaKmvcav, on AdKcov. ArjXov oSv &s kv oh 
 dara^ki to irpoTiivojievov ov crvy^^aiprjreov dnXms. 
 
 "Orav Se SvoTv ovtoiv darepov fjikv ovtos e| dvdyKrjf Bdrepov 
 ilvai SoK^, Oarepov Se tovto fir] e| dvdyKijs, kpayrwfievov npS- 
 Tepov Set TO eXaTTOv SiSouar yaXeTrmrepov yap cruXXoyia-aaSai 
 eK TrXeiovcov. Edv 8 kiriyeipfj on rm jiev e<rnv kvavriov t£ 
 8 oiiK eanv, dv 6 Xoyos dXrjOfjS ■§, kvavriov (pdvai, ovojia St 
 fjifj KetaQai tov eTepov. 
 
 Enel S evia fiev S>v Xeyovcriu oi iroXXol tov jirj arvyycupovvTa 
 y^evSeadaL dv (paiev evia 8 oxi, oTov oa-a diufuSo^ovaiv (norepov 
 yap <f)6apTri f\ dddvaTOS rj '^V)(fi tS>v ^axov, ov 8id)pi<TTai roii 
 iroXXoTsy ev oTs ovv dSrjXov noTepays eiwOe Xeye<r6ai to irpo- 
 Teiv6/j.evov, noTepov Ss al yvrnfiai (KaXovcn yap yvS/ias Kat Tas 
 dXrjOeis 86^as Kal Tds oXas dTrocpdva-eis^V ^ d>s ■^ 8idjieTpoi 
 dcrvfifieTpos, eTi o5 TdXrjQes djKpiSo^eTTai, /idXia-ra nera^pav 
 dv TLS XavOdvoi Ta ovo/iara irepl tovtwv (^8ioc. jiev yd,p to 
 d8rjXov eivai iroTepms e^et TaXrjBes^, ov 86^ei aocpL^ea-Oai, Sia Se 
 TO dfi(j)i8o^eTv ov So^ei ■yp'ev8ear6ai.Y j) 8e /leTa^opd Troirj(Tei tov 
 Xoyov dve^eXeyKTOv. 
 
 "Etl oa-a dv Tis irpoaia-OdvrjTai twv epayrrj/jidTCOV, npo- 
 eva-TaTeov Kal vpoayopevTeov oiira yap dv fidXiara tov 
 TTwdavo/ievov KoaXvcreiev. 
 
 XVIII. Enel 8' ka-Tlv fj fiev 6p6^ Xv<tis kfi^dvLo-LS ifrevSovs 
 avXXoyiafiov, nap onoiav kpcoTrjaiv avfi^aivei to -^evSos, o Se 
 ■^evSfjS (TvXXoyia-fibs Xeyerai Six&S (^ yap ei arvXXeXoyLO-Tai 
 ■\jrev8os, tj el p.^ div (rvXXoyia-/jibs SoKeT eivai onXXoyKr/jLos), «") 
 dv fj T£ eiprjiievr] vvv Xvais Kal -f) tov cpaivofiimv a-vXXoyKr/iov 
 
EAErXDN. 59 
 
 Properly expressed questions may be answered simply or with 
 a distinction : the understood but unexpressed portions of ob- 
 scure or elliptical questions are the harbours of fallacy. Do you 
 grant that what is of the Athenians is the property of the 
 Athenians ? Yes. And so in other cases ? Yes. Is not man 
 of the animals? Yes. Man therefore is the property of the 
 animals. But man is said to be of the animals because he is an 
 animal, as Lysander is said to be of the Spartans because he is a 
 Spartan. Obscure questions, then, are not to be granted with- 
 out distinction. 
 
 When of two propositions the truth of the first involves the truth 
 of the second but not reciprocally, if we have the option we should 
 graat the truth of the second. For the questioner will have to 
 argue with greater trouble and at greater lengfth. If he tries to 
 prove that one term has an opposite, another not ; if he is right, 
 we should say, they both have, but in one ease it is nameless. 
 
 The world has some opinions which it considers it false to 
 contradict, in others it is undecided and permits contradiction, 
 as, for instance, on the question whether the soul is mortal or 
 immortal. Sometimes, again, the natural interpretation of a 
 thesis is doubtful : whether, that is to say, it is to be taken in 
 a metaphorical sense, like a proverb, which is a practical aphorism 
 in a figurative dress, or in a literal sense, like the mathematical 
 theorem that the diagonal of a square is incommensurate to the 
 side. In such a ease, when moreover the doctrine is problematic 
 and the world is undecided, we may safely adopt a metaphorical 
 interpretation : the doubtfulness of the meaning saves our inter- 
 pretation from seeming sophistic, the indecision of the world 
 saves our assertion frojn seeming false, and the presence of 
 metaphor is a bar to confutation. 
 
 Foreseen questions should be anticipated by protestations and 
 distinctions ; for this disconcerts the questioner. 
 
 XVIII. One true solution of a false proof is the indication of 
 the false premiss that causes the false conclusion. False proof, 
 however, not only means a conclusive proof with a false con- 
 clusion, but also an inconclusive though apparent proof*- An- 
 other solution, then, will be the indication of the premiss 
 
60 HEPI I0<t>l2TIKnN 
 
 vapa TL cpaiverai twv kpoDTrfudrmv SiopdeoaLS. "iicrre avfi^aiva 
 tS>v Xoycav rovs fikv crvWeXoyiafievovs dveXovra, rovs oe (paivo- 
 /levovs SieXovra \veiv. fldXiv S' kwel rcav ovXKiXoyKTji^vmv 
 Xoymv 01 fitv dXrjOes ot 8e y^evSos exova-i to av/iTripaa-fia, to^s 
 filv Kara, to avunipaafia yjrevSeis SL)(as kvSkyeTai Xve.LV Kal 
 ydp TOO dveXiiv Ti tSiv rjpayrrjiJ,ei/a>v, Kal tw SeT^ai to trv/jTre- 
 paarjia 'i^ov ou^ oijtcos" toi>s Se KaTo. tols npordaeii t5 dviXuv 
 TL [loyov TO yap avinripaafia dXijOis. "Oa-re tols ^ovXofikuois 
 XveLv Xoyov wpcorov fiev (TKenTeov et avXXeXoyiiTTaL fj dcrvWo- 
 yiaTOS, eiTa troTepov dXrjBks to ovfiTrepaa/ia rj yjrevSoi, oirm rj 
 SLaipovvTes ^ dvaLpovvTiS Xvco/iev, Kal dvaipovvTes tj &8e fj SiSi, 
 Kaddirep eXe^^'? TrpoTspov. AiacjiipeL Se nXeLaTOv kpmTd>nevby 
 Ti Kal fifi XvfLV Xoyov to fikv yhp rrpoiSeTv )(^aXeTr6v, to Se 
 KaTOL a)(oX^v iSeiv ^aov. 
 
 XIX. T5>v jxev ovv irapa tt}v o/jLoovv/iiai' Kal Trjv a/i^t|3o- 
 Xiav kXkyycov ol fikv 'i)(ovaL tSiv kp(OTr)iidT<ov tl irXeim arniaivov, 
 OL Se TO avfinepaa/ia iroXXaxas XeyojjLevov, oiov kv jiev tS 
 (TLyrnvTa Xeyeiv to a-v/jLirepaafia Slttov, kv Se t5 p-ri avve- 
 TTLo-Taa-OaL^ tw kirL<TTdnevov ev twv kpayrrjiidTCiv djiiftL^oXov. 
 Kal TO Slttou oTe fiev eaTLv ore S" ovk 'icTTLV, dXXd arjuaiveL 
 
 TO OLTTOV TO fieV OV TO O OVK OV. 
 
 "OaoLS fiev ovv kv rS TeXeL to ■7ToXXa-)(S>s, &v jirj irpoffXd^rj 
 TTjv dvTi<paa-iv, ov yCveTaL eXey)(os, otov kv tw tov tv(()Xov opdv 
 dvev yap dvTi(f)dare(os ovk rjv eXeyyps. "Oo-ols S kv TOif 
 kprnTrijiacrLV, ovk dvdyKrj Trpoarrocpfja'aL to Slttov ov yap irpos 
 TovTo^ dXXa Slo, tovto 6 Xoyos. ' Ev dp-)(fj /iev ovv to SlttXovv 
 Kal ovofia Kal Xoyov ovtcos dwoKpiTeov, otl ecTTLv ms, ecrri o W 
 oil, wanep to a-LyStVTa Xeyeiv, otl ecrTLV coy, eart 5 o)? ov. 
 Kal tA SeovTa^ irpaKTeov eaTLV a, e<jTL 5' h. ov- Ta yap Seovra 
 XiyeTaL 7roXXa)(a)S. ' Eav Se XdOfi, knl reXeL irpoa-TiBevTa t§ 
 ApayrrjcreL SiopdaiTeov^ . ''Ap eoTt^ aLycovTa XeyeLV ; Oi, aXka 
 TOvSe a-LySivTa. Kal kv to'ls eypvaL Se to TrXeovayw^ kv toM 
 ■jrpoTda-ea-Lv o/ioicos. Ovk dpa crvveirio-TavTaL otl kiTLffTavTai ; 
 Nai, dXX' ov\ oi oUtcos kvLa-TdfievoL- ov ybip TaiiTov k(TTiv on 
 
EAErXDN. 61 
 
 that causes the false appearance. Conclusive proofs are solved 
 hy contradiction of a premiss, inconclusiv%proofs by distinction. 
 Again : — conclusive proofs either have a true or a false conclu- 
 sion. Those whose conclusion is false may be solved in two 
 ways, either by contradicting a premiss or by a counterproof 
 directed against the conclusion^ : those whose falsity is confined 
 to the premisses, by contradiction alone, as the conclusion is 
 true. Accordingly when we wish to solve a proof we must first 
 look to see whether it is conclusive or inconclusive, and, if 
 conclusive, whether the conclusion is true or false; and then 
 solve it either by distinction or contradiction, and in the latter 
 case either by enstasis or by counterproof, as I said before^. It 
 is very different to solve a proof under interrogation and after- 
 wards. To anticipate is difficult ; to detect a fallacy at leisure 
 is easy. 
 
 XIX. When there is an ambiguity in a term or a proposition 
 of a confutation, the ambiguity sometimes lies in the premisses, 
 sometimes in the conclusion. In the argument about speech of 
 the speechless the conclusion is ambiguous^ : in the argument 
 about the unconsciousness of knowledge a premiss is ambiguous. 
 The ambiguous proposition is true in the answerer^s sense, false 
 in the opponent's. 
 
 When the ambiguity lies in the conclusion, unless the con- 
 clusion is previously denied by the respondent, there is no 
 confutation, as we may see in the argument about sight of 
 the blind ^, for confutation requires contradiction. When the 
 ambiguity lies in a premiss the semblance of confutation does 
 not require a previous contradiction of the ambiguous proposi- 
 tion; for then the ambiguous element is not the subject or 
 predicate of the thesis confuted, but the middle term of the 
 proof. The thesis should at starting be stated with a distinc- 
 tion, if it contains any ambiguity. We should maintain, for 
 instance, that speech of the speechless is possible in one sense 
 and not in another, and that what is necessary ought sometimes 
 to be done, sometimes not, as the word is ambiguous. If the 
 ambiguity is not at first detected, we should afterwards restrict 
 and correct the thesis. Is speech of the speechless impossible ? 
 -No, but speech by the speechless is. So when the ambiguity is 
 in the premisses. Is not knowledge conscious ? Some is, that 
 
62 HEP I I0<PI2TIKnN 
 
 ovK ea-Ti (TvviiTL(TTaa6ai koI oti toijs mSt iTna-Ta/iivovs ovk 
 
 io-TLv. "0\cas T€ /jLaxeriov, Siv Koi airXms auWoyi^TiTai, on 
 
 OVK 8 'i(f>r](Tev dTre<prj(re Trpdyfia, dW' ovofia- ma-r ovk 
 
 XX. *Pavepbv 8e Kai revs rrapa rrjv Siaipeaiv Kal avvdeaiv 
 TrSy Xvreov av yap Siaipov/iefos Kal (rvvTiOenevos 6 Xoyof 
 'irepov a-rjfiaivr]^ <jvfirrepaii/ofj,eyov Toivavriov XeKTeov. Eiirl Sk 
 ■irdvTes ol tolovtoi Xoyoi iraph Tr]v (rvvOecnv rj Siaipeo'iv. ''Ap 
 (p eiSes ai> tovtov rvnTOfievov, Tovrm ervTrrero oSroy ; Kal & 
 eTvirreTO, tovtw cri) eiSes ; e^et jiev ovv Ti KaK t&v dfufti^oKm 
 epcoTrj/idrtov, dXX ian naph crvv6e<nv. Oii ydp eari Svttov to 
 napa rrjv SiaCpeaiv oii yap 6 avTos Xoyos yiverai Siaipov/ievos, 
 eiTrep firj Kal to opos Kal opos Ttj irpoa-mSia Xe)(6€v a-rjiiawei 
 erepov^. AXX kv fikv roTs yeypa/i/iivois ravTov ovojia, orav e/c 
 tS)V avTwv (TTOLyeuav yeypafifievoi' 57 Kal dxravTcos, KdKeT S" ijSrj 
 Trapd(Trjfj,a iroLovvraij rd 8e (j)6eyy6fi€va ov Taiird. "Dot ov 
 Slttov to rrapa Siaipeaiv. ^avepov 8k Kal oti ov TrdvTes oi 
 eXeyxot irapd to 8itt6v, Kaddwep Tivis <f)a<nv. 
 
 AiaipiTiov ovv tS dnoKpivoiiivw' ov yap TavTov iSeiv Toh 
 6(pdaX/j.oTs TvnTOfievov Kal to <j>dvat l8eTv toTs otpOaXjim 
 TVTTTOfievov. Kal 6 Evdv8Tifiov 8e Xoyos, ap oT8as (ri) vvv 
 ovcras kv Heipaie? TpiTJpeis kv ZiKeXia av ; Kal trdXiv, ap 
 ea-Tiv dyadbv ovTa a-Kvria fioyOripov eivai ; eir] 8 av ns 
 dyaOos Cov (TKVTeiJs /jL0)(6rip6s' ma-T iarai dyaOos (TKVTeiiS 
 fj.0)(6r]p6s. ''^Ap S)v al kiTKTTrifiai (TTTOvSaiat, <Tnov8aTa tol iiaorj- 
 fj-aTa ; tov Se KaKOV (nTOv8aTov to jidOr^fia^ ■ (nrovSaiov &pa 
 fLdOrjua TO KaKOV. ' AXXii firjv Kal kukov Kal p-dBrtp-a to KaKov, 
 Sa-Te KaKOV /j.d$T]fia to kukov. '/4XX' kaTl KaKwv anovSata 
 kiriarrinr}. '^Ap dXrjQes elrreiv vvv on ad yeyovas ; yeyovai 
 dpa vvv. *H dXXo a-Tj/jLaivfi 8iaLpe6kv dXrjOes yap eiveiv vvv 
 OTI (ri> yiyovas, dXX' ov vvv ykyovas. '^Ap d>s Svvaaai Kal h 
 
EAErXDN. 63 
 
 is to say, such and such a kind of knowledge ; for there is a 
 difference between the restricted and unjestricted premiss. If 
 the questioner argues without regard to the distinction^ we must 
 contend that he has contradicted the name and not the reality, 
 and therefore has not confuted. 
 
 XX. It is evident how fallacies of composition and division 
 are to be solved. If the composition or division produces a 
 difference of signification, when the opponent draws his con- 
 clusion from the premisses in one signification, we must say 
 they bore the other. The following arguments depend on com- 
 position and division. Was the man beaten with that with 
 which you saw him beaten, and did you see him beaten with 
 that with which he was beaten' ? The reasoning has something 
 of the fallacy of ambiguous proposition, but belongs to a distinct 
 class, the fallacy of composition. We have not here a single 
 proposition with a double meaning, for the division produces 
 two propositions, just as the characters, oros and horos, are the 
 sign of two different sounds, distinguished by the breathing 
 though not by the accent. The written word may be the same 
 when it has the same letters in the same order, though even 
 written words are now distinguished by accents and aspirates, 
 but the spoken words are undeniably different. The fallacy of 
 division, then, does not consist in ambiguity, nor is ambiguity 
 the principle of all sophism, as some have asserted^. 
 
 The answerer must distinguish and point out the difference be- 
 tween seeing with the eyes a man beaten and seeing him beaten 
 with the eyes. So in the argument of Euthydemus. Do you 
 in Sicily know at this moment there are triremes in the Pirseus*? 
 Again : a good shoemaker can be a bad shoemaker, for a good 
 man may be a bad shoemaker, therefore he is both a good shoe- 
 maker and a bad shoemaker^. Again: if the knowledge of a 
 thing is good, it is a good thing to learn : the knowledge of evil 
 is good, therefore evil is a good thing to learn. But evil is evil 
 and a thing to learn, therefore it is an evil thing to learn. As 
 it is true that the knowledge of evil is good (the fallacy must lie 
 in the rest of the reasoning). It is true to say in the present 
 moment you are bom : then you are born in the present 
 moment. No : the division makes a difference : it is true in 
 the present moment that you are born but not that you are 
 
64 HEP I IO<f>IZTIKnN 
 
 Svvaaai, ovTW Kal ravra TTOLrjaais ay ; ov Ki6apiCa>v 5' exets 
 Svva/iLv rov KL6api(iLV Kidapiaais &u dpa ov KiOapi^wv. *H oii 
 
 TOVTOV €Y6t T^ 8vUCC/ilV TOV OV Kldupi^COV KlOapL^fLV, fflXX oVe 
 
 oil noiei, rov noielv. 
 
 AvovcTi Si TLves TovTOU Kal dXXcos. El yap eSooKev aiy 
 Svyarai iroieLv, ov (fyacn ovii^aiviLv fifj KiQapi^ovra KiOapi^uv 
 ov yap nduTcos m Swarai TroteTv SeSoa-Bai iroLrjO-^iv ov rairov 
 S' eivai o)? Svvarai Kal navTCOi toy Swarai noieTv. 'AXXa 
 <f)avepov OTi ov KaXms X6ovaiv tS>v yap iraph ravTov Xoymv 
 fi avrfj Xvcris, avrrj S ou^ apfioaei ejrl wavras ovSe iravrm 
 epcoTcofievovs, dXX ecm irpos tov epcoT&vTa,- ov npos rov 
 Xoyov. 
 
 XXI. riapd 8k TTjv TrpoacpSiav Xoyoi fiev ovk ilaiv, ovre rS>v 
 yeypa/jL/ievcov ovre tS>v Xeyofievcov, ttXtju et rcves oXiyoL yi- 
 voivT dv, OLOv oStoj d Xoyoy. '^Apd y ka-rl to ov KaraXveis 
 oiKia ■ Nai. OvKovv to ov KaTaXveis tov KaTaXveis aTro^aais ; 
 Nai. "Ecprja-as S tivai to o5 KaToXijeis oiKiav fj oiKia dpa 
 dn6<f>a<ns. '/2y Br] XvTiov, SrjXov ov yap Tavrb crtifiaivei o^v- 
 Tepov TO Se ^apvTepop ^rjOev. 
 
 XXII. ArjXou 8k Kal toTs irapa to axravrcoi Xeyea-Oai ra 
 /ifj TuvTo, TTcSy diravTrfTkov, eireiirep e)(^ofiev to, yevq tSiv KaTi]- 
 yopLwv. jikv yap eScoKSv epooTrjOels fifj imdpj(iiv Ti Toirmv 
 Sera Ti kaTi a-r}/j.aiy€r 6 S e8ei^ef imdpyov ti tS>v irpos tl rj 
 iToaSiv, SoKovvTcov Se ti k<TTi arj/iaiPeiv 8id ttiv Xe^iv, oiov ev 
 rmSe ra X6ya>. '^Ap ki/Se^^erai to airro dfia TTOieTv t€ koI 
 ireiTOLriKevaL ; Oii. 'AXXa firjv opdv ye tl dfia Kal ewpaKevat 
 TO avTo Kal KaTO, Tairrh kvSeyeTai. '^Ap kcrTi ti tSiv irda-yeiv 
 TTOieiv TL ; Ov. OvKOVv TO Te/iveraL KaieTai aladdveTaL oholcos 
 XkysTaL, Kal irdyra 7rda-)(^eLi' tl a-rj/iaiveL' woXlv Se to XeyeiV 
 Tpeyeiv opdv ofioims aXXijXoiy XeyeTar aXXd firjv to y opdv 
 ata-Odvea-Oai tl kcrTLV, wa-re Kal irdayeiv tl dfia Kal. iroieiv. 
 El Se Tis kKei Soi)s /xfi kvSey^eaOaL dfia tovto iroLeiu Kal iretroir]- 
 KevaL, TO opdv Kal icopaKevaL ^air] kyxoapeiv, oUnrn kXrjXeyKTaL, 
 el fifj Xeyoi to opdv TroieTv tl dXXd irdcrxeLV irpocrSeT yb.p 
 
EAErXDN. 65 
 
 bom in the present moment. — Do you do what you can and 
 as you can? Yes. Not harping, you* can harp. You harp, 
 then, not harping. No : you have not the power to harp not 
 harping, but when not harping you have the power to harp. 
 
 The solution some propose is different. If it is granted that 
 a man does a thing as he can, they say it does not follow that 
 he harps not harping, because it was not granted that he does 
 the thing in all the ways in which he can. The solution is 
 clearly bad, for faUades identical in principle should admit of 
 the same solution ; but this solution will not apply to other 
 fallacies similar in principle, nor to every mode of interrogation. 
 It is a solution relative to the individual arguer, not to the 
 argument. 
 
 XXI. AccENTTJATiOK scarcely gives rise to any fallacy either 
 in writing or speaking, but a few might be invented like the 
 following: — ^A house is where you lodge {ou with circumflex 
 and aspirate), you do not lodge {ou with unwritten grave accent 
 and soft breathing) is a negation, therefore a house is a nega- 
 tion. The solution is plain, for the word is not the same when 
 the accent is grave and when it is circumflex. 
 
 XXII. It is plain that we must solve fallacies from similarity 
 of expression by pointing out the difference of category denoted 
 by similar words. The thesis denies the existence of a sub- 
 stance, and the questioner proves the existence of a relation or 
 quantity that seems to be a substance from the form of ex- 
 pression. For instance ; can we be making and have made 
 one and the same thing ? No ^. Why, we can be seeing and 
 have seen one and the same thing. Can an action be a passion ? 
 No. Why, to be cut, to be burnt, to be affected by a sensible 
 object, are similar expressions, and all denote passions. Again, 
 to say, to run, to see, are similar expressions. Now to see is 
 to be affected by a sensible object, therefore it is both an action 
 and a passion. In the former example, if I asserted in my thesis 
 that one could not be making and have made the same thing, 
 and granted that one could be seeing what one has seen, I am 
 not confuted unless I grant that seeing is making. This addi- 
 tional premiss is required, but the hearer thinks that when I 
 
 F 
 
66 PEPI IO<P/ITIKnN 
 
 ToijTov Tov epcoTrj/xaTOS- d\\' ino tov dKovovTOS vnoXafi^dveTat 
 SeSoDKevai, ore rb refiveiv iroieTv ti Koi to rerfiriKevai wenoLrj- 
 Kevai eStoKe, koi Sera dWa oixoicos Xiyerai. To ydp Xombv 
 aiiTos npocTTLBrja-LV 6 dKoimv a>s o/ioioas Xeyo/ievov to Si Xe- 
 veTM jikv ovx ofjioims, (ftaiverai, Se Sid Trfv Xt^iv. Th avrh 
 Se (rvji^aivii onep kv tous 6p.a>vvfiiair oifTai ydp kv roh 
 o/jLtov^fiois 6 dyycbs Tmv Xoywv o ecjirjaev d7ro(f)fja-aL irpayjia, 
 oiiK Sfo/ia- TO Se eTi irpocrSeT kpcorijfiaTos, el k<f) ev /SXIttooi/ 
 Xeyei to ofidivvfiov ovrms ydp Sovtos eaTai eXey)(ps. 
 
 "OfioLOL Se Kal o'iSe ol Xoyoi tovtois, el 6 tis e)(cov iiffrepou 
 fir) e^ei dire^aXev 6 ydp eva jiovov diro^aXmv daTpdyaXov 
 ov)( e^ei SeKa daTpaydXovs. *H b jiev /if/ e)(et irpSrepov e\<ov, 
 dwofii^XrjKev, ocrov Se ftfj exei fj oaa, oiiK dvdyKTj Tocravra 
 dnoPaXeiv. Epcorrjaas ovv 8 fX^'» avvdyei ewt tov Sara' t^ 
 ydp SeKa rroard. El ovv i^peTO k^ dpyfjs ei oaa tis jiri iyti 
 vp&repov eyoiv, dpd ye dno^e^XTjKe Toaavra, oiiSels dv eSaiKev, 
 dXX ^ TOcavTU ^ TovTwv Ti. Kal on Soirj av tis 8 lifi e^"' 
 ov ydp exet eua fiovov daTpdyaXov. *H ov SeScoKev 8 oiiK 
 ef^ej', aXX' ms ovk e'^e, tw eva. To ydp jiovov ov ToSf 
 a-Tjfiaivei ovSe ToiovSe ovSe TOtrovSe, aXX' coy ex*' npos ti, ofov 
 oTi ov iier dXXov. "Qarrep odv el rjpeTO dp' 8 /iij "? ^X^' 
 SoiT] dv, fifj (pdvTos Se epoiTO el Soir] dv tis re Taverns ji^ 
 eytav Ta\e<os, (prjaavros Se avXXoyi^oiTO on Soit] dv tis S fifi 
 eX^t. Kai (pavepbv oti ov (TuXXeXoyiaTar rh ydp Tayews ov 
 T6Se SiSovai dXX' &Se SiSovai kanv as Se fifi ex« ris. Soil] dv, 
 ofov rjSeotis eymv Soit] dv XvTrrjpois. 
 
 "0/j.oioi Se Kal ol ToioiSe vravTes. "^Ap jj fifj exet X^'P' 
 TJuTTToi dv ; fj m n^i exei otpdaXfiS iSoi dv ; ov ydp e)(ei eva 
 fiovov. Avova-i fiev oSv Tives XeyovTes Kal d>s e)(ei eva jilivov 
 Kal o^BaX/iov Kal dXX' onovv 6 irXeim ex<ov. 01 Se Kal a>S 
 8 ex^i eXa^ev^- eSiSov ydp fitav /j.6vov o&ros ■^fj^ov Kal oSToy 
 
EAErXQN. 67 
 
 granted that to be cutting is to be making, and to have cut 
 to have made, I also granted that the rftnaining forms denote 
 corresponding categories. The hearer himself grants that the 
 remainder have a similar signification, whereas the signification 
 is different, though the forms are similar. What happens in the 
 fallacies of ambiguous term happens here. In the fallacies of 
 ambiguous term the uninitiated fancy that the reality is contra- 
 dicted as well as the name, whereas confutation requires a fur- 
 ther admission, that one reality is denoted by the ambiguous 
 name. If the answerer grants this, he is confuted. 
 
 Similar to these reasonings are the following. What one 
 had at first and has no longer he need not have lost, for if he 
 had ten dice and loses one he has no longer ten. No. What 
 he had at first and has no longer he must have lost ; though he 
 need not have lost as much or as many as he had at first. The 
 thesis spoke of the substance that he has no longer, the con- 
 clusion speaks of the quantity. If it had been asked, when a 
 man has a certain number of things at first and not subse- 
 quently, must he have lost them all ? it would have been answered. 
 No, he need not have lost them all, but he must have lost some 
 of them. Again : — A man may give away what he has not got, 
 for he may have many and give away only one. No. He does 
 not give away a thing which he has not got, but a thing which is 
 not related in the giving as it was in the having, if he had many 
 and gives only one, for only denotes neither substance, nor quality, 
 nor quantity, but relation, namely dissociation from others. When 
 the thesis is that a man cannot give what he has not got, if it is 
 granted that a man may give quickly what he has not got 
 quickly, and I infer that a man may give what he has not got, 
 my argument is inconclusive : for quickly does not denote sub- 
 stance but manner, and the manner of giving may be different 
 from the manner of having ; for a man may have with pleasure 
 what he gives with pain. 
 
 Similar, too, are the following : — Suppose the thesis to be, a 
 man cannot see with an eye he has not nor strike with a hand 
 he has not. But a two-eyed or two-handed man has not only 
 one eye or hand but may see or strike with only one. Some 
 meet the argument by contradicting the premiss which denies 
 that a man has only one eye or anything else when he has more 
 
 F 2 
 
68 nEPI IO<t>IITIKnN 
 
 y ?Yet, ^aa-i, /iiav fiovrjv iraph, tovtov yjrfjtpoi'. 01 S' eiiBiis 
 Trjv kpm"r}<nv^ dvaipovvres, on evSi^erai o fi^ eXa^ev ex*'". 
 ofov olvov Xa^SvTa rjSvv, 8ia((>dapevTos kv rfj Aiji/ret, e^eiv' 
 6^vv. '/4XX' owep kXe\Brj Koi irpSrepov, oStoi iravres oi irpbi 
 rbv \6yov aXXA irpoy tov dvOpamov Xvova-iv. Ei yhp rjv aSrr] 
 Xv(ns, Bovra to dfTiKei/ievov oux ofov re Xijeiv, KaOdirep iirl 
 rZv aXXwv otov, el ea-ri fikv t eari 8 t oi! rj Xvais, av anXwi 
 SS Xeyea-dai, av/nrepaiverar k&.v de [irj avfiirepaivTjTai, ovk av 
 fit] Xva-is' kv Se rots irpoeiprj/jLivois navTcav SiSo/iivoov- ov8k 
 ^afJLev yii/eadai crvXXoyicriiov. 
 
 "En 8e Kal 018" eial toutcdv rmv Xoymv. '^Ap h ykypavrai, 
 eypa^iro^ ; /"eypawrat 5e vvv on ai KaBtjaai, ■^evSfis XSyor 
 TJv 5' dXrjdrls, or kypd^iTO' dfia Spa kypd^ero yfrevBris Kai 
 dXrjOijs. To yhp -^evBrj ^ dXrjOfj Xoyov fj 86§av eTvai ov roSt 
 dXXdi, T0i6f8e a-r]/J.aivei' 6 yap airrbs Xoyos Kal kirl Ttjs 86^ri?. 
 Kal dp' 8 navOdvei. 6 jiavQdvoiv, tovt kvrlv 8 fiavOdvei ; fiay- 
 Bdvei 8k ns rh Ppa8i> Ta\v. Ov rotvvv 8 jiavBdvu aXX' ay 
 fiavOdvii eiprjKev. Kal dp' 8 pa8i(ei TiS irarei ; ^a8i(H 8i 
 rtjv ■fifiepav oXrjv. *H ovxt Pa8i(u dXX' ore Pa8i(H upt]K(.v. 
 Ov8' &rav rr)v KvXiKa vivuv, 8 irivei dXX' e| o£. Kal dp' ns 
 ot8ev, fj fiadrnv ^ eipmv otSev ; &v Se to ji^v eSpe to 5* e/iafle, 
 Td diKJxo ov8kTepov. *H 8 filv d-rrav, A 8\ ovx airaura ®. Kal 
 
EAErxnN. • 69 
 
 than one. Or suppose the thesis to be. What a man has re- 
 ceived and not parted with he possesses ; ^and the premisses, He 
 received only one ballot, but, having several before, does not 
 possess only one : conclusion. Therefore he does not possess 
 what he received. Some solve this by contradicting a premiss, 
 and maintaining that he possesses only one from this donor : 
 others by contradicting the thesis, and asserting that it is pos- 
 sible not to possess what one received; to receive sound wine, 
 for instance, and if it was injured in the storage, to possess sour. 
 All these solutions, like some mentioned before, are addressed, 
 not to the argument but to the arguer. In every true solution, 
 an admission contradicting the allegation of the solution would 
 make the confutation valid, as in the other . examples. For 
 instance, if the solution is a distinction, an admission that the 
 premiss is true without distinction would make the conclusion 
 valid. Where a valid conclusion .does not follow from the con- 
 tradictory of the solution, that solution cannot be true. In the 
 above examples, even if all is supplied which the proposed solu- 
 tions allege to be wanting, there still is no conclusion *. 
 
 The following arguments belong to the same class. Suppose 
 the thesis to be, that the same statement cannot be both true 
 and false. Then because what is written was written a certain 
 time ago, and what is written, namely, that you are seated, is 
 false now, though true when it was written ; the arguer con- 
 cludes that what was written was both true and false. But the 
 falsity or truth of a statement is not its substance (what is 
 written) but its quality : and so of opinion. Again : — what a 
 man learns is what he learns : a man learns a slow march quick 
 (quickly), therefore quick is slow. Here the subject which a 
 man learns is confused with the rate of his learning. Again : — 
 what one walks he tramples on : a man walks a day ; therefore 
 he tramples on the day. Here we change from space to time. 
 Again : — when a man is said to drink a cup, the expression con- 
 fuses the vessel and the wine. Again : — suppose the thesis to 
 be, that the same thing cannot be both known and unknown ; 
 then because all that a man knows he knows either by teaching 
 or discovery ,• and if part of his knowledge was taught him, and 
 part discovered, the whole was neither taught nor discovered, 
 I conclude that the whole was both known and unknown. The 
 
70 nEPI ZO^IITIKDN 
 
 OTi eari ris rpiros dv^pumos'' vap aiiTov Kal Toi>s Ka6' e/co- 
 a-Tov. To yhp dvOpamos Kal &irav to koivov ov roSe ti, dXXi 
 ToiovSe Ti ^ npos ri rj irws ^ rwv towvtcov ti irrjfiaii/tl, 
 'OjiotoDt B\ Kal eirl tov KopiaKOS Kal KopiaKOS /lovaiKos, no- 
 Tepov TavTov rj eTepov ; to /lev yhp ToSe ti to Si ToiovSe 
 a-rj/jLaivei, &<tt' ovk ea-Tiv avTo fK6ea-6ai^. Ov to (KTi6eff6ai 
 Se iroieT tov TptTov avOpcmrov, aXXcfe to ojrep ToSe ti ftvai 
 <rvy)(oopeTv, Ov yap earai ToSe ti etvai ojrep KaXXias Kal mip 
 dvOpamos eoTiv. 068 ei tis to eKTiOififvov firj oirep roSe ti dvai 
 Xeyoi aXX orrep iroiov, ovSev Sioiaref earai yhp to irapa robs 
 iroWods ev ti, oTov 6 dvOpamos. <t>avepov oSv oti ov Soriov 
 ToSe Ti eTvai to koivt} KaTTjyopov/ievov enl ndaiv, dXX' rjroi 
 TTOiov 17 npos Ti ^ no<rbv 17 tZv tolovtcdv ti a-rjfiaiveiv. 
 
 XXIII. "OXeos S' kv ToTs irapa ttjv Xe^iv Xoyois del Karh. 
 TO avTiKeifievov earTat 17 Xvcris rj trap 6 eaTiv 6 X6yos. Oiov 
 el napa avvOemv 6 Xoyos, fj Xvais SieXovTi, el Se rraph. Siai- 
 pe(Tiv, avvOevTi. fldXiv el irapa vpoamSiav o^etav, ■q jSapeia 
 npoacoSia X6aii, el Se irapa fiapeiav, 1) o^eia. El Se irap 
 o/ioovvfitav, ea-Ti to avTiKeijievov ovojxa ehrovTa Xveiv, oiov ei 
 efi'^v)(ov ^ av/jL^aivei Xeyeiv, dwo^rjaavTa fifi eivai, SrjXovv W 
 ea-Tiv efi'^\ov el S' d'^)(^ov e<pri(rev, 6 S' 'ifii^ypv avveXa^ie 
 aaTO, Xeyeiv d)S evTiv d'<^-)(ov. 'Ofioicof Se Kal eirl Trjs dfi^i- 
 poXiai. El Se irap oiioioTrjTa Xe^ems, to dvTiKeifievov earai 
 Xva-is. ~ Mp o /ir) exei, Soirf dv tis ; *H ovx S /i^ exei, aK>! 
 d)S oiiK e)(ei, oiov eva fiovov daTpdyaXov. '*Ap h iiri<naTai, 
 tj fiaB^v ^ eipa>v eiriaTaTai ; 'AXX' ov-^ h eiriaTarai. Kal el 
 & ^aSi^ec iraTeT, dXX' oi^x ore. 'O/ioms Se Kal eirl t&v 
 dXXtov, 
 
EAErXiiN. 71 
 
 solution is, that the premiss asserted, that all he knew distri- 
 butively, not all collectively, was from x)ne of these sources. 
 Again, the proof of a third order of man, besides the individual 
 man and the ideal man, depends on the confusion of category. 
 For man and other generic terms are not names of substances, 
 but of quality, or relation, or mode, or some other accident. So 
 in the problem whether Coriscus and the musician Coriscus are 
 different or the same, one term expresses a substance, the other 
 a quality which cannot be really isolated. It is not, however, 
 the isolation that produces the third order of man, but the 
 assumption that the generic man is a substance, for without 
 this, what is common to Callias and the generic man could not 
 seem to be a substance. And what is isolated may be considered 
 as not a substance, but merely a quality, without any logical 
 inconvenience, for we shall still have a one besides the many, 
 for instance, the generic man ^. We must maintain, then, that 
 genera are not names of substances, but merely names of quali- 
 ties, or relations, or quantities, or other accidents ^°. 
 
 XXIII. When language is the source of fallacy, the opposite 
 interpretation to that which produces the fallacy furnishes the 
 solution. If composition produces the fallacy, division gives the 
 solution ; if division, composition. If acute accentuation creates 
 the fallacy, grave accentuation supplies the solution; if grave, 
 acute. If an ambiguous term is misinterpreted, give the oppo- 
 site interpretation. If the thesis said a thing was animate, and 
 the terms prove it inanimate, interpret them so as to leave it 
 animate : if your thesis said it was inanimate, and the terms 
 prove it animate, interpret them so as to leave it inanimate : 
 and so with ambiguou^ propositions. If similarity of expression 
 leads to confutation by one interpretation, the opposite interpre- 
 tation provides the solution. If the thesis is, that a man cannot 
 give what he does not possess, then your concession must be ex- 
 plained to be, that the possessor of many things who gives only 
 one, gives, not a thing that he does not possess, but a thing 
 that is not related to other gifts as it was to other possessions. 
 Each element of a man's knowledge is known either by tradition 
 or by discovery, not the sum total. A man tramples the way 
 he goes, not the time. And so in the other cases. 
 
72 nEPI IO<PIITIKnN 
 
 XXIV. Ppos Se Tovs napa to avfi^e^riKos /iia fiev ^ airfi 
 Xija-is npbs anavras. 'Eirei yhp dSiopiorov e<m rb ir&ri Xe- 
 KTeov knl tov irpdyiiaTos, orav inl tov crufi^i^riKOTOS virdp-)(ri^ 
 Kal en kv'unv [ikv SoKeT Kal (paaiv, eir kficov 8' oil (paa-iv dvay- 
 Koiov ehai, prjriov ovv (rvfji^i^acrQevTas ofioims irpbs dvavras 
 oTt ovK dvayKoiov. "Eyiiv Sk SeT 7rpo<j>epeiv rb ofov. Eial 
 Se ndvres ol roLoiSe rmv Xoymv irapk to avfi^e^riKos. ''Ap 
 oTSas o fj,eXX(o <re kpayrdv ; ' Ap oiSas Tbu irpoaiovTa ^ tov ey/te- 
 KaXvfifikvov ; ''Ap' 6 dvSpids <r6v kaTiv epyov, ^ <rbs 6 kvwv 
 iraTTJp ; ^Apa to, oXiydKiS oXiya oXiya ; 'Pavepbv yap kv airatri 
 ToijTois oTi oAk dvdyKt] Tb kut^ tov avfiPe^tjKOTOs Kal Kara 
 TOV Trpdy/iaTos dXrjdevea-6af /iovois ydp toTs KaTa ttjv oixriav 
 dSia^opois Kal ev oSariv arravTa SoKeT ravTa, irndpyeiv. Tw 5" 
 dya6£ ov ravrov kaTiv dyaOa t efvai Kal fieXXovTi kpayravBai, 
 ovSe Tw TTpoaiovTi ij kyKeKaXvfifievm irpoaiovTi. re uvai Kal 
 Kopi(TK<u. " QaT OVK ei olSa rbv KopiaKov, dyvoco 8e Tbv npoa- 
 lovTa, Tbv avTbv oi8a Kal dyvoSf oii^ el tovt kaTW- kfiov, etrn 
 8" epyov, kfiov kariv epyov, dXX ^ KTrjjia f\ irpdyfia fj dXXo n. 
 Tbv aiiTov 8e Tp&irov Kal knl tS>v dXXwv. 
 
 Aijova-i Se Tives dvaipovvTes^ rfiv kpcorrjirLV <f>aal yhp evoe- 
 yeadai Tairrb irpay/ia elSevai Kal dyvoeiv, dXXd firj Kara 
 Tairro- Tbv ovv npoaiSvTa ovk eiSSres, Tbv Se KopiaKOv eiSores, 
 TavTb fiev eiSevai Kal dyvoeiv <f>a(Tiv, dXX' ov Karh Tairo. 
 KaiToi irpZTov fiev, KaOdtrep fjSri einofiev, SeT rmv irapa 
 ToiiTb Xoycov t^v avr^v eTvai SiopOaxriv aiiTt) S' oiiK e<nai, 
 dv Tis /iTi knl TOV eiSevai aXX' knl tov eivai rj ttSs e\eiv to 
 avTb d^ioofxa Xafi^dvn, oTov el SSe ka-Tl narrjp, ea-ri Se aor tl 
 
EAErXQN. 73 
 
 XXIV. All fallacies from the equation of subject and accident 
 admit of the same solution. It is undetarmined when the sub- 
 ject has the attributes of its accident, and sometimes it is be- 
 lieved and maintained to have them, sometimes not. We must 
 therefore reply to every conclusion based on this principle, that 
 it does not follow ; and we must be prepared with an example ^. 
 The following arguments- depend on the equation of subject and 
 accident. You do not know what I am going to ask you about ; 
 I am going to ask you about the nature of the Summum 
 Bonum ; therefore you do not know the nature of the Summum 
 Bonum^. You do not know the person approaching with a 
 muffled face ; he is Coriscus : therefore you do not know Co- 
 riscus ^. The statue is a worl^manship ; the statue is yours : 
 therefore the statue is your workmanship. The dog is yours ; 
 the dog is a father : therefore the dog is your father *- A small 
 number multiplied by a small number is a large number. Then 
 a four multiplied by a four is a large number; but a four multi- 
 plied by a four is a four ; therefore a four is a large number '. 
 What is true of the accident is not of necessity true of the 
 subject (and vice versa) : for only those things whose entire 
 essence is one and indistinguishable have all their attributes in 
 common. But being the Summum Bonum is not exactly the 
 same as being about to be asked : nor is approaching with a 
 muffled face exactly the same as being Coriscus. So if I know 
 Coriscus and not the person approaching, it does not follow that 
 I know and do not know the same person : and if this is mine, 
 and a workmanship, it is not my workrnanship, but my chattel 
 or property ; and so in the other cases. 
 
 Some solve the difficulty by distinguishing the thesis and 
 making the fallacy consist of Ignoratio elenchi. They say we 
 may know and not know the same thing but not in the same 
 respect : that, if you know Coriscus and do not know 
 who approaches, you know and do not know the same per- 
 son, but not in respect of the same predicate. But, in the 
 first place, as I said before 7, all fallacies on the same prin- 
 ciple ought to receive the same solution. Now this solution 
 would not apply if we argued, not about knowledge, but 
 about existence or relation : if, for instance, because this slave 
 is a father and this slave is yours, I argued that he is your 
 
74 HEP I IO<t>IITIKDN 
 
 yap in kviav tovt iarlv oKrjdh koI ei/8ex^Teu TaiiTo fl- 
 Seuai Kal dyvoeiv, d\\' evravBa ovSev KotvoDveT to Xe^Oev. 
 OvSev Se K<o\ijei tov avrbu Xoyov irXeiovs fio)(6ripias e^eiv 
 aXX' ovx ^ ndarfs ajiaprtas kfupdvuns Xv<ris etrriv eyx<opet 
 yhp 8ti /lev ■^evSoi avXXeXoyuTTai SeT^ai riva, nap' b 8e fi^ 
 Sei^ai, oTov TOV Zi^voavos Xoyov, oti ovk eaTi Kivrjdijvai. "iia-re 
 Kal ei Tis €ni\eipoir] arvvdyeiv d>s dSvvaTOV, afiaprdvei, k&v h 
 f/vpiaKis ■p cnXXeXoyitrfiivos' oii yap kariv avrrj Xvo-ts. ''Hv 
 yiip fj Xvais kfi^avtcris ■^evSovs avXXoyur/ioG, nap' 8 ^^ei/fiijy ii 
 ovv fifi cruXXeXoyta-rai rj Kal dXrjOes ^ yjrevSos enixeipu avvd- 
 yeiv, 17 eKeivov SijXoxrty Xvcris eariv. "la-cos Se Kal tovt' eir' 
 evmv ovSev KmXijei avfi^aiveiv nX^v kni ye To&rcov ovSe tovto 
 So^eiev &v Kal yhp tov KopiaKov oti KopiaKos oi8e, koI rh 
 npoaiov OTI npoa-iov. ' EvSkyeaOai 8e 8oKeT to airrb el8ivai Kal 
 firj, oTov OTI jikv XeuKov el8evai, oti 8k /lovaiKov p.^ yva>pi((iv, 
 o6t(o yaip TO aiiro o?8e Kal ovk oI8ev aXX' ov KaTa Taiirov. To 
 8f npotriov Kal Kopia-Kov, Kal oti npoaiw Kal oti KopiffKOt, 
 oTSev. 
 
 'Ofioms 5' d/iapTavova-i Kal 01 XvovTes, on anas dpiS/ibs 
 oXiyos, &(Tnep of>s eino/iev ei yap jiri avfinepaivo/ievov, tovto 
 napaXinovTes, dXrjBes ovjinenepavQai <f>a(ri, ndvra yhp ehai 
 Kal noXtiv Kal oXiyov, ajxapTdvovaiv. 
 
 "Evioi 8e Kal t& 8itt& Xvovai toUs avXXoyia/iovs, oTov on 
 troy koTi naT^p ^ vibs ^ SoiiXos. Katroi (j>avepbv ms el naph 
 Tb noXXa)(S>s Xeyea-Oai (ftaiveTai 6 eXey^os, 8ei Tovvo/ia fj tov 
 Xoyov Kvpims efvai nXeiovcov Tb 8e t6v8' eivai TovSe TiKvov- 
 ovSels Xeyet Kvpias, et SeanoTrjS koTi TeKvov dXXa naph to 
 axip.^e^r]Kbs fi (ruvOeais^" kaTiv. '^Ap' karl tovto <r6v ; Nat, 
 "EaTi 8e tovto tckvov <rbv dpa tovto tckvov oti avfi^e^riKiv 
 elvai Kal <rbv Kal TeKvov aXX' ov abv TeKvov. 
 
 Kal Tb eTvai tcov KaK&v Ti dyadov 17 yh,p ^povtjais eanv 
 kmaTrjiir) Totv KaK&v. Tb 8e tovto tovtcov etvai ov XeyeTai 
 noXXax&s, dXX& KTrjfia. Et 8' dpa noXXaxm (kuI yap tov 
 dvOpoonov tS)v (m<ov <pafiev elvai, dXX' oil ti KTrjfxa) Kal kdv n 
 
EAErXDN. 75 
 
 father. Though the solution is applicable with some predicates, 
 and the same thing, for instance, may be Jfnown and unknown 
 in different respects, with other predicates it is inapplicable. 
 In the second place, the same argument may have several 
 faults, but it is not the exposure of any fault that is solution j 
 for the falsity of the conclusion may be demonstrated without 
 explaining why the reasoning is fallacious. To solve Zeno's 
 proof of the impossibility of motion, we ought not to try to 
 prove the opposite; for though we gave ten thousand valid 
 proofs, this would be no solution; for it would not disclose 
 where the vice of his argument lay. If an argument is incon- 
 clusive, or concludes what is true or false from false premisses, 
 the exposure of this vice is solution. In the third place, though 
 this distinction of the thesis may be admissible in other cases, 
 it is not admissible here : for here you know that Coriscus. is 
 Coriscus, and that he who approaches approaches. But the 
 same subject can only be known and not known in respect of 
 different predicates ; known, for instance, to be white, and not 
 known to be musical. Here the same person is known to be 
 Coriscus and not known to be Coriscus, or known to approach 
 and not known to approach. 
 
 So it is wrong to solve the fallacy about number by retract- 
 ing the thesis that a number cannot be both great and small*. 
 When an argument is inconclusive, to overlook the want of 
 cogency, and maintain the truth of the conclusion, is bad logic. 
 
 Some class these fallacies under the head of Equivocation, 
 maintaining, for instance, that yours means either your father, 
 your son, or your slave. But a term or proposition is only am- 
 biguous when it has a plurality of proper significations ^ ; and 
 this man''s child cannot properly signify a child that is this 
 man's slave. It is the equation of subject and accident that 
 produces the fallacious combination. Is it yours ? Yes. Is it a 
 child? Yes. Then it is your child. No. It is yours, and a 
 child, but not your child. 
 
 So too the proof that some of evil is good, (for wisdom is 
 knowledge of evil,) is referred to the class of ambiguity. But 
 the expression of a thing (the genitive case) is not ambiguous, 
 as it only properly denotes property (has a possessive force). 
 Granting, however, that the genitive is ambiguous, (for when 
 
76 PEPI IO<PIITIKnN 
 
 npbs TO, KaKh Xeyrjrai as tlvSs, Si& tovto tS>v kukwv kariv, oKK 
 oil TOVTO tS)v KaKwv^^ ; Haph to irrj ovv Koi &ir\m (paiveTai. 
 KaiToi evSi\eTai laoos dyaOov elvai Ti t5>v KaKwv SittSis, aXX 
 ovK €7rt Tov Xoyov tovtov, aXX' et ti SovXov eir/ dyaOhv fio-)(6i]- 
 pov, fiSXKov. "la-cos S' ovS' oijtcos' ov yap el dyaQov Koi tov- 
 tov, dyaQov tovtov dfia. OvSe to tov avQpamov ^dvai tS>v 
 ^mcav iivai oil Xeyerat TroWaySis' ov yhp ef woTi ti (Trjiiaivojiiv 
 d(f>e\6vTfS, TOVTO Xeyerat TroXKayms' koi yap to ^fiiav drrov- 
 T€s tov eirovs Sos fioi 'IXidSa crrjuaii/o/iey, olov to firjviv dfiSt 
 Bid. 
 
 XXV. Toils Se rrapa to Kvpicos T6Se ^ Trg ^ noO rj nm rj 
 irpos Ti Xeyea-Qai Kal fifi dirXSis, XvTeoti (tkottovvti to avuirt- 
 paafia rrpos Trji/ dvTi(]>aaiv, el evSeyeTai TOVTcav ti TreirovBevai. 
 7a yhp kvavTia Kal Tk. dvTiKeifieva Kal (f>da-iti Kal dirb^tKriv 
 anXSts /iev dSvvaTov imdpyeiv t5 aiiTw, nfj fievToi eKdrepov fj 
 irpos TL ^ TTcas, ^ TO jiev irfj to S' awXms, oiiSev KmXvei. "Hot' 
 fl ToSe fiev &nX5>s ToSe Se nfj, oiiir<o eXey)(os. Tovto S ev t^ 
 avjiirepdanaTi deeoprjTeop Trpor t^v dvTicpaa-iv. 
 
 Elal Se irdvTes ol toiovtoi Xoyoi tout eyovTes. ^Ap evSe- 
 yeTai TO firf hv eivai ; i4XXa firjv eaTi ye ti [ir] ov. 'Ojioims Si 
 Kal TO ov oiiK earai' ov ydp earai ti twv ovtcov. "^Ap' evSe- 
 yeTai Thv aiiTov a/ia eiiopKeiv Kal einopKeiv ; ^Ap ey)(a>pei tov 
 aiiTov ajia r£ avT& weiOeaOai Kal dneiOeiv ; *H cure to ehai 
 Ti Kal etvai TaiiTov ; to Se fifj ov ovk, el eari ti, Kal eariv 
 dnXm' oiiT el eiiopKei ToSe ^ TJjSe, dvdyKt] Kal eiiopKelv o S 
 6[i6aas eiriopKTJa-eiv eiiopKei eTnopKwv tovto /lovov, evopKei Se o^ 
 oiiS' 6 drrei$(ov TreiOeTai, dXXd ti ireiOeTai. "0/j.oios 8' 6 X6yos 
 Kal irepl tov ^evSea-Oai tov aiiTov a/j.a Kal dXr/de^eiv dXXa 
 Sih, TO fifi eivai eiiOediprjTov,^ irorepms dv tis diroSoir) to anXSis 
 dXfjdeijeiv ^ ■'^evSeaOai, Svo-koXov ^aiveTai. KmXvei S' avTov. 
 oiiSev dwXms p-ev etvai ■\lfevSfj, irfj S' dXr]6ii ^ tlvos, Kal eivai 
 
EAETXiiN. 77 
 
 we say man is of the animals we mean he is a species, not 
 the propertyj of the animals ; that is to«iBay, the genitive may 
 have either a possessive or a partitive force,) still when we 
 express the relation of wisdom to evils by putting evils into 
 the genitive, we do not mean that wisdom is absolutely of 
 evils, but that wisdom is a correlative, namely, the knowledge 
 of evils. The fallacy then lies not in ambiguity but in the con- 
 fusion of absolute and restricted propositions. If, however, the 
 expression that there is a good of evils, is not ambiguous when 
 we aflSrm that wisdom is of evils, do we not obtain an ambigu- 
 ous conclusion when we assume a good slave belonging to bad 
 masters ? Perhaps not even then, for a thing that is good and 
 of the bad is not therefore a good of the bad '2. The expression 
 that man is of the animals is not ambiguous '", for ellipsis is not 
 ambiguity, for we may call unambiguously for the Iliad by 
 saying, "Achilles wrath"." 
 
 XXV. Faxlacies from the confusion of absolute or unrestricted 
 propositions with propositions restricted in mode, place, degree, 
 or relation, are to be solved by comparing the conclusion with 
 the thesis, to see whether there is any restriction on either side 
 to prevent their being contradictory i. For contrary, opposite, 
 negative and affirmative predicates cannot both belong to the 
 same subject absolutely, but may both belong restrictedly, or 
 one restrictedly and the other absolutely. If one belongs abso- 
 lutely and the other restrictedly, there is no confutation. We 
 must therefore compare the conclusion with the thesis. 
 
 All the following arguments have this defect.— Thesis : what 
 is not, cannot be. But what is not, is what is not. — Thesis : 
 what is, cannot not-be. But what is, is not, for it is not some 
 special thing. — ^Thesis : the same man cannot be perjured and 
 keep his oath. — Thesis : the same man cannot at the same time 
 obey and disobey the same command. In the first two ex- 
 amples to be restrictedly something and absolutely to be, are 
 not the same. What is not, is restrictedly something, but abso- 
 lutely is not. Again, a man may be unforsworn in a definite 
 particular but not absolutely. If he swore to perjure himself 
 and keeps his oath, he is unperjured in this particular but not 
 absolutely. Again, he who disobeys, though not obedient abso- 
 lutely, may be obedient to a particular command. So it may 
 
78 nEPI IO<t>IITIKDN 
 
 dXfjBTJ Tivd, dXrjOfj 8e jifi. '0/jlouos Se Kot ewl Tmv npos n 
 Kal nov Kal ir&re' navres yitp ol toiovtoi \6yoi traph tovto 
 avu^aivova-iv. "^Ap rj iyUia f] 6 irXovros dyaBov \ ' A}0\.h. tS 
 £<Ppovi KOI jir) 6p6m xpco/jievca ovk dya66v dyaBw dpa Kal 
 ovK dyaOov. '^Apa rb vyiatvuv ^ ^ Sijvaa-Oai kv TroXet dyadov • 
 '/4XX' ianv oVe aii ^eXriov Taiiroy dpa tw avr^ dyaOhv Kal 
 OVK dyaBov. *H ovSev KwXvei aTrX&s ov dyaffbv r&Se /ifj dvai 
 dyaOov, ^ rSSe /iei/ dya66v, aXX' ov vvv fj ovk kvTavQ' dyadov. 
 ''Ap' h ii-q PoiXoiT dv 6 <pp6vi/ios, KaKov ; ' Airo^aXeTi/ 5* ov 
 ^ovXerai rdyaOov KaKov dpa rdyaOov. Ov yap ravTov elireiv 
 rdyaQov effai KaKov Kal to awojSaXeir rdyaOov. 'Ofioims Sh 
 Kal 6 Tov KXewTov Xoyoy. Ov yhp ei kukov eariv 6 KXeirTrjs 
 Kal TO Xa/ScH/ earl kukov ovkovv Th KaKov ^ovXeTai, dXKa 
 TayaOov to yap XajSetj' dyaOov ^. Kal i] pocros kukSv 
 kariv, aXX' ov to diroftaXiiv vocrov. '^Apa fh SiKaiov tov 
 dSiKov Kal TO SiKaicos tov dSiKcos alpeTcorepov ; /4XX' diroOayeTv 
 dSiKcas alperaTepov. '^Apa SiKaiov kari tA aiTOv ex*"' fKUffTov ; 
 *y4 S' av Tis KpivTj KaTd 86^av tt^v ainov, Kdv ^ ■^evS^, Kvpid 
 k<TTi.v kK TOV vojiov TO avTo dpa SiKaiov Kal ov SiKaiov. Kal 
 TTorepa SeT viKav* Thv to, SiKaia XeyovTa ^ tw Td dSiKa ; 
 'AXXd fifiv Kal TW dStKovfievov SiKaiov kaTLv iKavm Xeyuv Si 
 eiraOep' Tavra S ^v dSiKa. Ov yap et TraOetv ti uSIkods 
 alpiTov, TO dSiKoos alpeTWTepov tov SiKaims' dXX' dwXas fikv 
 TO StKaCoos, ToSl fiivToi ovSkv KoaXvei dSiKas ^ SiKaitof. Kal rh 
 e\eiv Td aiiTOV SiKaiov, to 8e TdXX&rpia av SiKaiov Kpuriv 
 fjievToi TUVTr/v SiKaiav eivai oiSev KcoXvei, olov dv f kutoi. S6§av 
 TOV KpivavTOS' oil ydp el SiKaiov toSI ^ d>Si, Kal dwXms SiKaiov. 
 'Ofiotas Sk Kal dSiKa 6vTa ovSev KcoXvei Xeyeiv ye aiiTO, SiKaiov 
 eivai' oil ydp ei Xeyeiv SiKaiov, dvdyKrj SiKaia elvai, &<nrep ovS 
 el m^eXi/iov Xeyeiv, axpiXifia, 'Ofioims Se Kal knl twv SiKaimi. 
 "QvT oi/K el TO. Xey6fieva dSiKa, 6 Xeyeov dSiKa viK& Xeyei 
 ydp & Xeyeiv k<rTl SiKaia, dnXms Sk Kal naOeiv dSiKa. 
 
EAErXnN. 79 
 
 be proved that the same person at the same moment may utter 
 truth and falsehood. The doubt whether a proposition ought 
 to be called absolutely true or absolutely false causes the only 
 difficulty. A statement may be absolutely false and par- 
 tially true, that is, partially but not absolutely true. There 
 may be similar restrictions in relation to time, and place, as in 
 the following arguments : Health and wealth are good, but to 
 the fool and person who misuses them they are evil. Therefore 
 they are both good and evil. — Office and political power are 
 good, but to the same person there is a time when they are evil. 
 The same thing therefore is both good and evil. But a thing 
 may be good absolutely, yet not to this individual ; or good to 
 this individual, yet not at this time and place. Again, What 
 the wise avoids is evil ; he avoids lost good ; therefore good is 
 evil. No. Good is not evil but an evil thing to lose. The 
 argument about the thief is like this. The thief is an evil but 
 a good person to catch j so that we desire what is good, not 
 what is evil, when we desire his capture. So sickness is an evil 
 and a good thing to get rid of. Again, right is better than 
 wrong, and to act rightly than to act wrongly : but it is better 
 to be put to death wrongly. — It is just that a man should have 
 his own : but a conscientious judgment, though it adjudicates 
 a man's property to his neighbour, is just. The same thing 
 therefore is just and unjust. — Judgment should be given for the 
 party asserting rights, not for the party asserting wrongs. But 
 the victim of injustice ought to obtain judgment when he 
 relates his grievances, that is, his wrongs. With reference to 
 the last three examples, we may observe that to suffer wrongly 
 may be preferable, though what is done wrongly is not abso- 
 lutely preferable to what is done rightly. What is done rightly 
 is absolutely preferable ; what is done wrongly only in certain 
 special particulars. Again, it is absolutely just that a man 
 should have his own, and not just that he should have what is 
 his neighbour's ; though such an adjudication is just in a quali- 
 fied sense, if honest. But what is just in this sense is not abso- 
 lutely just. Again, wrongs may be right to allege, and the 
 rightness of the allegation does not make them rights any more 
 than the expediency of the allegation makes them expedient, 
 and vice versa. Although, then, the things alleged are wrongs, 
 
80 HE PI I0<t>l2TIKnN 
 
 XXVI. Tors Se napa rbv opia/iov yivo/iivois tov eXeyxov, 
 KaBdirep inreypd^r) irporepov, diravTtjreov aKOirovai to oiz/i- 
 irepaaua npbs Trju dvTi^aaiv, ortroas earai to avTo Kal kutSi to 
 avTo Kal npos to avTo Kal d>cravT(os Kal kv t& avrm ')(fiov<o. 
 ' Eciv S' kv dpyfi irpo(repT]Tai, ow)( o/ioXoyrjTkov as dSvvaTOv to 
 a{iTh eivai SiirXdaiov Kal /ifj SiirXda-iov, dXXa (puTeov, fiij jikvToi 
 atSt, &s nor ^v to kXey)(e<r6ai SuofioXoyrjfiivov. Elal Se irdv- 
 Tes oiS" oi Xoyoi waph. to toiovto. "^Ap' 6 elSws fKaarov on 
 eKaoTov, oiSe to "irpdyfia, Kal 6 dyvoStv &<ravTms ; EiSms Se m 
 Thv KopifTKov oTi Kopia-Kos, dyvootrj &,v otl jiovaiKos, &<m TavTo 
 kirtaraTai Kal dyvoet. 'A pa to Terpdnrjyy tov Tpmrixios 
 fiu^ov ; rkvoiTO S dv kK Tpiirriy^avs TeTpdirri)(y KaTo. to /jirJKor 
 TO Se jiel^ov kXaTTovos fjieT^ov aiiTo dpa aiiTov fiei^ov Kal 
 eXaTTop. 
 
 XXVII. Tovs Se napd Th aiTetaOai Kal Xafi^dveiv to kv 
 ^PXV Ttwdavojievca jikv, dv rj SrjXov, ov SoTeov, ovS dv evSo^ov 
 ^, XeyovTa TdXrjOis. *Av Se XdOrj^ t^v dyvoiav Sid t^iv //ox- 
 Or/piav tS>u ToiovTcov Xoyoov eis tov kpayrStvTa /leTaarpewTeov mv 
 01) SieiXeyiievov 6 yap eXeyxos dvev tov k^ dp-)(rji. EW on 
 kSS&Tj oiJ^ o)S TOVTca )(pr]a-o/ievov, dXX as npbs tovto avXXoyi- 
 ovfikvov TovvavTiov, f) knl Tmv nape^eXey)(cov. 
 
 XXVIII. Kal Toi>s Sid tov napeiro/ievov <TV/iPifid^ovTas ot 
 avTov TOV Xoyov SeiKTeou. 'Eari S\ Sitti} fj t&v eirofievtov 
 aKoXovdrjais. *H ydp d>s rS kv fiepei to KaOoXov, olov dv- 
 Bpanco (aov d^iovTai ydp, ei tSSc jieTd TovSe, Kal t6S' elvai 
 jieTd TovSe. *H KaTd Tds dvTiOeaeis^- et ydp ToSe T&Se aKO- 
 XovBeT, Tw avTiKeifteva Tb dvTiKeifievov. flap' 8 Kal 6 tov 
 MeXiaaov Xoyos' ei ydp rb yeyovbs €;(€« dp)(rjv, Tb dyevqrpv 
 
EAErxnN. 81 
 
 it is not wrong allegations that carry the judgment, for the 
 things are right to allege though absolutsly wrongs and wrong 
 to undergo. 
 
 XXVI. Fallacies that omit some element in the definition 
 of eonfiitationj as was suggested above, must be solved by ex- 
 amining whether the conclusion is contradictory of the thesis, 
 and regards the same terms, in the same portion, in the same re- 
 lation, in the same manner, in the same time. The thesis when 
 first advanced should admit that the same thing may be double 
 and not double in any way that falls short of the conditions of 
 contradiction. The following arguments depend on this. He 
 who knows a subject to have a predicate knows the subject, and 
 so he who is ignorant. If, then, I know that Coriscus is 
 Coriscus, and am ignorant that he is musical, I know and am 
 ignorant of the same subject. — A thing four cubits high is 
 higher than a thing three cubits high : but what is three cubits 
 high may grow to be foxa cubits high. What is greater is 
 greater than what is less. The same thing, therefore, may be 
 greater and less than itself, and in respect of the same dimen- 
 sion, namely height. 
 
 XXVII. In fallacies from begging and assuming the point 
 in issue, if we are aware in time we should deny the proposition, 
 even though it is probable, and say, as we fairly may, that it 
 cannot be granted but must be proved. If it escaped us, the 
 badness of the reasoning enables us to turn round and impute 
 the blunder to the opponent, who ought to have known that it 
 IS no confutation to assume a contradictory proposition : and we 
 may say that we admitted the proposition, not as a premiss but 
 as a thesis to be confuted, or as a premiss, not of the main 
 reasoning, but of a by-confutation i. 
 
 XXVIII. Fallacies from the relation of antecedent and con- 
 sequent can only be exposed when the false conclusion is drawn. 
 There are two modes of falsely inferred sequence. Either when 
 animal, the universal, follows from man, the particular, it is in- 
 ferred that man, the particular, reciprocally follows from animal, 
 the universal : or, the relation of the contradictories of the ante- 
 cedent and consequent is supposed to correspond directly to the 
 relation of the antecedent and consequent. If A, that is, follows 
 -B, it is assumed that not-^ follows not-5, as in Melissus' argu- 
 
 G 
 
82 HEP I lOfPIITIKDN 
 
 d^ioT /irj eY^'"* ^''"''' ^' «y«'"7''''y ° oiipavos, kol airfipos. To 
 8' ovK eoTTiv dvairaXLV yap rj dKo\ov6r]<TiS. 
 
 XXIX. "Oaoi Ti TTccpa. to TrpocmOevai tl avWoyi^ovraij 
 (TKonuv el d<f>aipoviJLevov crvfi^aivei firjSev tjttov to dSvvaTOv, 
 KcLiriLTa TOVTO kii^avKTTeov, Kal XeKTeov w eScoKev ov^ my 
 SoKovv dXX coy TrpbH tov Xoyov, 6 Se Kt\pr]Tai ovSev wpos tov 
 Xoyov. 
 
 XXX. ripos Se Toiis TO, nXeico epeoTrj/iaTa ev noiovvTas 
 evOiis kv dp-j^rj SiopiaTeov. 'EpmTrja-is yap fita irpos ^v /iia 
 diroKpLcrh ea-Tiv, acrT oilre irXeia Ka& ivbs oiiTe ev kutu iroX- 
 Xwf, dXX tv KaB ivos (pareov fj dwo<paTeov. "Dairep Se eirl 
 T&v oficovv/icov oTe jjiev dn^olv ore S" ovSeTepm inrdpyei, mare 
 fi^ aTrXov ovTOS tov epcoT'^naTos dirXas aTTOKpiPOfievois ovSev 
 avfi/Sawei ndayeiv, o/ioims Kal eirl to^jtcov. "Oray fiev ovv ra 
 trXeico tS) evl rj to ev toTs ttoXXoTs vndp^tj, rm arrXws Sovn 
 Kal dfiapTovTi Tavrrjv ttjv dfiapTiav ovSev iirepavTia>iia crvji- 
 ^aivef OTav Se Tm fiev tZ Se /irj, ^ nXeioa KaTb, nXeiovav, Kai 
 e(TTLv my {mdpyei dji^oTepa d/i^orepois, eari S coy ovx xmdpyii 
 TrdXiv, &<TTe tovt evXalSrjreov. OIov eu TolcrSe roFy Xoyoty. 
 Ei TO jiev eaTLV dyaOov to Se KaKov, oTi TavTb} dXir]6ei eiirew 
 dyaQov Kal KaKhv Kal ndXiv [iriT dyadbv /irJTe KaKov ovK eari 
 ykp eKdTepov eKdTepov, ma-Te ravTo dyaOov Kal KaKov Kal ovr 
 dyaBov oiJTe KaKov. Kal ei eKaaTov airrb airS tout&v km 
 dXXov eTepov eirel S' ^ ovk dXXois Tairrii,, dXX' airroTi, Kal erepa 
 aitTmv, TavTO. eavToh eTepa Kal Tairrd. "Eti el to jiev dyadov 
 KaKov yiveTai, to Se KaKhv dyaBdv ecTiv, Svo yevoiT S,v^- 
 
EAErXDN. 83 
 
 ment. If the generated is limited he assumes that the ungene- 
 rated is unlimited : that is to say^ becaiile, if the heavens are 
 infinite in space, they are eternal in time, he assumes that, if 
 they are eternal in time, they are infinitp in space. But this is 
 not so ; for the sequence of the contradictories of an antecedent 
 and consequent is the inverse of the original sequence. 
 
 XXIX. In fallacies where a superfluous proposition is foisted 
 in as the cause of an absurd conclusion, we must examine 
 whether the suppression of the premiss would interrupt the con- 
 clusion ; and after shewing that it does not, we may add that 
 the premisses which really cause it were not granted because 
 they were believed, but because the questioner seemed to wish 
 to use them against the thesis, which he has failed to do. 
 
 XXX. Seveeal questions put as one should be met at once by 
 decomposition of the complex question into its elements. Only 
 a single question admits of a single answer : so that neither 
 several predicates of one subject, nor one predicate of several 
 subjects, but only one predicate of one subject ought to be 
 afiirmed or denied in a single answer. When we have an am- 
 biguous subject, sometimes a predicate is true of both or neither 
 of the things signified; and though the question is equivocal, 
 a simple answer exposes us to no confutation. The same thing 
 happens when many questions are asked. When several pre- 
 dicates are true of one subject, or one predicate of several 
 subjects, a single answer, though a dialectical error, involves 
 us in no confutation. But if a predicate is true of one sub- 
 ject and not of others, or several predicates are propounded 
 of several subjects, and each is true of each but not all of all, 
 a single answer involves confutation and must be refused. For 
 mstance, if A is good and JB evil, if we say that A and S are 
 good and evil, we may be interpreted to say that the same 
 things are good and evil and neither good nor evil, for A is not 
 evU and £ is not good. Again, if A differs from £, and we 
 say that A and £ are the same as themselves or different from 
 themselves, we may be interpreted to mean that A is different 
 from A or that A is the same as £. Again, if A becomes good 
 and £ becomes evil, and we say that A and £ become good and 
 evil, we may be interpreted to mean that each becomes both 
 good and evil. Again, if A and £ are unequal, and we say 
 
 G 2 
 
84 nEPI IO<t>IITIKDN 
 
 AvoTv re koL dviacov iKarepov aiirh aiirZ iffov, aa-re ha koX 
 dviaa aiirk ai/ToTs. 
 
 'EfLTTiTTTOva-i filv ovv oStoc Kul els dWas Xva-eir Kal yctp 
 TO dficpco Kal TO airavra irXeiat a-rj/iaiveL- oijKOVP TavTov, wXiji/ 
 Svoua, avfi^aivei (pfjo'ai Kal aTTOipf\<Tav tovto S ovk rjv eXey- 
 Xoy. 'AWa (pavepbv ori fifj fiids ipmrrjarems twv wXeiovrnv 
 yivoiiivmv, aXX' %v Kad' ivbs <f)dvTOS f) diro^dvTOi, ovk ecrTat 
 TO dSvvaTOv. 
 
 XXXI. flipl Sk t5>v dtraybvTctiv els ravro voXXaKis e/jreo/, 
 ^avepov as ov Soriov twv npos Ti Xeyojikvcov a-rjuaiveiv n 
 ycopi^onevas KaO' amhs Ths Karrfyopias, oTov SinXdaiov dvw 
 Tov SnrXdtnov ■q/J.ta-eos^, oti e/j,<f>aii'eTaL. Kal yap to, SeKa kv 
 Tois ivbs Siovcri SiKa Kal Tb noLrja-ai kv tw jMrj iroirjirai, koI 
 oXoDS kv Trj diro^daiL j) ^dcns' dXX Hfims ovk ei tls Xeyoi toSI 
 /if/ eivai XevKov, Xkyei avTo XevKov eivai. Tb 8e SnrXdtrLov 
 ovoe (rrjuaivei ovoev la-cos, cocnrep ovoe to ev Tfi awo^affei • ei 
 S' dpa Kal arifiaivfi, dXX ov ravTb Kal avvrjprjfikvov. OvS ij 
 kmaT'qfir} kv tw ei'Sei, oTov el ea-rtv rj laTpiKr) kmcTTrJiMr], airep 
 TO KOivov kKelvo S" ^v kTrio'Trj/it] kincrTrjTOV. 
 
 ' Ev Sk Tols Si &v SrjXovraL KaTtiyopovjiivois TdvTO^ XeKreov, 
 (By ov Tb aiiTb )((opls Kal kv tZ Xoyco Tb SrjXovfJievov. Tb yap 
 KoTXov Koivj] fjikv TO avTO Sr/XoT knl tov o-i/jlov Kal tov poiKov, 
 wpocTTLdi/jLevov Sk oiiSkv KCoXijei, dXXd Tb p.kv Trj ^ivl to Sk tS 
 (TAfeXet arj(j.aiv€L*' ivOa fikv ydp Tb ai/xov, ev6a Sk to ^ai^bv 
 a-rj/xaiver Kal oiiSkv Sia<pip€i elneiv fis a-ifirj ^ ^Is koCXt). En 
 oil SoTeov rfjv Xi^iv kut evdv- ■^evSos ydp kcrTiv. Ov yap 
 kiTTL TO aifibv ^Is koiXt] dXXd fiivbs toSi, oTov irdOos, &<fT ovoev 
 dTOTTov, el T) /dty 17 aifif} pis k(TTiv e-)(ov<Ta KoiXorrjTa ptvos. 
 
 XXXII. riepl Sk TWV a-oXoiKio-fiwv, nap' 6 ri fiev (paivovTai 
 a-vfi^atveiv, e'iironev vpoTepov, d>s Sk Xvreov, kir avrmv tcov 
 X6ywv ea-Tai cpavepov. " AnavTes ydp ol ToioiSe tovto fiovXav- 
 Tai KaraaKevd^eiv. ^Ap' 8 Xeyeiy dXrjOws, Kal eaTi tovto 
 dXrjdws ; 4>jis S' ehat ti Xidov ea-Tiv dpa ti XiBov. *H to 
 
EAErXQN. 85 
 
 they are equal to themselves^ we may be interpreted to say that 
 they are equal to one another. • 
 
 These fallacies admit of other solutions, for themselves and all 
 are ambiguouSj meaning either each respectively or all promis- 
 cuously. So that only the same name, not the same thing, is 
 affirmed and denied of the same subject ; which, we agreed, is 
 no confutation. If however a single answer is not given, but 
 a single predicate affirmed or denied of a single subject, no 
 semblance of confutation can be fabricated *. 
 
 XXXI. Reductions to pleonasm must be opposed by denying 
 that a relative name has any meaning when separated from tlie 
 correlative, as double separated from half in the phrase double 
 of half, though it appears as a factor in the expression. For 
 ten is a factor in the expression ten minus one, and doing in the 
 expression not-doing, and the affirmative in all negative expres- 
 sions : yet to deny a thing to be white is not to affirm it to be 
 white. Double then, extracted and isolated, has no meaning 
 any more than the affirmative in the negative expression : or, 
 if it has a meaning, not the same as the factors combined. So 
 when we name a specific science, say, medical science, the factor 
 science is not the same as the genus science, for the latter is 
 correlative to the general object of science. 
 
 When the subject of an attribute enters the definition of the 
 attribute, we must say that the attribute does not mean the 
 same when conjoined with the subject and when separate. For 
 though curved, the generic element, is only part of the meaning 
 of aquiline and bandy when they are isolated, yet when these 
 terms are joined to nose and leg they may lose the other part 
 of their meaning; for aquiline nose and bandy leg mean no 
 more than hooked nose and crooked leg. Further, we must 
 deny the accuracy of the definition of aquiline and bandy ; for 
 aquiline is not a hooked nose, but a nasal quality or shape ; and 
 it is not strange that an aquiline nose should be a nose having 
 a nasal curvature °. 
 
 XXXII. Apparent solecisms depend on the cause that has 
 been explained. The mode of solving them will be manifest in 
 an example. The following arguments attempt to prove sole- 
 cism. S (nominative) is {M) that (nominative) which (accusa- 
 tive) you truly affirm S (accusative) to be. You affirm S (accu- 
 
86 HEP I IO<PIITIKnN 
 
 Xeyuv XiOov ovk earl Xeyeiv S aXX' 6v, oiiSe tovto dXXa. tovtov. 
 El oSv epoiTO Tis, ap ov dXrjdm Xeyeis, ecrri tovtov, ovk &v 
 SoKoiTj eXX-qvi^eLV, acrrrep oils' el epoiTO, ap' rju Xeyeis uvai, 
 iCTTiv oStos ; EvXov 8' elireiv^ ovros, fj oaa firJTe 6tjXv firJT 
 appev crrjiiatvei, ovSev Siacpepei. Aib Kat ov yivsTai o-oXokkt- 
 fios, el o Xiyeis eivai, etrrt tovto ; ^vXov Se XeyeLS eivaf e<TTiv 
 apa ^vXov. '0 Sk Xi6os Kai to ovtos dppevos ex*' KXfj(nv. El 
 Srj TLs epoiTo, S.p oSroy eaTiv avrr] ; eira ndXLv, tl S ; oi5)( oSroy 
 eoTt Kopca-Kos ; eiT ehreiev, ea-Tiv dpa oStos avrq, ov avXXeXo- 
 yia-Tai tov aoXoiKurfiov, ovS el to KoplcrKos aij/iaivet mrep 
 avTrj, fjifj SiScocri 8e 6 diroKpivonevos, dXXa SeT tovto Trpoaepayrri- 
 6fjyaL. El 8e firjT ecrTiv firJTe 8i8(ocriy, ov avXXeXoyicrTai ovre 
 T& ovTL ovTe wpbs Tou rjpayrrjfievov. OfJ-olcos ovv 8ei KOLKti tov 
 XlQov crrjiiaiveiv ovto^^- El 8e /j.rJTe ecTTt jiriTe 8iSoTai, ov 
 XeKTeov TO (rvfiirepacriia' (jiaiveTaL 8e irapa to ttjv dvofioiov 
 tttSxtlv tov ovofiaTos o/ioiay (paiveaOai. 'Ap dX-qOes eariv 
 e'meLv otl ecTTiv avrr}, onep elvai (j)TJs a.vTr\v \ Elvai Se (p^s 
 dcTTTiSa' 'e(TTLv dpa avTrj dantSa. *H ovk dvdyKr), el firj to 
 aSTTj dcnriSa crrjuaLvei dXX dcnris, to 8 dairiSa Tavrijv. OiS 
 el 6 (f)T}S elvai tovtov, eaTiv ovtos, (prjs 8 eivai KXewva, etrTiv 
 dpa ovtos KXecova- ov yap eaTiv oUtos KXewva- etpr]Tai yap 
 OTi (f>rifj.i eivaL tovtov, eo'Tiv oStos, ov tovtov oiiSe yap S.v 
 iXXrjvi^oi oijTWS to epa>Trjp.a Xe)(^6ev. 'Ap eTria-Tatrai tovto; 
 TOVTO 8' ecTTi Xi6os' eirio'Taa-ai dpa Xi6os. *H ov TavTo (tt)- 
 jiaivei TO tovto kv rS dp' ewio'Taa'ai tovto kuI ev tZ tovto St 
 XiQos, aXX' ev fiev rw irpwTm tovtov, kv Se rS vaTepm oinos. 
 "^ Ap o5 eTn(TTr\p.y\v eyeis, eiria-Tacrai tovto ; eTriaTrjfirjv 8 e)(eis 
 Xidov eTrta-Taaai dpa XiOov. *H to fiev tovtov XiOov Xeyeis, 
 TO Se tovtov XiOov kSoOrj 8', oS eTrta-Trjfirjv ^X^'^' kwiaraa-dai, 
 ov tovtov, dXXd tovto, Sctt' ov Xi6ov dXXa XiOov. "Otl p.tv 
 ovv 01 TOLOVTOL T&v Xoy<ov OV avXXoyi^ovTai aoXoiKiafibv aXKa 
 (ftaivovTai, Kal Sid ti re <paivovTai Kal irais dnavTTjTeov Trpos 
 avTovs, (fiavepov e/c tS>v elprjfievwv. 
 
EAErXDN. 87 
 
 sative) to be P (accusative). Therefore S (nominative) is P 
 (accusative). No. When P the prediciite is masculine, the 
 neater pronouns ikat and wAicA may be replaced by masculine 
 pronouns which distinguish the nominative and accusative 
 cases'. If I asserted with masculine pronouns^ S (nominative) 
 is that (accusative) which you truly maintain it to be, I should 
 speak ungrammatically, just as much as if I said a woman is he 
 whom you affirm her to be. Neuter predicates do not distin- 
 guish the nominative and accusative, and give rise to no 
 apparent solecism. It is the masculine and feminine forms, 
 whether the object denoted is really masculine and feminine or 
 not, that occasion solecism. If I am impugning the thesis No 
 man is a woman, and obtain the premiss, Coriscus is a man, if 
 I say at once therefore a man is a woman, I have not proved 
 the solecism, assuming Coriscus to be a woman, unless this 
 premiss is granted by express concession. If Coriscus is not a 
 woman, and not admitted to be a woman, 1 have not proved my 
 conclusion either absolutely or relatively to this opponent. So 
 in the first example it must be expressly granted as a major 
 premiss, that M nominative is P the accusative : if it is not 
 really so, and is not granted to be so, the conclusion does not 
 follow. It seems to follow because in the neuter pronouns the 
 nominative and accusative are not distinguished. The nomina- 
 tive of S is (M) the nominative of the noun whose accusative 
 you affirm the accusative of S to be. You affirm the accusative of 
 S to be the accusative of P. Therefore the nominative of S is 
 the accusative of P. This is a non sequitur ; for the nominative 
 of S was affirmed in the minor premiss to be the nominative of 
 a certain name. Again, from the premisses: This, man (nomi- 
 native) is he (nominative) whom (accusative) you affirm him 
 (accusative) to be : you affirm him (accusative) to be Cleona 
 (accusative) J it does not follow that this man (nominative) is 
 Cleona (accusative), for the major premiss does not affirm that 
 he (nominative) whom you affirm him to be is Cleona (accusa- 
 tive), and the minor premiss affirmed that S (nominative) was 
 he (nominative) not him (accusative), and any other expression 
 would have been ungrammatical. You know M (accusative) : 
 M (nominative) is P (nominative) ; therefore you know P 
 (nominative). No. if is anibiguous : in one premiss it is 
 
88 HE PI IOt>IITIKDN 
 
 XXXIII. AeT Se Kal Karavoeiv on TrdvToav tZv Xoycav ol 
 fiiv eia-L /5aovs KariSeiv ol Se ■)(a\eirci)TipoL, napa t'l Kal kv t'ivi 
 irapaXoyi^ovrai rbv aKovovra, voWdKis ol avTol eKeivoLS ovres. 
 Tov adrov yap \6yov Set KaXeTv tov naph ravTo yivofievov 
 6 avTos Se Xoyos toTs fiev irapa Tr]v Xi^iv Toh Sk Trapb, to 
 av/iPe^TjKbs ToTs Sk nap erepov So^eiev &.v eivai Siii, to /j,eTad)i- 
 po/ievov^ eKaaTov /ztj o/j-oicos eivai SijXov. "Dairep ovv kv Toh 
 naph TTjv ojMcovviiiav, ocnrep SoKeT Tpoiros evrjOecrTaTos eivai twv 
 TTapaXoyLajiStv, to, fjikv Kal toTs Tvyovatv kari SrjXa (Kal yhp ol 
 Xoyoi (TxeSbv ol yeXoToL TrdvTes eial irapa tt/v Xk^iv, olov dvrjp 
 f<p€peTo KaTo. KXifiaKos Sicppov, Kal oirav crTeXXea-Oe ; Trpbs rfju 
 Kepaiav. Kal noTepa tS>v fiocov e/nrpoaOev re^eTai ; ovSeTepa, 
 dXX oTTia-Qiv a[i(fxo. Kal KaOapbs 6 ^opias ; ov SfJTa' dwiK- 
 TovrfKe yap Tbi> TrTW)(bv Kal tou wvovfievop*. ' Ap E'6apyo$] 
 ov SfJTa, dXX AvoXXaiviSris. Tbv avTbv Se Tpairov Kal tw/ 
 dXXcov a)(^eSbv ol nXeiaToi.^ Ta Se Kal tovs e/nretpoTaTovs 
 (jtaiveTai XavQdveiv a-qfielov Se tovtcdv oti /j.d)(ovTai ttoXXukk 
 irepl T&v ovo/idrcov, olov nSTepov TavTov arjiiaivti KaTO, iravrcov 
 rb hv Kal to ev fj erepov. ToTs p-ev yap SoKeT TavTov (rrj/miveiv 
 rb ov Kal to ev ol Se rbv Zrjvcovos Xoyov Kal HapfieviSov Xv- 
 ov(n Sia rb TroXXa)(ws <f)dvaL rb ev XeyeaOai Kal rb ov. Ofioimi 
 Se Kal irepl tov avfiPe^rjKOTOS Kal wepl tSiv dXXwv eKaarov^ ol 
 /lev eaovTai ^aovs ISeTv ol Se ^aXevSrepoi Tmv Xoycov Kal 
 Xa^eTv ev Tivi yevei, Kal norepov eXey)(os fj ovk eXey)(os, ov 
 ^aSiov 6/ioia>s irepl irdvrcov. 
 
 " Eari 8k Sptfiij^ Xoyos octtis dnopetv iroieT ndXiara' SaKVfi 
 yap oliTOS ndXia-ra. ' Airopia 8' ecrrt Sitttj, r) fikv kv tois (TvX- 
 XeXoyicr/xevois, o ti dveXu tis twv eprnT-qfidTcav, r) S' kv rot? 
 
EAErXDN. 89 
 
 nominative in the other accusative. What (genitive) you have 
 perception ofj that (accusative) you perceive. You have percep- 
 tion of a stone (genitive); therefore you perceive of a stone 
 (genitive). No. Of that (genitive) is of a stone, and the pre- 
 miss waSj what you have perception of, not of that but, that 
 (accusative) you perceive. Therefore you perceive — not of a 
 stone but — a stone. These arguments then do not really prove 
 solecism: why .they seem to do so, and how they are to be 
 solved, is plain from what has been said*. 
 
 XXXIII. It must be observed that in some arguments it is 
 easy, in others difficult, to detect what and wherein is the 
 fallacy, even when the arguments are identical. Arguments 
 may be called identical when they depend on the same principle 
 or belong to the same class. An identical argument may by 
 one be referred to the head of equivocation ; by another to the 
 equation of subject and accident, by another to another prin- 
 ciple, because in its successive application to different spheres 
 the principle is not equally patent or disguised. For instance, 
 fallacies of ambiguity are supposed to be the easiest of detec- 
 tion^, and some are obvious to the dullest, for almost all repar- 
 tees and ridiculous turns depend on this principle 3. Thus : 
 Down stairs a man tumbled (carried) — a chair. — ^Whither are 
 you bound? (Where do you fasten the sails when you take 
 them in?) To the yard arm. — Which cow will calve before 
 (the other) ? Neither : both behind. — Is it a set (pure) Boreas ? 
 No : he has killed a beggar. — Who was the purchaser ? Evar- 
 chus ? No : ApoUonides (extravagant) : and so on. Others 
 even the acutest fail to detect. A proof of this is the number 
 of controversies that depend on words; for instance, on the 
 ambiguity of Unity, and Being. Some suppose these tenns to 
 be univocal ; others solve the arguments of Zeno and Parme- 
 nides by shewing them to be equivocal. In the same way 
 fallacies that depend on the equation of subject and accident and 
 the other principles are sometimes easy sometimes hard of detec- 
 tion. The classification, too, of a fallacy, and the decision whether 
 an argument is fallacious or not, vary in difficulty. 
 
 The cleverest argument is that which causes most doubt and 
 embarrassment. Doubt is of two kinds : in dialectic reasoning 
 we doubt which proposition is false ; in eristic reasoning we 
 
90 HE PI IO<PIITIKnN 
 
 epiariKoTs, rrm fi'Tij" tls to irporaQiv. Aioirep kv rols irvWo- 
 yiariKoTs oi SpifivrepoL \6yoi ^rjreTy fiaXXov iroiovaiv. " Ecttl 
 Sk avWoyiaTiKos fiev Xoyos SpLfivraros, &,v e| on jjidKurTa. 
 SoKovvTcov on fidXiara evSo^ov avaipfj. Eh yap a>v 6 Xoyoy 
 /jLeTariOefiivrjs'' rrjs dvTi(f>dae(os airavras ofioiaus f^ei Toiis 
 ovWoyLO-fiovs' del yap e^ kvSo^aav 6/j.oims ivSo^ov dvaip-qa-a ^ 
 Karaa-Kevda-ei, Sioirep dnopeiy dvayKoiov. MakLora fuv oSv 6 
 TOLOVTOS SpLfivs, 6 k^ taov to crvfnrkpaafia troimv rotr kpwrrj- 
 fiacri, SevTepos S' 6 k^ airdvT(ov dp,0L(ov ovtos - yap 6/j.oims 
 noi'qa-et. dnopeiv ottoiov tSiv kpcoTrj/iaTcov dyaipereov. Tovro 
 Se )(^a\eTr6v dvaiperkov plkv ydp, o tl 8 dvaiperkov, dSrjXov. 
 T&v S kpuTTiKwv SpifivTaros fikv 6 npSiTov ei6i>s dSijXos iron- 
 pov avXXeXoyicTTai fj oil, Kal TTOTepoy wapa ylrevSos ^ Siaipeaiv 
 kcTTiv ri Xvaris, SeuTepos Se tS>v dXXwv 6 S^Xos /lev otl irapa 
 Siaipecnv tj dvaipeaiv kari, /ifj ^avepbs S a>v Sea tivos t5>v 
 r/pcorrjuevrnv dvaipeaiv fj SLalpecnv XvTeos kariv, dXXa, irorepov 
 avTT] irapd to avfnrepa(r/j.a fj irapd Ti tS>v epayrrmdrcov kariv. 
 
 ' EvioTe fiev oSv 6 jirj <TvXXoyur6eh Xoyos eifjOrjs ka-Tiv, kav § 
 Xtav dSo^a fj ■^evSfj to, XrmiiaTa- evioTe S oiiK d^ios KaTa- 
 (jtpovelo'OaL. "Orav /lev ydp kXXeiTrr) ti Tmv toiovtwv kprnrrj- 
 jxdTcav, nepl ov 6 Xoyos Kal Si o, Kal fi-q irpoaXa^atv tovto koI 
 fifj (TuXXoyia-diievos evfjdrjs 6 avXXoyia-pos' orav Se twv e^mOev, 
 ovK evKaTa<f)p6vr]Tos ovSajjims, aXX' d jikv Xoyos eTneiKrjs, o S 
 kpcoTcov fipcoTr/Kev ov KaXcas. 
 
 " EtTTi re, mcmep Xveiv ore jjiev npos tov Xoyov OTe Se npo? 
 Tov kpcoTMVTa Kal TTjv kpSTTjaiv OTe Se irpbs ovSeTepov tovtcov, 
 o/xoiios Kal kpcuToLv ecTTi Kal a-vXXoyi^eaOai Kal irpbs Trjv 6e(riv 
 Kal TTpbs TOV dnoKpivojievov Kal Trpbs rw y^povov, orav fj rrXeiovos 
 •^povov SeojievT) fj Xvcris f] tov TrapovTos Kaipov rb SiaXe-)(6^vai 
 
 Trpbs TfjV XVCTLV. 
 
 XXXIV. ' Ek TTOcrmv fiev ovv Kal iroicov yivovTai Tois Siw- 
 Xeyo/ieyois ol TrapaXoyiap,oi, Kal nms Sei^o/jtev re ■^evSojie- 
 vov Kal rrapdSo^a Xeyeiv iroLT^a-o/iev, eTi S" kK tlvcov avfi^aivei 6 
 <ToXoiKia/i6s^, Kal w&s kptoTtjTiov Kal tis fj Td^is twv kpmr\- 
 
EAErxnN. 91 
 
 doubt how a proposition ought to be worded. Accordingly dia- 
 lectic paradoxes are the more stimulative of inquiry. The 
 cleverest dialectic argument is that both of whose premisses are 
 extremely probable, while the thesis confuted is also extremely 
 probable. Then a single syllogism by successive substitution 
 of the contradictory of the conclusion for one of the premisses 
 makes three syllogisms of equal probability and improbabilityj 
 in each of which highly probable premisses lead to an equally 
 improbable conclusion, which must occasion embarrassment. The 
 cleverest, then, is one where the improbability of the conclusion 
 equals the probability of the premisses : the next is where the 
 premisses are equally probable ; for then we shall doubt which 
 of them ought to be denied. One must be false, but we have 
 no indication which*. The cleverest eristic reasoning is where 
 the preliminary decision is difficult, whether the reasoning is 
 conclusive or inconclusive : that is, whether the solution is by 
 negation or distinction. The next is where the doubt is, not 
 whether the solution is by negation or distinction but, which 
 proposition is to be denied or distinguished, and whether it is 
 one of the premisses or the conclusion that requires distinction". 
 
 An imperfect proof is contemptible when the premisses are 
 very improbable or false, but it may be respectable. If some of 
 the propositions about the subject or predicate or middle term 
 are wanting, and are neither assumed nor proved, the argumen- 
 tation-is quite a failure; but when they are assumed without 
 proof and only some preliminary premisses are wanting, the 
 argument is respectable though badly developed^''. 
 
 As solution is either addressed to the proof, or to the prover 
 and his questions, or to neither ; so questions and proof may be 
 addressed either to the thesis, the answerer, or the time, when 
 the solution requires more time than is allowed, or the questioner 
 has time for a rejoinder^^. 
 
 XXXIV. The number and nature of the sources of paralo- 
 gism, the means of eliciting false or paradoxical propositions, 
 the mode of producing solecism, the mode of questioning, and 
 the arrangement of questions, the utility of this kind of argu- 
 
92 HEP I IO<t>llTIKDN 
 
 fidrcov, in wpos ri \pria-Liioi rravres ela-lv ot toiovtol Xoyot, Kal 
 nepl diroKpia-eoos dirXm re irda-rjs Kal 7ra>s Xvriov tovs \6yovi 
 Kal TOVS a-oXoiKia-jiovs, eipifcrSa) rrepl anavTCov r]fuv Tavrd. 
 AoLTTOv Se irepl r^s e^ dpy^fis vpoBecrecos dvafivrjo-aaiv dnuv 
 Ti Ppa-)(y TTepl avrfjs Kal reXos ewideTvai toTs eipr]fj.ivoL5. 
 
 HpoeLXSfieOa jiev ovv ebpeiv S'dya/j.iv riva avXXoyi<rTiKrjv wepl 
 Tov Trpo^XriOevTos eK rStv inrapyovTOiv as evSo^oTdrcov tovto 
 ydp 'ipyov earl rfjs SiaXeKriKfjs Ka6' avrijv Kal rfjs ireipa- 
 (TriKfjs. Ewel 8e wpoa-Karaa-Kevd^erai. irpos avrfiv Sid rfji/ rrjs 
 (TO^LcrrLKfjs yeirviacnv, d>s ov fiovov neTpav Svvarai Xa^elv Sia- 
 XeKriK&s dXXd Kal coy elScus, Sid rovro ov fiovov ro XevOev 
 epyov vireQeneQa rfjs irpayfiareias, to Xoyov Svvaadai Xa^eiv, 
 aXXd Kal oircos Xoyov inreyovres <f)vXd^ofiev rrjv Beaiv ms Sl' 
 evSo^ordrav o/iOTporras. Trjv S' airiav elprfKaiiev roiurov, evel 
 Kal Sid rovro ZcoKpdrrjs rjpdyra, dXX ovk dtreKpivero' wfioXoyei 
 ydp ovk eiSevai, AeSrjXcorai S ev rots nporepov Kal trpos 
 TToaa Kal eK iroa-cov rovro earai, Kal oQev eimoprjo-ojiev tovtwv, 
 en Se irws epcorrjreov rj raKreov rfjv epcorrja-iv iraaav, Kal irepi 
 re aTTOKpia-ecov Kal Xvaecov rmv rrpos roijs avXXoyio'/iovs. AeSrj- 
 Xcorai Se Kal nepl rwv dXXmv, 6<ra rrjs aiirfjs fiedoSov rm 
 XSyoiv etrriv. flpbs Se rovrois rrepl rS>v irapaXoyicr/imv SieXrj- 
 XvOafiev, wamep elpiJKafiev ijSrj irporepov. "On fiev ovv e^ei 
 reXos iKav&s & wpoeiXopieOa, <f>avep6v. 
 
 Aei 5' rifids /ifj XeXrjOevai to crvp.^e^rjKos irepl ravTrfv Trjv 
 irpayiiareiav. Tmv ydp eiipiaKO/iivcov dwdvrwv rd ftev irap 
 irepcov Xr]^6ivra irporepov neTTovrj/ieva Kard fiepos kmSeSmKev 
 inrb tcov irapaXa^ovreov varepov rd S' e^ V7rap\fjs evpicrKo- 
 fieva jJLiKpdv ro irpwrov eiriSoaiv Xaji^dveiv eicoOe, ^r/cripai^ 
 repav /levroi ttoXXS rfjs varepov eK rovrcov av^rjorems. /Me- 
 yiarov ydp ta-cos dpy(^ iravros, Scrirep Xiyerai' Sib Kal \aXe- 
 wSrarov ocrm ydp Kpdna-rov rfj Svvdfiei, roaovrm p.iKpoTaTov 
 hv rS jxeyeOei \aXeTrdyrar6v ecrnv 6(p6rjvai. Tavrrjs ^ eiprj- 
 /levrjs ^aov rb rrpoa-nOevai Kal avvav^eiv rb Xonrov kanv 
 orrep Kal irepl roi/s ^rjropiKods Xoyovs a-v/i^e^riKe, a)(eSov Si 
 
EAErXQN. 93 
 
 mentation^ the mode of answering and solving confutations and 
 solecisms, have been successively examined* We may now recal 
 to mind our original design and, with a few brief observations, 
 bring our treatise to a close. 
 
 Our aim was the invention of a method of reasoning on any 
 problem from the most probable premisses that can be found *. 
 This is the proper function of Dialectic and Pirastie. But it 
 arrogates a further province from its vicinity to Sophistic, 
 professing not only to test knowledge with the resources of 
 Dialectic, but also to maintain any thesis with the infallibility 
 of science. Besides, therefore, the above-named function, the 
 examination of pretensions to knowledge, we included in the 
 faculty we were investigating the power of defending any thesis 
 by probable premisses without self-contradiction 3. The reason 
 is what we mentioned before*, as may be seen from the fact that 
 Socrates only questioned and never answered, because he con- 
 fessed ignorance. We indicated the number of problems ^ and 
 the sources or repertories of proofs, the right mode of question- 
 ing and arrangement 7, the right mode of answering and solu- 
 tion, and the other matters pertaining to the system; and we 
 afterwards treated, as was just remarked, of paralogism. The 
 task, then, which we undertook is completed. 
 
 A fact, however, in the history of this art is worthy of notice. 
 Inventions are either the final shaping of what has been partly 
 ■elaborated by others, or they are original discoveries and but 
 roughly shaped. The latter are the more important. The first 
 step, according to the proverb, is the grand thing and the most 
 diflScult; for first beginnings are as small and inconspicuous as 
 
94 HEPI IO0IITIKON 
 
 Kat irepl rocs dWas Trdaas rixi^as. Ot jikv yap ray apxati 
 eiipovTes iravTeXms enl fiiKpov ti Trporjyayov ol 8e vvv eiSo- 
 Kifiovvres irapaXa^ovres irapa iroWZv oiov e/c SiaSoxfjs 
 Karbt. fiepos npoayayovTcov ovtcds rjv^rJKacn, Tia-ias fiev nerb, 
 Toiis TrpaiTovs, Qpaa-vfiayips Se /xera Tiaiau, QeoScopos Se fiera 
 rovTov, Kal voWol ttoXX^ avvevrjvoxacn /liprj' Sionep ovSev 
 Oav/jLacTTov ex^"' ''"' '"'^V^'^^ '''V" tIxi/tj)/. TavTrjs 8e rf/s npay- 
 fiareias oil to fiev ^v rb S' ovk ^v Trpoe^eipyaa-fievoy, aXX' 
 ovSev TravTe\S>s VTrfjpxev. Kal yap t&v irepl Tois kpKTTiKov^ 
 Xoyovs jiLcrQapvovvTaiv ofjioia rt? rjv ^ iraiSevcris rfj Fopyiov 
 irpayfiaTiia. Aoyovs yap ol fiev prjTopiKOvs ol 8e kpayrrjTiKovs 
 kSiSoaav kKjiavQdveiv, eh ofiy TrXeta-rdKLS kjirriiTTeLv wri6r](rav 
 eKarepoL rois aXXriXcoi/ Xoyovs. Aiowep rayeia fuv dreyvos S' 
 riv rj SiSaaKaXia toTs /iav6dvova-i nap avTwv ov yap Teyvrji' 
 dXXa TO, aTTo rfjs reyyrjs SiSovres waiSeveiv VTreXd/i^avov, 
 axTirep &v ei tis kinaTriiirjv <f)d(rKcov napaSdxreiv knl to /irjSev 
 1T0VUV Toijs TToSas, iiTa crKVTOTO/UKrjv /j,ev firj SiSda-Koi, fir]8' 
 oQev Swrja-eTai wopi^ea-Qai to, TOiavra, Soirj Se noXXa yevq nav- 
 ToSaTrStv inroSrifidTcov ovtos yap fie^oTJOrjKe fiev irpos ttju 
 Xpeiav, Texyriv 8' ov irapeSmKeu. Kal irepl jiev Tmv pr]TopiKm 
 {jwrjpxe iroXXh Kal iraXaih tol Xeyofieva, irepl Se tov ovXXoyL- 
 ^ecrOai . iravTeXm ovSev eiy(oiiev irporepov dXXo Xeyeiv, dXli ^ 
 rpi^fj^^ {rjTovvTes iroXiiv xpovov kirovovfiev. El Se (paiveiai 
 Oeaaafievois vfuv wr kK toiovtcdv k^ dpyrjs iiirapxpvTmv eyeiv rj 
 (ledoSos iKavZs naph. Tas dXXas irpay/iaTecas rits e/c irapaSo- 
 aems rjv^rifievas, Xoiirbv Siv e'lrj iravrmv {>fiS>v fj tS>v ■qKpoap.evaiv 
 epyov Toh jiev irapaXeXeififiefOLS ttjs (leOoSov a-vyyvw/iriv tok 
 S" eipri/iivoLS iroXXfjv exeiv ydpiv. 
 
EAErXDN. 95 
 
 they are potent. When they are once accomplished the re- 
 mainder is easily added or developed. Ihis was the history 
 of rhetorical composition and of most other arts. The original 
 inventors made but small progress. The great modern profes- 
 sors inherited from their predecessors many successive improve- 
 ments and added others. Tisias after the first inventors, Thra- 
 symaehus after Tisias, Theodorus after Thrasymachus, and many 
 others, contributed various portions. Accordingly, it is no 
 wonder that the art has now a certain amplitude^. But the 
 system I have expounded had not been partially, though, imper- 
 fectly, elaborated by others : its very foundations had to be 
 laid 9. The education given to their pupils by the paid teachers 
 of Eristic was like that given by Grorgias to his pupils in 
 Rhetoric. B-eady-made speeches^", oratorical or interrogatory, 
 which were considered to cover the topics of the rival professors, 
 were given to the pupil to be learnt by heart. The training 
 accordingly was rapid but unscientific. Instead of art, the pro- 
 ducts of art were communicated, and tbis was called education. 
 One might as well have promised to communicate an art for 
 protecting the feet, and, instead of teaching the art of shoe- 
 making, have presented the learner with an assortment of 
 shoes. This would be supplying his wants but not teaching 
 him an art. But the teachers of rhetoric inherited many prin- 
 ciples that had been long ascertained : dialectic had absolutely 
 no traditional doctrines. Our researches were tentative, long, 
 and troublesome. If, then, starting from nothing, the system 
 bears a comparison with others that have been developed by 
 division of labour in successive generations, candid criticism 
 will be readier to commend it for the degree of completeness to 
 which it has attained than to find fault with it for falling short 
 of perfection. 
 
NOTES. 
 
 CHAPTER I. 
 
 1] For the difference between a sophistic proof and a paralo- 
 gism see ch. viii. 
 
 2] For the meaning of Ifis, compare Topica, 8. % : Upo(j)epov(n 
 yap OTi Trj vyitla, kX&TTOvi ovti ayaBZ rrjs ive^Cas, jj.e'iCov KaKOV 
 avrUeiTai, ttjv yap vdcrov /xeifoz; KaKov (IvaiTrjs Ka^t^Cas. '(Against 
 the assumption that the greater evil is opposed to the greater 
 good), they adduce the enstasis that health, a lesser good 
 than bodily vigour, has a greater evil for its opposite ; for sick- 
 ness is a greater evil than want of bodily vigour/ And Topica, 
 5- 7- Ofiot'ftjs l^f' larpos re irpbs to ttoltjtikos vyieCas elvai koI yup.- 
 vacTTTis Tipbs TO TiotTjrtKos fvf^ias. ' The function of the gymnastic 
 trainer is the production of bodily vigour, as the function of the 
 physician is the production of health/ 
 
 3] ^v\eTiK&s. This seems an allusion to the choral exhibi- 
 tions at Athens. Each tribe (0iiA?}),' through its choragus, 
 furnished a chorus, and was emulous for its reputation, which 
 depended on its evavbpta, i. e. amfidTav p,iye6os nal pdp-ri, the size 
 and strength of the choristers, as well as their vocal powers, 
 ei^avia. Xenophon, Mem. 3. 3. Ot ^vXeTai, therefore, implied 
 in ^vKiTiK&s, are 01 ■}(opevTaC. 
 
 4] Kop,pM(TavTfs. In the Gorgias sophistic is said to be the 
 counterpart or analogon of Kopp.a>TiKri, a fraudulent art, which by 
 means of shape and colour and sleekness and dress counterfeits 
 the beauty and good condition which are properly produced by 
 gymnastic. Ko/ix/iUTtK?) is to yvp-vaaTiK-fi, and dv|f07rot?jriKrj is to 
 laTpiKTj, as croipia-Tturi is to vop.o6e.Ti.Krj, or pr]TopiKr\ is to StKaoTtKTj. 
 
 H 
 
98 NOTES. Chap. I. 
 
 5] AiOdpyvpos, ' a compound of silver and lead ; or, vitrified 
 lead collected in separating lead and silver.' lAddell and Scott. 
 
 6] We have a similar definition in Topica, 1. 1, where speech 
 {k6yos) is made the genus : 'Eori hr] trvkkoyicrixos Koyos iv iS rediv- 
 Toov Tiv&v hipov Ti T&p KSLixivuiv ff avdyKTfs avix^aCvfl. bia rmv 
 Keiixevcov. 
 
 7] Understand after &v, not alu&v, hut eX.iy■)^mv. To'iros is 
 here used for yieos, for, speaking properly, the to'ttos or ahia is 
 TO. ovoixara, the eXeyxoi are 8ia tS>v ovofiarmv. 
 
 8] Ta TTpdyimra ^IpovTas, ' moving, manipulating, the ob- 
 jects,' appears to he a metaphor derived from the phrase raj 
 ^j/^ijyovs (pepeiv, which shortly follows. 
 
 9] Aoyos may mean an argument, or a proposition, or a defi- 
 nition, or a circumlocution. It usually means an argument, but 
 when in close antithesis to ovojxa it means a circumlocution or a 
 complex, as opposed to a simple, term. 
 
 10] Ot aKovovres are the audience present at a controversy. 
 See ch. viii, Ilap' oa-a yap ^aiverai roTs a.K(y6ov(Ti,v as ■tipmvqp.iva, 
 iTv\\ekoyL(rdai, irapa ravra kSi» tu diroKpti/ofx^vb) 8dfetev. Also 
 eh. XV, 'Ez'foTe yap oLovrai koL ovtoI SeScok^vui koi tois aKovovai 
 ^alvovrai. On this point an unknown paraphrast, edited by 
 Spengel, says the only thing that he says worth quoting : Oi 
 yap aKpoaral Ir Tois 6taAe'fe(Ti KpiTal ttjs vlKr)S rois aymn^oiiivots 
 KdOrjmai. ' The audience present at a controversy are the judges 
 who decide which disputant is victorious.' This writer trans- 
 forms some of Aristotle's cramped statements into very sonorous 
 periods, hut is of no value as a commentator. 
 
 11] In ordinary Greek SoSj'ai \6yov is to render an account, 
 Xafieiv \6yov to audit an account. In logical language 8owoi 
 \6yov is the function of the answerer, Ka^elv \6yov of the ques- 
 tioner. In ch. xxxiv. the former of these functions is said 
 to be the more sophistical branch of dialectic, because the 
 answerer pretends to science, which the questioner disclaims. 
 In ch. xi. it is explained how the pirastic questioner, himself 
 making no pretensions to knowledge, may be competent to ex- 
 amine the knowledge and expose the ignorance of the answerer. 
 Throughout the present treatise however, in accordance with 
 the title, it is usually the questioner that is supposed to be the 
 sophist, and the respondent who is the honest reasoner. 
 
Chap. I. NOTES. 99 
 
 12] AijvaiJ,is, capacityj is in the intellect; •npoaipecris, purpose, 
 in the will. The antithesis between thest terms may throw 
 light on what Aristotle conceived to be the relation between 
 sophistic and dialectic : 'Opav be koI et ri t&v yjreicT&v ^ (pevKT&v 
 els hivafiiv 17 ro bwarov IdriKev, oXov rdv oro^toTTJi' fj bidjSoXov rj 
 K^iirTTiv Tov bvvapi.evov \A0pa to, aWorpia Kke-nreiv. OvSeis yap t&v 
 elpr)\i.ev(ii>v tu Swaros etvai ti tovtcov toiovtos kiyerai' bvvarai p.ev 
 yap /cal 6 6eos kcu, 6 cnrovbaios to, ^av\a bpav, a\V ovk ettri toiovtoi' 
 iravTei yap 01 (j)avXoi Kara mpoaipecnv Xeyovrai. "En ■naa-a Swajiis 
 T&v dtper&V (cat yap al t&v <j)avK<ov bwdptets alpeTaC, bib xal tov 
 Oebv Kot TOV oTTOvbaiov e^etv (pafiikv avrds, bvvaTovs yap etvai to, 
 <f>av\a TrpoTTeiv. . . , H 6( ti t&v iv 8t;o yiveciv ^ Tr\e(o<nv els 
 Qijepov eOriKev. 'Evia yap ovk ea-riv els kv yivos deivai, oXov tov 
 i^evaKa icaJ tov bid^oXov ovre yap 6 Trpoaipovp,evos abvvaT&v b4, 
 oiff 6 hvvap,evos jxi] Trpoaipovfxevos be, bia^oXos rj <p4va^, d\X' 6 
 cifu^o) TavTa exaiV &<tt ov deTiov els ^v yivos aXK' els afx^oTepa 
 TO. elpnp.iva. Topica, 4. 5. ' We should look to see whether a 
 thing to be blamed or shunned has been referred to the genus 
 Ability or Able. Whether, for instance, the sophist, calum- 
 niator, or thief has been defined to be a man able to appropriate 
 secretly his neighbour's property, et cetera. It is not ability to 
 perform these things to which these names are given, foT God 
 and the virtuous have ability to do evil though not the inclina- 
 tion ; it is on account of his volition that we call a person bad. 
 Again, every power is a thing to be desired, even the power to 
 do evil, and this accordingly we ascribe to God and the virtuous, 
 for we suppose they have the power without the will. . . . Again, 
 we must observe whether a species that falls under two or 
 several genera has been referred solely to one, for some things 
 cannot be placed in a single genus, as, for instance, the impostor 
 and calumniator: for neither the will without the power nor 
 the power without the will makes the impostor or calumniator, 
 but both united. They ought therefore to have a double genus.' 
 Upos be ToruTois on ttjs avTr\s [eaTi Texi^js] to re mOavov koL to 
 ^aiv6p.evov Ibeiv irWavov, ua-irep Kal eul ttjs biaKeKTiKtjs avXKoyio'p.ov 
 Te Kal <f)aiv6f/,evov (TvWoyi(rp.6v 6 yap crocpia-TiKos ovk ev tj) bwdpiei 
 aX\' ev rfi irpoaipicrei. Ukfiv ivTavda p-iv eoroi 6 p,^v Kara tt/v 
 ema-Trjfxrjv 6 b^ KaTo, ttiv Tipoaipeaiv priTap, Ixei 8^ a-ofjuaTrjs piev 
 Kara rrji' TrpoaCpemv, biakeKTiKos be ov Kara ttjv -npoalpecnv oKKa 
 
 H a 
 
100 NOTES. Chap. I. 
 
 Kara Ty\v bwajxiv. Rhetoric, I. I. ' Again, it is the function of 
 a single art to investigate the means of both true and false 
 persuasion, as dialectic examines both genuine and apparent 
 proof. For a man is not a sophist who has the power to deceive 
 without the will. In the sphere of oratory, however, [there is 
 a want of distinctive names, for] both the science of wrong per- 
 suasion and the science combined with the purpose of wrong 
 persuasion are called rhetoric ; whereas in the sphere of dispu- 
 tation [the power plus] the will to deceive is called sophistic, the 
 power without the will, dialectic' "En be ravavrCa Set bvvaaOai 
 nelBuv, KadAnep Koi iv rois (ruWoyicr/iois, o^;( oircos afi-^OTepa. Tip&T- 
 TODHfv, ov yap 6et ra (jjavXa iitLduv, &KK' iva fjJ\Ti XavOavji irus exei, 
 Kai oTtats &KKov xpoifxevov tois Aoyots p.r] Sixaius avToi Kveiv excojifv. 
 T&v iJLfv ovv &K\cov Tf)(y^v ovhffiia TavavrCa cruAXoytferat, fj be 
 biaXeKTLKrj Kot fj prjTopiKT] p.6vai tovto -noiovcnv, Ofioiias yap ti(Tiv 
 ap-cjiOTepaL t&v ivavrCaiv. Ta jueVroi vnoK^lixeva itpaypaTa oux 
 6p,oCcos ^X^'j ^^' "^' Ta\r)6r] koX to, fieXriu) rrj (f)V(rei ivavkkoyuno- 
 Tepa Kal TtiOavdrepa, &s airK&s eheiv. Rhet. I. I. 'The power 
 of maintaining opposite conclusions is desirable in rhetoric as 
 well as in dialectic, not that we may practise both its branches, 
 for we must not persuade to evil, but that we may understand 
 the process, and, if another makes a sinister use of reason, may 
 counteract his sophistries. No science proves contrary conclu- 
 sions except dialectic and rhetoric, which are equally related to 
 the right and the wrong conclusion. Facts, however, are not 
 equally favourable to both ; for the true theorems and just con- 
 clusions are supplied by nature with more evidence and means 
 of persuasion than the contrary, as a general rule.' From these 
 passages and eh. xxxiv. it appears that the present treatise may 
 be considered as the last book of the Topica, or general treatise 
 on dialectic J from eh. ii, however, it appears to be an inde- 
 pendent substantive treatise. 
 
 13] Did the sophist ever exist ? Was there ever a class of 
 people who professed to be philosophers and to educate, but, m- 
 stead of method or a system of reasoned truth, only knew and 
 only taught, under the name of philosophy, the game of eristic ? , 
 When we read Whately's Logic we see that to him the sophist 
 he so often mentions is merely an ideal, the personification of 
 a bad argument. Grote says, the only reality corresponding to 
 
Chap. II. NOTES. 101 
 
 the name are the disjeeti membra sophistse in all of us, the 
 errors incidental t<o human frailty in th£ search after truth. 
 But, if we accept the testimony of Aristotle, there were certain 
 definite individuals who, by the common consent of the think- 
 ing Hellenic world, had coined more fallacies than is permitted 
 to human infirmity, and were consequently recognized by the 
 educated as utterers of counterfeit wisdom, clever charlatans, 
 intellectual Cagliostros, pseudo-philosophers, because indifferent 
 to the truth. We must not suppose that the name was applied 
 ,to thinkers merely because their opinions were heterodox or un- 
 palatable to their contemporaries; for it was never applied, as 
 far as I am aware, to Leucippus or Democritus. The question, 
 however, is more interesting to the historian than to the logician. 
 To the logician, sophistry, like dialectic and science and philo- 
 sophy, is merely an ideal. 
 
 14] The kinds of sophistical reasoning are enumerated in 
 ch. iv. and v, the branches of the faculty in ch. iii, the elements 
 of the profession, if different from the last, may be the functions 
 of questioning and answering, the other components of the art 
 are arrangement and the remaining topics treated in ch. xv. 
 and xvii. 
 
 CHAPTER II. 
 
 1] A fourfold division of reasonings has been given in the 
 Topica, but instead of pirastic the pseudographema (for which 
 see ch. xi) is mentioned. 'Airobei^is jnev ovv ia-rlv orav k^ a\r]- 
 6&V KOI Ttp(iiT<i>v 6 avWoyiajj.bs f, ri Ik Towirraiv h bid tivcov TTpc&Tcav 
 Koi aXrjd&v TTJs TTfjol avTo, yvdxreuis t7\v ap^^v €^A.?j^e. AtaAe/trtKos b\ 
 mWoyitT^i b e^ evbo^cov o-uAXoytfo/;i€vos. . . . 'Epiorixos 8' lort av\- 
 Aoyio-/Ltos d Ik (jjaivoixevciiv fvbo^av jxr) ovTa>v be, koI 6 1^ evbo^cav rj 
 <l>aivo[i,ivmv ivbS^uiv (f)aLv6fj,evos .... 6 ^ev ovv Trporepos t&v prjBevrav 
 ipUTTiK&v avWoyitrjx&v koX (TvWoyuTjws Xiyi(j6u>, 6 8e Xomos Ipt- 
 <rrtKOs pkv (TvWoyicriws, iTvWoyi(riJ,os 8' ov, Iwet8?) cjiaiverai ixev (tv\- 
 Xoyl^ecrdai avWoyiCeTat, 8' ov. "En be Trapa Toiis elprjixevovs ^Ttavras 
 (rvX\oyi,afi,oi)s oi iK t&v Ttepi Tiva^ IwtcrrTjjiias olKeiwv ywofxevoi Ttapa- 
 XoyuTixoL . . . . o^re yhp If a\r]6&v Kot Trpdraiv a-vX\oy[(^eTai 6 yjrev- 
 boypa^&v ovr' If evbo^cov .... aA\' Ifc t&v oliceCcov jxev tjj eTiLcrTifiiJ,ri 
 Aj/jK/iiarui' ovK aXrjB&v be toi' cTv\Koyt,crij,ov woteirai. Topica, I. I. 
 
102 NOTES. Chap. II. 
 
 ' Demonstrative proof is based on true and elementary premisses, 
 or on theorems that have been proved by true and elementary 
 
 premisses. Dialectic proof is based on probable premisses 
 
 Eristic proof is based on premisses which seem but are not pro- 
 bable, or is seeming but not real proof based on probable or 
 seemingly probable premisses. . . . The former kind may be called 
 absolutely proof, the latter is not proof without qualification but 
 eristic proof, for it is only simulated proof. Different from all 
 these are the paralogisms based on premisses peculiar to a cer- 
 tain sphere of subject-matter for the premisses of the geo- 
 metrical paralogism are neither elementary truths nor proba- 
 bilities .... but are propositions peculiar to a certain sphere and 
 false.'' 
 
 2] This famous dictum should be compared with other pas- 
 sages which require less faith on the part of the learner. TcS it\v 
 yap fiavO&vovTi deriov ail to boKOVvra, (cat yap ovS e-ni^npii ^tvhos 
 ovbels bibdcTKeiv. Topica, 8. 5. 'A learner should admit what- 
 ever he believes, for no teacher tries to prove what is false.' 
 Elsewhere we are told that the learner, or answerer in didactic, 
 should be less ready to concede premisses than the answerer in 
 dialectic. "Orai' 8' ^ irpoi to dfico/xa kol ttiv itpoTatriv p,ei(ov ipyov 
 8ta\ey^i'ai ?j rqv decriv, bianop'^cTeiev av ns irorepov Oireov to, toi- 
 avTa rj ov. Ei yap jxf) drjcrei aW' &^i(i(rei Kal irpbs tovto bLaKfytaBai, 
 jw.etfoi' TTpoa-rd^fi tov ev ap)(fi neipievov el bl ^jjo-et, irtoreufrei ef 
 rJTTov nKTT&v. El p^v ovv bit p.r] yaKeTK&Tepov to Trpofikrum ttouiv, 
 deriov, ei hi bia yvapifiatriptov avWoyCCeadai, oil Oiriov, *H tu fiew 
 fiavOavovTi ov deriov hv /xtj yvcapip^repov y, tu be yvp.vaCop,ev(f 
 Bereov hv akrjdes p,6vov (jiaCvrjTai. "Xlore ipavepov Sti ov^ ofiolas epio- 
 T&vrl re koHL bibavKOVTi d^mreov riOivai,. Topica, 8. 3. ^ If a pre- 
 miss is harder to prove than the conclusion, ought it, or ought 
 it not, to be granted by the answerer ? If he refuses to grant 
 it and requires it to be proved, he imposes a task more difficult 
 than the original problem ; if he grants it, the grounds of proof 
 will be less evident than the conclusion. If the problem ought 
 not to be made more difficult, the premiss should be granted; if 
 the grounds of proof should be more evident than the conclusion, 
 it should not be granted. We decide that a learner should grant 
 no premiss that is not more evident than the conclusion; the 
 dialectician who argues for practice should grant any which 
 
Chap. IV. NOTES. 103 
 
 appears true. The same rules, then, do not apply to dialectic 
 and didactic' _ 
 
 3] The only extant passage in which Aristotle defines the 
 nature of pirastic premisses is in cli. xi. This cannot possibly 
 be referred to by the words iv hepois. These words then indi- 
 cate a lost work on Pirastic. 
 
 4] This treatise, then, was written after the Analytica Poste- 
 riora, which treats of Demonstration. The first chapter of the 
 Analytica Priora refers to the Topica, which was therefore written 
 previously, as we might have judged from comparing the degree 
 of precision with which the process of reasoning is handled in 
 the two treatises. But the eighth book of the Topica refers 
 to the Analytica Priora (see chap, ii and 13). This book 
 therefore must have been added subsequently. The seventh 
 book of the Topica may seem to refer to the Analytica Poste- 
 riora : « riviav 6e Set [opoi;] KaTacTKev&^eiv, bidtpinTai jxev ei> erepots 
 hxpi^ia-Tepov, irpbs be rrjv TtpoKeitiivi^v jxidohov 01 avToX tottoi xP')"''- 
 iwi. Topica, 7- 3- But in the Analytica Posterior a the rules for 
 estabhshing a definition are not given under the form of loci, 
 and the words iv hipois may refer to some other treatise. The 
 Sophistici Elenchi was written before the Hermeneutiea, which 
 refers to it in ch. 11, under the name of to, mriKd. The seven- 
 teenth chapter of the second book of the Analytica Priora refers 
 to the Sophistici Elenchi under the name of to, Tomxti. This 
 chapter therefore, and probably others in the second book, must 
 have been added subsequently, as the mass of the treatise was 
 written before the Sophistici Elenchi. The Rhetoric was written 
 after the Topica and Analytica Priora, which it refers to in the 
 second chapter of the first book. It speaks of to. epLcrriKd in the 
 twenty-fifth chapter of the second book, but, to judge from the 
 inferior precision with which it handles the subject of fallacies, 
 was probably written before the Sophistici Elenchi. 
 
 CHAPTER IV. 
 
 1] Verbal fallacies of course vanish in translation. In the 
 following translations much licence has been taken, and the 
 result is but lame. 
 
104 
 
 NOTES. 
 
 Chap. IV. 
 
 rpanixaTiKiq is defined to be the art of reading and writing : 
 eTsi(TTri)xr\ tov yp6ri\rai to vitoyopevOev koI tov avayv&vai. Topica, 6.5. 
 The teacher was said to aTro(nofj,aTlCeiv, or {mayopeveiv, when he 
 dictated a word to be written or spelt. The boy who caught and 
 understood the word, that is, who could exactly appreciate a 
 complex sound and decompose it into its letters or elementary 
 sounds, was said in the language of the school to navOdveiv. 
 He was ypap-p-ariKos, master of alphabetic science. The example 
 is taken from the Euthydemus of Plato (§§ ia-i8): it may be 
 thus analysed. Suppose that the thesis to be confuted is & nav- 
 Bdvoiv avemcrTriiJLcov. We have two syllogisms : — 
 
 6 p,av6A.vmv to. 
 
 a/noGTOiiaTi^6p,eva 
 
 6 jxavB6,vatv to. 
 
 aTroa-ToixaTi^ofjteva 
 
 6 [xavBdvcov 
 
 Major, 
 Minor, 
 
 ypap,p,ari,Kos' 
 
 Conclusion, 
 Again : 
 
 p.av6dvii: 
 ypajxixanKos. 
 
 Major, 6 ypapLfiariKos fm(rTrip,(ov 
 
 Minor, 6 fxavOdvuv ypaixp-ariKos' 
 
 Conclusion, . ■ . 6 p,avddvcov eiri.a-T'qp.tov. 
 
 The minor term (fjtavddvwv) is ambiguous. 
 
 TO, biOVTa 
 
 TO KUKa 
 
 TO, KaKa 
 
 ayaOd' 
 hiovTa' 
 ayadd. 
 
 2] Major, 
 
 Minor, 
 
 Conclusion, 
 The middle term is ambiguous. 
 3] Major, Bajrep dvia-Taro 
 
 Minor, 6 Kadii]p.ivos 
 
 Conclusion, .•. 6 KaOrjpAvos 
 The minor term is ambiguous. 
 
 Major, 8a-7rep vyid^ero 
 
 Minor, 6 Kdp,vmv 
 
 Conclusion, .'. 6 KdfW(av 
 The minor term is ambiguous. 
 
 Whately is inclined to rest the claims of logic to considera- 
 tion on the services she performs in teaching us the seat of 
 the ambiguities on which fallacies are built. This, he repeatedly 
 informs us, is the middle term. The above examples may shew 
 on how precarious a foundation he rests the claims of logic. 
 
 dvla-raro' 
 ea-TTjKf. 
 
 vyiaivef 
 vyidCero' 
 vyiaivfi. 
 
Chap. IV. NOTES. 105 
 
 4] Read uytdf eroi. In the next line we have MS. authority 
 for omitting the article before irpoTepov. « 
 
 5] Supplying a minor we obtain this fallacy : — 
 MajoTj Toiro o tis yivduKU yiv^cTxei' 
 
 Minor, at ypaipal tovto S tis yivJxTKW 
 
 Conclusion, . • . at ypa(\icu yiv(&(rKOV(n. 
 
 The major premiss is taken to mean, 
 
 aSrai &s ny yivdcTKei yiv^cTKOvcn. 
 It really means, 
 
 tIs yiV(otrK€L TOVTas hs ywdxTML. 
 There are therefore more than three terms, or we may say that 
 the middle is ambiguous. For a justification of the employment 
 of the feminine and masculine pronouns in the analysis of this 
 and the following fallacies, see eh. xxxii. 
 6] Major, tovto h Spa tis 6p^' 
 
 Minor, 6 Kiatv tovto h opa Tts" 
 
 Conclusion, .•. 6 idiav opa. 
 
 The major premiss is ambiguous. It really means, tovtov, hv opa 
 ns, opa : but it is taken to mean, o^tos, ov opa ris, opa. 
 7] Major, to (jifis elvai, ovtos 
 
 hp (TV </)^s eii/ai Itrrt to (fifis eTvai \Cdos' 
 Minor, av (pfjs etvai tovtov bv crv (^^s eifat* 
 
 Conclusion, .■. (tv (fjfis etvai A0os. 
 The middle is ambiguous if we employ the word tovto, but if, 
 as above, we use the masculine gender, there are two distinct 
 terms, one containing oSros, the other tovtov. 
 
 8] Suppose the thesis to be : Speaking of the speechless or 
 silent is impossible. We have the syllogism. 
 
 Major, Speaking of iron tools is possible : 
 
 Minor, Speaking of iron tools is speaking of the silent : 
 
 Conclusion, Speaking of the silent is possible. 
 Here the conclusion follows, but, as the minor term is ambi- 
 guous, does not contradict the thesis. A disputant in the Euthy- 
 demus denies the minor premiss, asserting that if we go by a 
 factory at work, we shall find that iron tools are the reverse of 
 silent : ''A\Kd y.oi Soxeis, ^v9vhr]p,e, ov KaOevbav eiriKeKoiixTJadai, Koi 
 fl otov re, \fyovTa fi/qbiv, \eyeiv, Kal (tv tovto holuv. 'H yap ov\ 
 otdv re, ecprj 6 Aiovvcrobaipos, (ny&vTa \fyeiv ; Ovb' 6tt<>)<ttiovv, ij 6' Ss 
 
106 NOTES. Chap. IV. 
 
 6 Kr^ertTTTTo?. "Oroi' oZv \i8ovs A^yjjs (cat fi;\a icot cribripia, ov ai- 
 y&VTa keyeis ; Ovkovv el ye eyd, e<j)ri, itapep^onai ev rois x.a\iieiois, 
 aKXa (ftOeyydneva Koi ^o&vTa (ieyiarov to, (Tibripia Ae'yerat idv ns 
 fii/zjjrai. EuthydemuSj § 67. 
 
 9] There is something wrong here. We may either omit km 
 p.ri yp6.(j)0VTa ypAipeiv, or Koi Tovff ixravTuts av Tts crvvdfj, rov p,ri 
 ypd<j)0VTa ypa^eiv. 
 
 10] Here again we require emendation. We obtain a mode- 
 rate amount of sense if we read, koX p,avd6.va>v yp6.p.iw.Ta &iiep iiav- 
 Q&vei eTiiarirai. 
 
 11] Major, Two and three (distributively) are even 
 
 and odd; 
 Minor, Two and three (collectively) are five ; 
 
 Conclusion, .-. Five is even and odd. 
 Whately adds : — 
 
 Major, All the angles of a triangle are equal to 
 
 two right angles ; 
 Minor, J 5 C is an angle of a triangle ; 
 
 Conclusion, .• . ABC is equal to two right angles. 
 How does the fallacy of conjunction differ from the fallacy of 
 disjunction? Whately says, when the middle is taken collec- 
 tively in the major premiss and distributively in the minor, we 
 have the fallacy of division; when it is taken distributively in 
 the major and collectively in the minor, the fallacy of compo- 
 sition. So when some other term and not the middle is am- 
 biguous, we might say the fallacy was one of division or com- 
 position, according as the term was taken collectively in the 
 premiss and distributively in the conclusion or vice versa. 
 Thus, Major, Three and two are two numbers ; 
 
 Minor, Three and two are five ; 
 
 Conclusion, . • . Five is two numbers ; 
 would be a fallacy of composition ; whereas, 
 Major, Five is one number; 
 
 Minor, Three and two are five ; 
 
 Conclusion, . • . Three and two are one number ; 
 would be a fallacy of division. This is intelligible, but cannot 
 have been Aristotle's view, for his first example of division would, 
 according to Whately's test, be a fallacy of composition. The 
 
Chap. V. NOTES. 107 
 
 point is hardly worth deciding ; for the fallacies in diction may 
 well be regarded as a single species^ or «t the utmost as two, 
 homonymia and figura dictionis. 
 
 12] Buhle, comparing Terence's line in the Andria, 
 Scis. Feci ex servo ut esses libertus mihi, 
 infers that this is a line of Menander. But if our chronologies 
 are correct and this line was quoted by Aristotle, it was older 
 than Menander. For we are told that Aristotle died in B.C. 3355, 
 and that Menander's first play was acted when he was still an 
 ephebus, i. e. between 18 and 30 years old, in B.C. 331. 
 
 13] To find any fault (ajxafiTla) in Homer was thought to be 
 a paradox, and adverse criticisms on him seem to have been 
 considered a branch of dialectic or eristic. The critic treated the 
 poet as pirastic treats the pretenders to other arts and sciences, 
 that is, he attempted to prove by the poet's utterances that he 
 was not a master of the art which he professed. Though, if such 
 criticisms were, as they ought to have been, based on principles 
 peculiar to esthetic science, when false, they would have been 
 pseudographic (see chap, xi), not sophistic. Perhaps, however, 
 the person confuted was not the poet, but the rhapsode, who 
 often attributed universal science to Homer. In the Poetics, 
 chap. 35, five loci («i8rj) of such criticisms (eTrtrtfujo-ets, vpo^k^- 
 Hara) are given, and twelve solutions. Some of the criticisms are 
 referred to the sophistic loci of accentuation, homonymia, amphi- 
 boha, division, ignoratio elenchi ; but the text is very corrupt. 
 
 14] The defence of these two passages by a change of accen- 
 tuation is attributed in the Poetics to Hippias of Thasos. The 
 first occurs in Iliad 23. 338 ; the second does not occur in Aga- 
 memnon's dream, but in Iliad ai. 297, where Achilles is encou- 
 raged by Poseidon. We may infer that our present form of the 
 text had not been established in the time of Aristotle. 
 
 IS] See Topica, 1.9. 
 
 CHAPTER V. 
 
 1] 2tijx^e;8)jKos here is opposed to ovcrCa, and means not only 
 what is usually called accident, but every predicate except defi- 
 nition or the whole essence of the subject. See ch. xxiv, where 
 the fallacy of accidens is discussed: Movois yap rois Kara ttjv 
 
108 NOTES. Chap. V. 
 
 ova-Cav adLa<j>6pois koI kv ov<tlv &TTavTa 8o/cei Tavra inrdp\eiv. ' Only 
 those terms whose essence is one and indistinguishable have all 
 their predicates' in common.' The words Ir ovtriv shew that 
 even genus is to be regarded as accident. Compare 'AAtj^k 
 yap vav to &v0ptlnT(D tivai fa)M etvai, &(TiT€p Koi Travra ^.vdpatuov 
 C^ov, a\\' ovx ovTots &(TTe ev flvai. Analytica Posteriora, 3. 4. 
 ' Humanity is animality and man is animal, but the ideas are 
 only partially, not totally, identical.' 
 
 2] Major, avdpatiros ov KopicrKos' 
 
 Minor, Kop[(rKos &v6pmi!or 
 
 Conclusion, . • . Kopia-Kos ov KopiaKos. 
 We have an undistributed middle. 
 
 3] Major, 2a>KpdTr)s &vdpmTror 
 
 Minor, KopCa-Kos ov StoKptirjjs" 
 
 Conclusion, . ■ . Kopla-Kos ovk avOpmnoi. 
 We have an illicit process of the major. 
 
 In the Euthydemus it is stated that Socrates is the son of 
 Sophroniscus, and that Patrocles is the son of the mother of 
 Socrates by her former husband, Chaeredemus. The sophist 
 then attempts to prove that either Sophroniscus or Chseredemus 
 is not a father. Oi/coi/z', rj 8' os, ^repos fjv Xatp^8r;/xos tov ■narpos; 
 Tovixov y , etprjv ky(L. ^Ap' ovv TTarrjp rjv irepos i)v -narpos ; ri av d 
 6 avrbs tu kCda; A^boiKa jJiiv fyaiy, ^<^r]V, firj <pav& viro crov avrSs' 
 ov jiivTOi fxoi 80KQ). OvKovv Srepos ei, I<^jj, tov \l6ov; "Erepos 
 fjiivToi. 'AWo Ti ovv irepos, ri 8' os, &iv \LOov ov XCdoi «; kuI 
 Irepos li>v xpijcov ov xpva-os ei; 'EtrTt raCro. Ovkovv koI 6 Xaipi- 
 Srjixos, i(t>ri, ^repos &>v Trarpos ovk &v Tiarrip etr). "EoiKev, rjv f ky&, 
 ov Trarfip eTvai. El yap 877 irov, ^(prj, irarrip eariv 6 Xaipehrifios, 
 vTSoka^utv 6 EvdvbrjfjLos, irdXtv av 6 'Sica^povLcrKos trtpos &)V Ttarpos ov 
 •narrip ecniv, ware av, S ^(iKpares, dirdTotp el. Euthydemus, § 6a. 
 'Chaeredemus then, said he, was other than a father? — Than 
 mine, said I. — Then how could he be a father if he was other 
 than a father? Are you the same as a stone? — I am afraid 
 you will prove me so, said I, but I believe I am not. — Then you 
 are other than a stone ? — Yes. — Being other than a stone you 
 are not a stone ; and being other than gold you are not gold ? — 
 True. — Chaeredemus, therefore, being other than a father is not 
 a father. — It seems he is not a father.^At least if Chaeredemus 
 
Chap. V. NOTES. 109 
 
 is a father, said Euthydemus breaking in, Sophroniseus being 
 other than a father is no father, and ydu, my Socrates, are 
 fatherless.' 
 
 4] In the Topica it is given as a dialectic maxim that when 
 a qualified assertion is true, the unqualified assertion is true; 
 although it is allowed that the principle has numerous excep- 
 tions. Toi> avTOV be rpo-nov a-KeTrriov Kcii im tov Kara tl koa, irore 
 /cat TToC" ei yap Kara tl evS^x^'""'; '^"'■^ aTrX&s ei'Stxerot. . . . "EvarTacris 
 oTi Kara n liev elcri (pvcru tr-novhaioi, otov k\ev6epioi r\ (juxppovLKoC, 
 airk&s be ovk elal (j>v<Tei (movbaioi. . . . Tbv avrbv be rpoTiov kol 
 TTov iJ,ev KaKov tov -narepa Oveip, otov ev Tpi/SaWols, aTiX&s b' ov 
 KaXov. . . To 8 OTrAdls ecrrlv o ixrjbevbs Trpoa-TeOevros ipels on KaXov 
 ecmv 71 TO evavTiov otov to tov Trarepa dveiv ovk epeis Ka\ov eXvai, 
 aWa Tiai koXov etvai, ovk &pa a-ir\&s KakoV aWa to tovs Oeoiis 
 Tifiav epeis xaKov ovbev -npoadeis, aiiK&'s yap koKov eort. Topica, 
 2. II. 'We should look to facts qualified in point of respect 
 or time or place ; for what is true in a certain respect is abso- 
 lutely true. . . . By way of enstasis it may be objected that partial 
 virtue is inborn, as liberality or an inclination to temperance, but 
 complete virtue is never inborn. . . . Again, locally it is a duty 
 to sacrifice one's father, as among the Triballi, but absolutely 
 
 it is not a duty Absolutely means, without the addition 
 
 of restrictive terms : as to sacrifice a father cannot be called 
 a duty without the addition, among the Triballi; whereas to 
 reverence the gods is a duty without any restriction.' 
 
 5] The opposition between absolute and relative motion or 
 rest accounts for the conflicting statements respecting a certain 
 doctrine of Plato in the Timseus. Well-informed writers have 
 declared that the earth is there represented as at rest : equally 
 well-informed writers declare that she is represented as in 
 motion. Which of these statements is true? Both. The 
 universe is represented as having a solid pole or axis which 
 revolves at a certain pace in a given direction and carries round 
 with it the rest of the universe. The earth is at the centre 
 of the universe and would revolve with it if she were not 
 rotating on the axis with exactly equal speed in the opposite 
 direction, {iKX.op.evriv, i.e. aveKiTTOfievriv, irepl tov bia TiavTos tt6\ov 
 Terafievov) . Shall we say she is at rest or in motion ? If the 
 revolution of the axis ceased while the counter-revolution of the 
 
110 NOTES. Chap. V. 
 
 earth continued, there is no doubt she would he in motion : if 
 the counter-revolution of the earth ceased while the revolution 
 of the axis continued, there is no doubt she would be in motion, 
 revolving with the rest of the world. While both revolutions 
 continue, it may be disputed whether we ought to say that she 
 is absolutely at rest though relatively in motion, or absolutely 
 in motion though relatively at rest. See the subject examined, 
 with a different explanation, by Grote, in his pamphlet on the 
 Timseus. 
 
 6] It would be a false classification (oXktj) to place ignoratio 
 elenehi, and, what may be identified with it, secundum quid, 
 among the fallacies in diction, because the similitude which 
 produces the deception is a real simihtude of facts or ideas, and 
 not merely a similitude of words. 
 
 7] There is a chapter on petitio principii in the Analytica 
 Priora, for which see Appendix A. 
 
 8] In the Rhetoric the fallacy of sig^s is enumerated as 
 distinct from the fallacy of consequences. From which we 
 may infer that the present treatise, containing the juster view, 
 is the later composition. 
 
 9] The nature of the fallacy of non causa pro causa has been 
 sufiiciently explained in this chapter, but as Whately confesses 
 that he cannot conceive what logicians mean by this term, in 
 Appendix B we have added a chapter on the same subject from 
 the Analytica Priora. 
 
 10] There must be something corrupt here : the translation 
 does not follow the text. 
 
 11] What Aristotle apparently means, and what we must 
 get from his words as best we may, is this : — An inconclusive 
 argument with true premisses in plurium interrogationum may 
 be converted, like any other fallacy, into a conclusive argument, 
 that is to say, a sophistic proof (see ch. viii), by the assumption of 
 false premisses. The premisses in this fallacy are of the following 
 form, (ch. xxx) : A and B are Cand D : where what is true of 
 A is false oi'B, and vice versa : whence a fallacy. If now we 
 assume on the contrary that A and B have the same predicates, 
 that if C or i> is afiirmed or denied of the one it is equally 
 (ofiolas) afiSrmed or denied of the other, we shall have valid 
 reasoning from a false assumption. 
 
Chap.VI. notes. Ill 
 
 CHAPTER VI.* 
 
 1] Substantive names (nomina siibstantiva) properly and 
 primarily belong to individual substances. Language extends 
 them^ secondly, to the genera of these substances ; and, thirdly, 
 to attributes (e. g. to-oVr/s, dvKroVjjs) . Realism ascribes substantive 
 existence to the second of these classes, if not to the third. 
 
 2] Mill says : " Logic postulates to be allowed to assert the 
 same meaning in any words which will express it — We require 
 the liberty of substituting for a given assertion the same asser- 
 tion in different words — We require the liberty of exchanging a 
 proposition for any other that is equipollent with it.^^ Criticisms 
 on Sir W. Hamilton, ch. 31. This postulate he identifies with 
 the axiom or principle of identity, which he thus expresses : 
 " Whatever is true in one form of words is true in every other 
 form of words which conveys the same meaning.''^ The dialectic 
 rule is not inconsistent with this, but only imposes on the dis- 
 putant before he changes a formula the necessity of obtaining 
 the assent of the respondent. A respondent could not refuse his 
 assent to any reasonable proposition without exposing himself 
 to the charge of hva-Kokia, perverse obstructiveness, which was 
 equivalent to defeat. If, however, the respondent was prepared 
 to brave the charge of Si/o-icoAta, the conditions imposed on the 
 opponent must have sometimes enabled the respondent to avoid 
 a formal confutation. Ov yap Ttpos rbv If m Koyov f/ diro'8eif is dWa 
 Trpos Tov iv rfi \j/vxfi, eiiel ovbi <Tv\\oyi(TiMS. 'Ad yap eariv ivarTrj- 
 vai irpbs tov Ifo) \6yov, aWa :rpos tov earn \6you ovk dei. Analy- 
 tica Posteriora, i. 10. 'It is not the spoken but the thought 
 proposition that carries demonstration or even ordinary proof; 
 for exception can always be taken to the verbal enunciation, 
 though not always to the thought enunciated.' [I have trans- 
 lated as if Aristotle had written ov yap h tov Ifco Xoyov rj airo- 
 8etfis aW e/c tov ev ttj v/fi^xf?- If Tpos is used in its proper sense, 
 i. e. (see ch. xix, note 4) as indicating not the premisses but the 
 conclusion of a demonstration, we must translate : ' The con- 
 clusion of demonstration is not the spoken but the thought 
 proposition.'' But the axiom, the indemonstrable foundation of 
 proof, of which Aristotle is speaking, could hardly be spoken 
 
112 NOTES. Chap. VI. 
 
 of as the conclusion of a demonstration. It seems, then, that 
 irpbs here is not used in its Aristotelian sense, but in the sense 
 which it bears in the formulas, irpos roivoiJM, irpbs rrfv bidvoiav, 
 which are examined in ch. x] . 
 
 3] There must be something wrong here. The translation 
 assumes the true reading to be, Oii yap el tovto di»ay/tr; to8' 
 ftvai, TOVTO 8' icrrl Xevnov, avdynr) irav kevKov rob' elvai. But if 
 this is Aristotle's meaning it is odd that the important word 
 Trav should have slipped out both of this and the following ex- 
 ample. The fallacy in these two cases may be described as the 
 equation of particular and universal. But this description will 
 not apply to the examples subsequently given. 
 
 4] The same instance of an accidental conclusion is given in 
 the Analytica Posteriora, 1.4: KadoKov be \ey<o b hv koto vavTos 
 
 T€ virApxri Kol Kaff avro to Ka96\ov be vTtdpxel tots oTav etil 
 
 roC TvxdvTos Koi ■npdtTov beiKvmfrai. OXov, to bvo opdas e)(eiv oiTe 
 Tip (rj(r)p.aTl eort KaOoKov Kofrot lori Seifat Kara arx-qixaros otl bvo 
 opdas ^xei, dW' oh tov tv)(6i)tos (r)(Tjfxoros, ovb^ XP'J'"'" ''¥ ''""X^vn 
 (7xi7/iaTi 6 beiKviJS, to yap Terpiyoivov rrxwa p^ev, ovk e^ei bi bio 
 opdais ta-as' to t laodKfkls ^xei p^^v to tv^ov bvo opdais ta-as, dA.V 
 ov vp&Tov, aWa to TpCyavov updrepov. *0 toIvvv to tv)(ov -npmov 
 beUvvTai bvo opOas exeiv 7\ cniovv &K\o, tovt(o xmApx^i Kadokov, /cat 
 jj aTT6bei$is KaO' avTo tovtov ecru, t&v 8' aWav TpoTtov Tiva ov Kofl' 
 avro' ovbe tov lo-otrKcXoCs ovk Ioti xadokov dA\ Iwi itXeov. 'A 
 commensurate proposition (a proposition whose subject and pre- 
 dicate are distributed and coextensive) is universal and essential. 
 .... Its subject is universal and the highest genus which can 
 be proved to universally possess the predicate. Kgure is not 
 commensurate to the predicate, containing angles equal to two 
 right angles, for some figures possess it but not all; nor can any 
 figure indiflferently, the tetragon, for example, be employed in 
 the proof. Isosceles possesses it universally, but is not the 
 highest genus which possesses it; for triangle is higher. Only 
 the universal and highest subject is commensurate, and only 
 such is essential : the others, including isosceles, are in a sense 
 accidental.' The expression, 6 beiKviis, seems to shew that Ari- 
 stotle is referring to some sophistical demonstration that had 
 been actually propounded. 
 
 5] The frivolous examples of confutation per aceidens hitherto 
 
Chap. VL NOTES. 113 
 
 given seem far too flimsy meshes to embarrass the man of 
 science, and it is here implied that, like othit fallacies, they can 
 only be valid when the premisses are false. But elsewhere we 
 are told that it is often very difiieult to discriminate between 
 accidental or illegitimate and essential or legitimate demonstra- 
 tion. The geometer, to avoid confutation by accidental syllo- 
 gism, is recommended to decline arguing except before a geome- 
 trical tribunal. Ei 8e 6ta\c'ferat yeaixfTpji fi ytafj.iTprq's, ovTias 
 ^avfpbv OTi Koi KaK&s, eav fK Tovrav rt beiKvvrj, et be p.-q, ov Ka\&s. 
 AfjXov 8' OTi ov8' iKtyxfi y€<ii>ij.4Tpr)V d\A' ^ Kara avfi^e^rjKOS. "Ho-t 
 ovK &v etjj fv dyea)/xeTf»j7-ois (Kpirais) Tiepl yeaj/xerptas biaXtKriov, 
 Xrjcrei yap 6 <j)av\(os biakeyojxfvos. Analytica Posteriora, I. I a. 
 ' In controversy with a geometer only conclusions from geome- 
 trical (essential) premisses are legitimate ; others, if they refute 
 him, only refute him accidentally, and not as a geometrician. 
 Therefore a geometrical controversy should be conducted before 
 a tribunal of geometers ; for, otherwise, ungeometrieal argu- 
 ments will pass without detection.^ As science advances it is 
 continually making the discovery that its earliest theorems com- 
 bined terms whose connexion was merely accidental. Aet 8e ixr) 
 Xavdaveiv, on iroWaKis a-vfifiaCvet biapxipTavnv, koX prj virApxeiv to 
 biiKVVfievov TTp&Tov KuOoXov, fj boKei beUwa-Oab koBoKov vp&Tov. . . . 
 Ae'ycB 6e tovtov ^ tovto anobei^tv, orav ^ irpdrov Kadokov. Ei ovv 
 rts bel^iiev on ai opdal ov avp.Ttl'nTovcn, bo^uev hv tovtov flvai tj 
 aTTo'Seifts Kvplms bia to iitl irair&v elvM t&v 6p6&v, ovk eoTi be' etirep 
 p,ri OTi 6)81 ta-ai yiveTai tovto, dA\' fi oTiaxrovv icrat. Kal et Tplytavov 
 p.r} ^v aWo rj ia-o(rKfkis, ^ to-ocrKeXes &v iboKft VTtapxuv. Kal ro 
 avoKoyov on IvaWa^, fj api.6p.ol koi § ypap.ij.al Kal fj aTspea Kal y 
 Xpovoi, &(nr€p ibeUvvTO tiotc x"P'S> ivbexop^^vov ye Kara i:ivT<ov pia 
 azobei^ei betxOrjvai. 'AAXd 8td to pr) thai oivopacrpevov tl irdira 
 TavTa Iv, api.6p.ol pi^kTj xpo*"" oTiptA, koI tibu bi,a<j>ipeiv oKki^kav, 
 X<»p« kkap^&viTo. Nw 8^ Ka66\ov beUvvTac ov yap § ypapp,al ri 
 if &pidpol virrjpxev, aKk' fj Tobl h KaOokov vnoTidevTai. VTrapxetv. Ata 
 TOVTO ovb'' av rts bd^y Kaff emaTov to TpCyutvov uTtobeiiei ^ piq ^ 
 eT^po on bijo opdas ex«' ^laiTTov, to laoTskevpov x^jp's koL to aKakr\- 
 vov Kal TO la-oo-Kekh, oiiwo) oT8e to Tpiyaivov on bvo 6p6als Xaov d 
 prj Tov tro^idTiKov Tpoirov, ovb^ Ka66kov rpiymvov, ovb' d p.r)biv iffTi 
 Tsaph Tama Tpiyodi/ov hepov ov yap § rpCycovov otbev, ovbi ■nav rpt- 
 yccvov dAA.' rj Kar api6p.6v Kar €i8os 8' ov tiav, k<u d p.7]biv iuTiv o 
 
 I 
 
114 NOTES. Chap. VI. 
 
 ovK olbe. Anal. Post. i. ^, 'It often happens that a conclusion 
 is not primary and commensurate, when it seems to be. . . . If 
 not primary and commensurate, the demonstration is not essen- 
 tial. Perpendiculars to the same line are parallel; but this is 
 not an essential proposition; for not only perpendiculars, but 
 all lines that meet another at equal angles, are parallel. Were 
 the isosceles the only known triangle, the property of con- 
 taining angles equal to two right angles would seem essen- 
 tially connected with isoscelism. The permutation of propor- 
 tionals, numbers, lines, solids, times, is not essentially connected 
 with number, time, dimension, but can be demonstrated at once 
 of the commensurate genus. It was formerly proved in detail. 
 They differ in species, and there was no name for their genus. 
 When you prove in detail of each species of triangle, equilateral, 
 scalene, isosceles, the equality of their interior angles to two 
 right angles, you may exhaust the possible cases but your pre- 
 dicate is not essential and commensurate, and you have only a 
 sophistical science. Your universal is numerical but not essen- 
 tial.' Conclusions from accidental premisses are not only 
 plausible but irresistible. Kairoi a.Trop'qcreiev &v tis "icrais, tiVos 
 iV€Ka ravra (to, avfx^i^rfKOTa ftq KaO^ avrA) Sei iptarav Tiepl Toiruiv, 
 (I ixT) AvdyKT] 70 (TD/Lnrepa(7jLta etvai. Ovbiv yap biaipfpei et tis ipo- 
 fjievos TO, tvxovTa ftra fiireter to <Tv}i,Tsipa(Tixa. Aei 6' kptoTOV o«x 
 a)S avayKoiov ttvai hih, to. ripaiTrnUva, dW' Sti \eyeiv avAyicri tu 
 eKeiva \eyovTi,, koI aKrjO&s Xeyeiv eav akrjd&s fj virdpxovTa. Analy- 
 tica Posteriora, i. 6. 'It may be asked of what use are acci- 
 dental premisses in dialectic, if they do not necessitate the 
 conclusion. Do we not first make some irrelevant remarks, and 
 then assert the conclusion, when we argue from contingent pre- 
 misses ? To which we answer that they are not propounded as 
 grounds of a categorically necessary conclusion; but because, 
 if they are conceded, by a hypothetical necessity the conclu- 
 sion is conceded ; and if they are true, by a hypothetical neces- 
 sity the conclusion is true.' Indeed all dialectic, as opposed 
 to science, consists of accidental ratiocination. '' Avntrrps^ei 8e 
 jmWov rh iv rois fiaBrJixaffiv, Srt ovbev 0T;fx/3e^?)KGS A.ajUjSavovo-ti' 
 (dWa Koi TovTio &i,a(j)fpov(n t&p kv rois 5ta\oyois) d\X opiffftovi, 
 Analytica Posteriora, i. la. ' The convertibility of conse- 
 quent and antecedent is more common in science than m 
 
Chap. VI. NOTES. 115 
 
 dialectic ; for dialectic employs accidental premisses, science 
 only definitions.' • 
 
 These conflicting views of accidental ratiocination may be 
 reconciled by dividing it into two classes : — 
 
 I. Reasonings that are inconclusive, i. e. dialectically unsound 
 and fallacious : 
 
 a. Reasonings that are conclusive, i. e. dialectically sound, 
 but, as not based on appropriate principles nor satisfy- 
 ing the other conditions of science, unscientific. 
 
 If we refer to the instances quoted above, a proof that all 
 figures contain angles equal to two right angles must be invalid 
 and undialectical, and belong to the first class; but a proof 
 that every isosceles contains them would be logically valid and 
 dialectical but unscientific, and belong to the second class. We 
 may observe that in the passage quoted above from An. Post. 
 I. 4, Aristotle only calls the latter conclusions in some sense 
 [rpoTtov TivS.) accidental. 
 
 6] This is unintelligible, and the text probably corrupt. 
 
 7] Bekker reads, tw ravr etvai atria tov a-vfiPaiveiv. This 
 looks like the vestige of a paraphrase : bei yap TaUr elvai atria 
 TOV (Tv)i,^aiv€iv TO (Tvii/nipa(Tiia. 
 
 8] The Hermeneutica, ch. ii, refers to this passage by the 
 words (V rots to-eikoI^. 
 
 9] It is clear that the words ovv irapa Trjv Xe^w should be 
 cancelled, unless for Xe^iv we read ?Aey£ti>. The slightest con- 
 sideration will suffice to shew that the two classes of fallacy, in 
 dictione and extra dictionem, do not correspond to sins against 
 the two elements of confutation, contradiction and proof. Of 
 the class in dictione, reasonings involving homonymia and am- 
 phibolia may, indeed, be conclusive when the ambiguity lies in 
 the extremes, but must be inconclusive when it lies in the 
 middle term. Of the class extra dictionem, the fallacies non 
 causa pro causa and ignoratio elenchi fail rather in contradiction 
 than in proof. Aristotle has elsewhere spoken correctly. In 
 the beginning of this chapter he implies (el /^eAXet eXeyxps rj itv\- 
 \oyi(rp.bs eaea-dai) that some of the fallacies in dictione are devoid 
 of proof as well as of confutation (contradiction). In ch. xix. 
 he says that homonymia and amphibolia may afiect either the 
 premisses or the conclusion, i. e. either the proof or the contra- 
 
 I a 
 
116 NOTES. Chap. VI. 
 
 diction. And in ch. x. he gives an instance of homonymia 
 (epic poems are a plane figure for they are a circle) affecting the 
 middle term, that is^ the proof: and observes that figura dicti- 
 onis may be treated as faulty either in the proof or in the' con- 
 tradiction. In ch. XXV. he seems to say that secundum quid 
 only fails in the contradiction, but it is clear that it may fail 
 either in the contradiction or in the sequence. 
 
 We may observe that we only give a semblance of unity to 
 the theory of fallacies by lumping them all together under the 
 definition of confutation, for the elements of that definition 
 are obtained by no systematic subdivision, and form, as far as 
 appears, a purely arbitrary and incoherent agglomeration. 
 
 CHAPTER VII. 
 
 1] A man might misplace his accents and yet be understood 
 in Greek society, unless the misplacement produced ambiguity. 
 
 2] 'Eir^oraTai. This must be wrong. We should read woiei, 
 or ireWei, or ^Tticnra, or emo-Trarai, or something equivalent. In 
 support of the last conjecture compare, ^Ap" ovv avro yiyvda-Koiv 
 avix^Tis, 7] ere otov pv)xrj tis virb tov koyov crvviiOurixivov avviiriima- 
 craro irpoi to za)(y <TVix(f>TJ(Tai ; Sophistes, 46. ' Have you any 
 good reason for your assent, or has the current of the language 
 to which you are accustomed hurried you along into an ill- 
 considered admission ?' Aristotle is thinking of realism or the 
 theory of ideas, which he says, ch. xxii, is founded on this 
 fallacy. 
 
 3] Reasoning to a certain extent is possible, as we see in 
 brutes, without words. But the development of language must 
 have been accompanied by a great increase of reasoning power. 
 Thenceforth in all reasoning there are two parallel trains, the 
 train of images and the train of words. When the train of 
 words precedes it awakes the train of images, if the words are 
 imitative, by the associative law of similarity. If the sounds 
 are not imitative, but interjectional, that is, produced according 
 to some physiological law by the action of the organs of sensa- 
 tion on the organs of expression, they afterwards suggest the 
 sensations that produced them by the associative law of eon- 
 
Chap.VII. notes. 117 
 
 tiguity in place and time. But in rapid thought the images 
 are very imperfectly excited. The mind^ emboldened by habit, 
 ventures to trust herself to the train of words through which 
 she can pass with great celerity without stopping to realize 
 them by images which would encumber her and clog her motion. 
 Rapid and powerful reasoningj then, takes place chiefly by the 
 verbal train. Reasoning without words is more likely to occur 
 in meditation than in conversation. See this subject discussed 
 by Mill, Examination of Sir W. Hamilton's PJdlosophy, ch. 17. 
 
 4] This sentence shews the afiinity, in Aristotle's mind, be- 
 tween the fallacies ignoratio elenchi and secundum quid (see 
 note 3 to ch. viii). In this treatise (see ch. v, vi, vii) e\- 
 Aet\/fts is always used to denote ignoratio elenchi. In the 
 Rhetoric, where the fallacies are enumerated, ignoratio elenchi 
 is not mentioned and eXAeii/rts designates the fallacy secundum 
 quid. 'AWos {totios) irapa ttjv fk\ei\jnv rod -nore nal ir&s' olov on 
 bLKaC(os 'Ake^avbpos el\.afie ttjv 'EXfvrjv, aipecris yap avrfj iboOri Trapa 
 Tov TTarpos. Ov yap ael tarais aWa to up&Tov nal yap 6 ■naT7]p 
 fxexpi ToijTov Kvpios. *H e? ns (pairj to tvttthv tovs e\iv0€povs 
 vfipiv elvaf ov yap ttAvtcds, dA.A' orav apx[l X^'^P^" &blKaiv. 
 Rhetoric, 2,. 24. ' Another class of fallacies depends on the 
 omission of limitations in time or manner : as the argument 
 that Helen had a right to elope with Paris because her father 
 granted her the option of her husband. But the option granted 
 was not perpetual but one that determined with her first choice, 
 for this was all her father had the power to grant. So the 
 statement, that striking a freeman is an assault, requires limita- 
 tion : for it is only an assault in him who strikes first.' The 
 moderns have created a distinction by confining ignoratio elenchi 
 to valid arguments with irrelevant conclusions, i. e. by confining 
 the omitted limitations to such as afieet the contradiction. 
 
 5] This chapter explains why the solution (\vcns) of an 
 inconclusive or illogical confutation is called Statpeerts (distinc- 
 tion). A conclusive or lo^cal confutation can only be solved by 
 shewing that one of the premisses is false {avaipea-isj . If this 
 is shewn by certain simple topics, it is called enstasis; if by 
 other topics, antisyllogism. Solution, then, is either enstasis, 
 which includes biaCpea-is and one branch of avaipecns, or anti- 
 syllogism, which is the other branch of avaCpea-is. Antisyllo- 
 
118 NOTES. Chap. VII. 
 
 gism, being a species of solution, is the disproof of one of the 
 opponent's premisses, not of his conclusion j for it would be an 
 abuse of language to call the disproof of a conclusion a solution 
 of the argument supporting that conclusion. 
 
 CHAPTER VIII. 
 
 1] Eristic proof is either inconclusive or contains a false pre- 
 miss. But it is not every false premiss that makes a proof 
 eristic. If the premiss, though unscientific, is a special proposi- 
 tion, referring exclusively to a particular subject-matter, the 
 proof is dialectic. Even the general propositions that charac- 
 terize dialectic, the topical maxims, must be accepted with many 
 limitations and exceptions, for dolus latet in generalibus ; and if 
 they are applied without these limitations and exceptions they 
 are open to enstasis, and the conclusion is false, but stiU, it 
 appears, the proof is regarded as dialectic. The basis of genuine 
 probability in these propositions saves their inaccurate applica- 
 tion from the stigma of sophistry. The false maxims that 
 constitute a proof eristic, that is, radically bad or vicious in 
 principle, are thirteen false propositions corresponding to the 
 thirteen fallacies. Ov yap irav to cj^aivonevov evbo^ov km, Io-tiv 
 fvbo^ov. Ovdiv yap t&v Kiyoixivtov ^vho^av eTrnroXaiov iyii iravre- 
 \&s TTjv (pavracriav, KaOAirep Ttepl ras r&v ipurnK&v \6ya>v apya^ 
 (rvp,j34pr]Kev ex^iv, IJapaxprJua yap Kal &)s etti to ttoXt) tois koi 
 juiKpa avvopav bwafievois (cardtSrjXos Iv avrois fj tov -^fybovs scttI 
 <pv(ns. Topica, i. i. 'Not every semblance of truth is probabi- 
 lity. Probability, as we use the term, has more than an abso- 
 lutely superficial semblance of truth, such as may be found in 
 the principles of eristic proof, whose falsehood a moment's con- 
 sideration discloses to all but the very dullest.' Of these 
 sophistic principles five might be identified with perversions of 
 dialectic maxims. The principles justifying the fallacies of 
 accidens, consequens, secundum quid, non causa pro causa, and 
 figura dictionis may be supposed to belong to the loci of subject 
 and accident, antecedent and consequent, whole and part, cause 
 and eifect, and conjugates or paronyms. But it must be con- 
 fessed, that it appears to be juster, instead of confining the term 
 
Chap. VIII. NOTES. 119 
 
 gophism to the application of the thirteen imaginary principles, 
 to extend it, in pirastic at least, by the criterion, ov Troiei 8^\oi» 
 «J ayvofi, to the misapplication of any dialectic maxim. For it 
 is evident that the false conclusion in which the respondent 
 might be landed by such a false premiss would not convict him 
 of ignorance in any special branch of knowledge which he pro- 
 fessed. Even if the false premiss is not a dialectic maxim, but 
 a specific proposition, not essentially (xafl' avTo) connected with 
 the subject of the problem, the pirastic confutation is sophistic. 
 And in spite of the expressions in this chapter, it is difficult to 
 believe that this was not Aristotle's view. 
 
 2] An argument is usually called appropriate (oJiceios tov 
 ■npayixaros, Kara to Ttpayfia) when it is scientific. Oirat yap iaov- 
 TUL Kol at ap^al olKeiai tov hiiKWfiivov. SuAXoytcrfxos p.\v yap 
 eorai koX &v€v tovtwv, dwo'Setfts 6' o^k earai, ov yap T!oirjcreL eiri- 
 (TTT^p.r\v. Analytica Posteriora, i . a. ' Then the premisses will be 
 appropriate to the conclusion. Otherwise the proof would not 
 be demonstrative or scientific' Arikov 8' ck ToiTUiv Ka\ on wq- 
 Oiis ot XaiJL^dvfiv oioiievoi KaX&s rcis apx6.s, iav ei/Sofos fi fj TipoTacru 
 Kal akrjdris. Oil yap to ev8o§ov ?; p.ri apx^ eaTiv, a\Ka to Ttp&Tov 
 Toii yevovs irepl 8 beUwTai, Kal TaKriOes ov Tiav oiKfiov. An. Post. 
 1.6. ' It is absurd to suppose that our assumptions are scien- 
 tific principles if they are only probable and true. Principles 
 are not probabilities but primary propositions appropriate to a 
 given sphere, and propositions may be true but inappropriate.' 
 XaXeTihv 8' eort to yv&vai el olhev rj ixyj. XaXenhv yap to yv&vai 
 el iK T&v fnAoTov {olKeCwv) apx&v ta-ptev rj p-r), oisep ((ttX to elhevai. 
 Olop^da 6', &v ix^iapLev e$ a\rt6ivS>v tlv&v (rv\koyi<Tp.ov Kal itpdtTatv, 
 eTiCa-Taa-Oai. T6 8' oiiK eaTiv, akka avyyevrj (ot/ceto) 8€i eiJ'at tow 
 ■irpdTois. An. Post. i. 9. 'It is hard to decide when our know- 
 ledge is science, for it is hard to decide whether the premisses 
 are appropriate, as they must be in science. We fancy when we 
 have a proof by trae and primordial premisses, that we have 
 science : not always, for they must also be homogeneous (appro- 
 priate) to the conclusion.' 
 
 Here, however, okeioi means, not scientific, but pirastic. The 
 premisses employed in pirastic are not in the highest sense 
 appropriate (tbia) to the subject, yet have a necessary connexion 
 with it {iTT6p.eva, see ch. xi) and so far may be called appro- 
 
120 NOTES. Chap. VIII. 
 
 priate. They are appropriate when compared with sophistic, 
 inappropriate when compared with scientific, proof. 
 
 3] Every inconclusive reasoning (TrapaXoytcryxds) from true 
 premisses may be converted into conclusive reasoning {<n\.\o- 
 yi(TiJL6<s) from false premisses. The fallacies become valid argu- 
 ments as far as the form is concerned if we substitute for the 
 true principles on whieh sound reasoning reposes false principles 
 to cover their faults and justify their sequence. It would re- 
 quire great art to put such propositions into a plausible form, 
 and seduce the respondent into the eoncessiop of them : but we 
 can conceive it accomplished. If such principles were formu- 
 lated, they would correspond to the axioms or Kotval apxai of 
 science, and the topical maxims or Koival apxal of dialectic, and 
 would themselves constitute the koivoI apxaC of sophistic. As 
 false metaphysical principles and false linguistic theorems or 
 rules of interpretation, they would imply, in the person who 
 conceded them, an ignorance of logic and metaphysic or lin- 
 guistic, but not of any other special science. For instance, a 
 geometer who incautiously admitted them, and was consequently 
 confuted on a geometrical question, might be proved to be an 
 unpractised logician, but would not be proved to be an impostor 
 in his pretensions to geometry. Arguments, therefore, derived 
 from such pseudo-loci are inadmissible in pirastic. 
 
 4] This recapitulation omits ignoratio elenchi, which indeed 
 may well be omitted, for it cannot be distinguished, as Aristotle 
 defines it, from secundum quid. Regarding it as the fallacy of 
 irrelevant conclusions, we might suppose we found a trace of a 
 reference to it in the word ItvTi^ainv ; but this term occurs in 
 the examination of secundum quid, ch. xxv. Some words, how- 
 ever, may have slipped out of the text in this recapitulation, 
 which, as it stands, is hardly the language of articulately speak- 
 ing men. It is not clear why, after his three previous enume- 
 rations of the fallacies, Aristotle recapitulates at all. Did he 
 intend to formulate the pseudo-axioms by which the sophisms 
 may be rehabilitated, and recite the list as a framework in which 
 the formulas might be inserted, but afterwards find his design 
 more troublesome of execution than he had anticipated, and 
 leave it unexecuted ? 
 
 5] For ■napaXoyicrixol read <To<ftoTtKot crvkKoyi,(Tjxoi, or rather 
 
CuAP. IX. NOTES. 121 
 
 ■^ivheis a-vWoyia-jjuyt, for a proof may be sophistic whose pre- 
 misses are true but accidental or inq|)propriate. If accidental 
 proofs are to be included under the thirteen fallacious loci, the 
 locus of aeeidens must embrace not only the paralogism of acci- 
 dens, but also all syllogisms professing to be scientific whose 
 terms are not coextensive j in other words, whose premisses are 
 not commensurate (koOoKov), i. e. universal and convertible ; in 
 other words, all syllogisms that fall short of demonstration {ano- 
 
 6] We should read or understand, to fxavov ro'Be n (rqixaiveiv to, 
 Karriyopovfieva, or to fxovov ro'Se arjixaCveiv to, ovTas KaTr]yopoviJ,eva. 
 7] There are, then, three gradations : — 
 
 (i) Valid proof (o-uAXoyta-jnos, or dirXSs a-vWoyitrixos). 
 (a) Proof by the false principles above described. This is 
 conclusive reasoning and real reasoning, but, as decep- 
 tive, it requires some qualification, and we call it 
 relative or sophistic proof (ixpos tovtov, or a-ocj)i<TriKos 
 avXXoyurixos) . 
 (3) Inconclusive reasoning, that is, no proof, but the mere 
 semblance of proof (<paiv6ix€vos aukKoyiiriios, or Trapa- 
 Aoyt(r//.os). 
 
 CHAPTER IX. 
 
 1] I. e. pseudographemas. 
 
 2] Euclid is said to have written a treatise on geometrical 
 fallacies. To expose false argumentation, says Plato investi- 
 gating didactic method in the Phasdrus, we require a knowledge 
 of the truth, and as error depends on the likeness and conse- 
 quent confusion of different terms, we must be able to~ distin- 
 guish the terms in question by definition and division. Aei 6,pa 
 Tov ii.i\\ovTa aTiarritreLV jxev aKXov, avTov he fn} ImaTfjinadai., Tr\v 
 ofioioTTfa T&v SvTotv Kal avojJ,ot.6Ti]Ta aKpi^&s hi.eibivai. — 'Av&yKT) 
 fjiev ovv. — -'H ovv otos re eorai, aKrideiav ayvo&v e/cdoroi;, Ty\v tov 
 iyvoovixivov op^oLOTryra p,i.Kp6,v re koI jxiy&kr\v ev tois aWois bia- 
 yiyvda-Ktiv; — ''AhvvaTOV. — Ovkovv toIs irapa to, ovra bol6,Cov(TL Kal 
 &'jraTO>p.evoLS hrjKov a)s fb Trddos toSto 81' ofioioTriTUiv Tiv&i> elmppvr), 
 — TLyviTai yovv ovrtos. — 'Eariv ovv oirus TiyviKOS Icrrat fiera/3t/3a- 
 iiiv Kara (rp,LKpov 8ia t&v op-oiOTriTWV, ano tov ovros exacrrore ewt 
 
122 NOTES. Chap. IX. 
 
 Tovvavrlov aitayatv, ^ avrhs tovto bia^evyew, 6 firj iyvapiKm & tanv 
 'iKacTTov r&v ovTotv ; — Ov firi wore. — Aoymv &pa rexyv^i ^ kraipf, 6 
 Trjv akrjOfLav im] flbiis, bo^as be Tfdr]pevK<is, yeXoidv nvA, m toiKe, 
 KoX &Texvov wape'ferai. — KivbvvevH. Phsedrus, 98. 'The power of 
 deceiving and avoiding deception requires an exact knowledge of 
 likenesses and unlikenesses ; and unless a man knows the true 
 objectj he cannot discriminate the degrees of likeness to it in 
 other objects. As, then, false belief and error arise from like- 
 ness, the art of leading away through gradations of likeness 
 from the true to the false, and of avoiding being thus misled, is 
 impossible without a knowledge of realities ; and an argnmen-- 
 tative art, armed with opinions instead of knowledge, is an 
 absurdity and not truly an art.^ The knowledge that Plato 
 requires for didactic may be divided into two portions, science 
 and logic j corresponding to the two portions into which law is 
 divided by the jurist, the substantive code and the code of pro- 
 cedure. Part will consist of specific doctrines {Ibiai. apxaC), and 
 belongs to the man of science, Euclid or Archimedes : part of 
 generic theorems, rather method than doctrine (koivoX dpx"')> 
 and belongs to the dialectician. Accordingly Aristotle bases 
 dialectic on the definition of genuine confutation (a\r)6ris ekey- 
 Xos), and makes solution proceed by division and discrimination 
 (6iotpe(7ts). But, in addition to this, didactic requires similar 
 definitions and divisions of the Ibiai. apxai. See Appendix E on 
 the limits of pirastic. 
 
 3] The common sources of probable proof are enumerated in 
 the Topica. 
 
 4] Does e)(oij.ev bi nap' oirocra yivovrai mean that the enstasis 
 is derived from the same topics as the proof; or does it mean 
 that in some lost chapters the varieties of enstasis had been 
 examined? A phrase of the Rhetoric seems to establish the 
 latter view : Ai 8' ei'o-Tcto-eis (jyepovrai, KaOdirep iv rois Towt/coty, 
 Terpax&s. Rhet. 2. 25. 
 
 5] Kai Tovs (jjaivoixevovs [eXeyxofs] is connected, after a long 
 parenthesis, with tov 6' ex t&v koiv5>v koX vno firjbepilav Ttxvqv 
 [ikeyxov] r&v biakeKTiK&p [fcrrl Oeapeiv]. 
 
Chap. X. NOTES. 123 
 
 CHAPTER X. 
 
 1] Of the name of the theorist now criticised, and the precise 
 nature of his theory, we have no information ; and without this 
 information it is diflScult to decide whether Aristotle^s argu- 
 ments are conclusive, and what is their precise drift. If we may 
 trust a partly unintelligible fragment of Eudemus quoted by 
 Simplicius, the theorist criticised in this chapter is no other 
 than Plato himself : "Eo-rt Se, is lotKe, to bioplCeiv ^Kaa-rov TTocrax&s 
 \4yeTai fi^ya Trpos aki^deiav. YIXAtohv re yap eicrayay^v to bicrabv 
 TtoWas aTTopCas ehvae, ■npay\xaTu>v S>v vvv ol (TO(f>L(rTai KaTa^eiyovaiv 
 mairep em ra ei'Sij, /cat irpos tovtois Tovvoixa t&v \6yaiv a(^(ltpiare. 
 Simplicius on Phys. Ausc. i. 3. 'To distinguish the various 
 meanings of equivocal terms is a great step in speculation. For 
 Plato solved many difficulties by introducing the doctrine of 
 various meanings and banished words from proof [distin- 
 guished reasoning addressed to the word from reasoning addressed 
 to the thought ?].^ But it would be rash to place much reliance 
 on a corrupt fragment, and it would be strange if Aristotle spoke 
 of Plato as ' certain persons.' The theorist seems to have hit, 
 somewhat vaguely, upon the distinction between word-thinking 
 and object-thinking, and to have held that the source of all 
 error is word-thinking. 
 The substance of Aristotle's criticism seems to be this : — 
 
 (i) The trains of word- thinking and object-thinking are parallel : 
 the same ratiocination may belong to both trains : and it 
 is impossible to say when it belongs to each. But if the 
 trains constituted two classes of reasoning, they ought 
 to be contradistinguished and mutually exclusive. 
 
 (2) Thought requires some further limitation to express object- 
 
 thinking. All word-thinking is thinking. The expres- 
 sion, addressed to the thought, therefore, is insufficient 
 to exclude word-thinking. 
 
 (3) The fact of being addressed to the thought is only an ex- 
 
 ternal relation of an argument, its relation to the respon- 
 dent. But the relations of a thing may vary by the change 
 of its correlatives, while the thing itself remains unchanged. 
 They are its most extrinsic and accidental attributes, and 
 cannot form the principle of its subdivision. 
 
124 NOTES. Chap. X. 
 
 But, it may be answered, are there not some arguments whose 
 essential nature is such that they cannot be represented by a 
 train of object-thought ? Yes : and these are recognized under 
 the head of fallacies in diction. But there is another class of 
 reasonings, independent of diction, and therefore belonging pos- 
 sibly to the train of object-thinking, which are yet fallacious. 
 
 2] So read for oloixtvos kpatTwrOai e<f> <p. 
 
 3] After a-rjiiaCveLV insert to kv a-rjixaivov. 
 
 4] The amphibolous reasoning about speech of the speechless 
 (ch. iv) is conclusive with an ambiguous minor term, that is, 
 the conclusion does not contradict the thesis. 
 
 The homonymous argument about Homer has an ambiguous 
 middle, and therefore is inconclusive. 
 
 In saying that the fallacy of the argument in figura dictionis 
 lies both in the sequence and in the contradiction, Aristotle 
 seems to mean, that we have the option of treating the conclu- 
 sion as contradictory but not legitimate, or as legitimate but not 
 contradictory. Thus : Thesis : — It is impossible to give what 
 one has not got. Confutation : — It is possible to give but few, 
 having many : to give but few, having many, is to give as one 
 has not got (see ch. xxii) : therefore it is possible to give ag one 
 has not got. This conclusion is valid, but does not contradict 
 the thesis. . The conclusion. Therefore it is possible to give 
 wkat one has not got, contradicts the thesis but does not follow 
 from the premisses. 
 
 The defects of accidens and consequens (illicit process and 
 undistributed middle) and petitio prineipii lie in the sequence : 
 of ignoratio elenchi and non causa pro causa in the contra- 
 diction : of secundum quid and verbal fallacies, sometimes in 
 the contradiction, sometimes in the sequence. We may distin- 
 guish, then, between conclusive syllogism and conclusive con- 
 futation. For in the second of these classes the syllogism is 
 conclusive, the confutation inconclusive. 
 
 5] This is a resumption of the second of his former positions : 
 viz. that a reasoning with unambiguous terms is not addressed 
 to the thought if the respondent thinks them ambiguous. 
 
 6] This is a resumption of the first of his former positions : 
 viz. that a reasoning with ambiguous terms is addressed to the 
 thought if the respondent thinks them unambiguous. What 
 
Chap. X. NOTES. 125 
 
 Aristotle says amounts to this : Word-thinking is thinking ; and, 
 after one has given the respondent tke option of assenting or 
 dissenting or distinguishing, it cannot be pretended that one 
 has not come at his real belief or thought. 
 
 7] Read eira IpmrTjo-aVco ny, or, eira IpcoTTjeravroff. 
 
 8] This seems to imply that the theorist maintained all 
 object-thinking to be infallible, and all confutation confined to 
 the sphere of word-thinking, and more or less invalid. 
 
 9] Aristotle elsewhere has himself used the antithesis which 
 he now so severely criticizes. Xpjjo-i/ior 8e to fxev Trocrax&s Aeye- 
 Tot iT!i<TKi(f>dai Tipos TO yCvfcrOai. /car' avTO to Trpayna Koi fijj irpos 
 TO ovofia Tovs <Tv\\oyi(Tp,ovs. 'AbrjKov yap ovTOi ttoo-ox&s KiysTUL, 
 ivbi)(^eTai jii^ cttI toutov tov re cmoKpivoixevov Koi top kpatT&VTa 
 (pipuv T-qv bidvoiav. 'Ep,<j)avi.a'9evT0S 8e TTOcra)^&s Ae'yerai Koi firl 
 tI (pipwv Tidrjcri, ye\oios hv (fiaivoiTO 6 ipuiT&v, ei p,r] irpos tovto tov 
 Xoyov TTOioiTO. Xprja-iixov be /cat wpos to jjiij TiapaXoyia-dfjval koi 
 irpos TO TrapdKoyicraadai. . . . Tomo 8' ovk kin tiAdtoiv bvvarov, a\K 
 oTav § t&v iroWax&s \eyop,iv(av to, pi,ev a\ri6r] to, 8e \j/evbrj. Topica, 
 I. i8. 'The use to the respondent of knowing the different 
 significations of a name is to confine the reasoning to the real 
 object of thought and prevent it from merely bearing on the 
 words. For if the varieties of signification are not known, the 
 questioner and answerer may be thinking of different objects: 
 but when the respondent has pointed out the different significa- 
 tions and which he intends in his premiss or thesis, it would be 
 ridiculous in the questioner to direct his reasoning to a different 
 object. The use to the questioner is, if the answerer is ignorant 
 of the different significations, to construct a paralogism. . . .This 
 can only be done when a proposition is true in one sense and 
 false in another.' O^ yap Trpos tov I£co \6yov f/ dii-o'Setfts, dAAd 
 irpos TOV ev ttj -^vxn. ^w«^ °^S^ o-uWoyio-juo'y ael yap ecmv Irorjjyai 
 ■npos TOV efft) Aoyoi', dAAa irpos tov ea-u) Xoyov ovk del. Analytica 
 Posteriora, i. lo. 'Proof and demonstration hinge, not on the 
 expressed, but on the conceived premiss. The expressed pre- 
 miss is always open to enstasis, the conceived premiss not 
 always.' If the answerer can often oppose to the expressed 
 premiss, Ifo) Ao'yoy, of the questioner an enstasis which is un- 
 available against the intended premiss, fa-oa Xoyos; surely the 
 questioner also can often construct with the expressed concession 
 
126 NOTES. Chap. X. 
 
 of the answerer or direct against his expressed thesis^ Ifw Koyos, 
 a proof which is impossible with the intended concession or 
 unavailable against the intended thesis. 'On jiev ovv avo ttjs 
 avTrj's eial biavoias aiJ.(j)6Tepoi oi \6yoi, StjXov. Eort 6 ov\ 6 avrbs 
 TpoTTOs zpoi &TravTas rrjs ivreiu^eas' ot [xkv yap ireidovs biovrai, oi 
 8e fiCas. O<T0i piev yap Ik roO omopjjcrai viriKa^ov oiirajs, rairmv 
 evtaros rf ayvoia' oil yap Ttpos rov \6yov dAAft Ttpbs ttjv biavoiav ^ 
 awcij/rrjo-ts aiiT&v. "Otrot 6e Koyov X'^P'-^ \eyov<n, tovtodv 8' ekeyyos 
 Xaais Tov T (V rfj ^avf] koyov Koi tov ev tois 6v6p,acnv. Metaphy- 
 sica, 3. 5. ' The doctrines that the same thing can be and not 
 bcj and that all opinions are truCj are clearly the same in prin- 
 ciple : but all disputants are not to be encountered by the same 
 method, for some require persuasion, others violence. Where 
 the opinion is the result of honest doubts it is an error which 
 can easily be healed. For here we have to encounter not words 
 but convictions [or, if ^vAvTria-is is the act of the respondent. 
 For here the opposition is not addressed to our words but to our 
 meaning]. Where it is merely maintained from the love of dis- 
 putation, the only remedy is confutation of the expressed and 
 verbal thesis by the expressed and verbal concessions.'' Here 
 we have an admission from Aristotle that in certain controversies 
 his own arguments would be addressed not to the thought of 
 the respondent but to his words. He considers the axiom or 
 principle of contradiction a necessary proposition and one that is 
 necessarily believed. If, then, it is denied by a respondent and 
 we argue in its defence, we cannot address his thought, that is, 
 argue against his conviction, for he has no conviction to be argued 
 against. In the passage from the Metaphysic, Aristotle speaks 
 with confidence of confuting the contradictor of the axiom, though 
 he admits it would be difficult : but the passage from the Ana- 
 lytic, which refers to the same subject, implies that the verbal 
 triumph would remain with the respondent who denied the axiom. 
 
 The different expressions of Aristotle respecting the anti- 
 thesis, addressed to the word, addressed to the thought, seem, 
 however, to be reconcilable. He does not deny the existence of 
 the antithesis, but denies that it constitutes a differentia of 
 arguments [ovk ecm biacpopa j&v \6y<ov) of so intrinsic and essen- 
 tial a character as to be fit to form the basis of a classification. 
 
 10] rFoterv has MS. authority and seems more natural than 
 
Chap. XI. NOTES. 127 
 
 iradfiv, which is Bekker's reading. Whichever we read^ the sense 
 is the same. The following propositio^j is only true where hoth 
 the units and twos are taken collectively. If we take either dis- 
 tributively, we affirm that each unit or each two is equal to four. 
 
 11] In ch. XV. the questioner is recommended to distinguish 
 and divide and exclude from his propositions any objectionable 
 interpretation in order to anticipate objection and obtain without 
 trouble the necessary premisses. But of course he would only 
 do this for his own purposes, that is, with the premisses capable 
 of being honestly employed, not with the premisses charged with 
 the fallacy. In ch. xvii. Aristotle goes further, and admits that 
 a confutation, where the respondent is taken by surprise in con- 
 sequence of overlooking distinctions, is not genuine : and that, 
 at all events, if the respondent is limited to answering Yes or 
 No, the distinctions ought to be drawn by the questioner. Nvv be 
 bia TO fjifi KoX&i ipmrav tows irvvBavofiivovs avdyKr] -npoaaTioKplvicr- 
 dai TL Tov ipcardixevov, bwpdovvra TfjV ixoxOrjpiav Trjs irportio-eMS, f-rreC, 
 bifkofxivov ye iKav&s, rj vaC jj otj dvdyxrj kiyeiv tov anoKpivofxevov. 
 
 Didactic reasoning differs from pirastic because the didactic 
 reasoner is supposed to be in possession of the truth : it differs 
 from apodictic or scientifie reasoning because, apparently, there 
 is but one genuine scientific proof of each theorem, whereas 
 didactic reasoning must be accommodated to the capacity and 
 character of the learner. The true problem of the Phsedrus is 
 the investigation of didactic method ; which seems to prove that 
 this dialogue was not an early Platonic composition, but written 
 after Plato thought he had said enough on the nature of the 
 elenchus or negative dialectic. 
 
 CHAPTER XL 
 
 1] ^aiv6ii,evo$ -nepl &v is the same as (^aivo^ievos Kara to ■npayiJ.a 
 above, and ^aivoixevos ■nepl T&vbe below. In fact, Tiepl T&vbe has 
 probably slipped out before (paivojjLevos in the present passage. 
 A man may be confuted and yet not proved to be in the wrong 
 on the point in dispute. He may be right in his special facts, 
 which may alone be important, but appear to be confuted by 
 failing to detect some slight mis-statement of a metaphysical 
 premiss, which is ill-apprehended because it is abstract, and is 
 
128 NOTES. Chap. XI. 
 
 not really an element of the doctrine in question. This species 
 of sophistic proof was discussed in ch. viii. 
 
 2] SiiWoynrjuoi would be a better reading, for the proofs in 
 question are not paralogisms. IlapaKoyKTixoi. howeverj may stand, 
 for the proofs in question may be compared either with scien- 
 tific proof or with the pseudographema, and the pseudographema 
 is a paralogism (TrapaAoytortKos e^ itpiafxivov rivos yivovs apx&v 
 below). The second species of sophistic proof simulates scientific 
 proof as the first simulated pirastic. We have not yet had it 
 in this treatise (except in note 5 to ch. vi), but it is alluded to 
 in the Analytic : 'Eirla-raffOai be oloiiiff' emirrov anX&s, aWa pifi 
 Tov <TO(j)i(rTiKbv rpoTTOv TOP Kara (TVix^ePrjKos, orav Tr)V r ahiav old- 
 jxfBa yivcacTKeLv bC rjv to Tipaypid ecmv, oti kudvov alrCa eort, Koi prj 
 evbix.f(r6ai tovt aAXcoj Ixetv. An. Post. i. a. 'Science absolute, 
 as opposed to sophistic science or accidental proof, is the know- 
 ledge of the cause and necessity of a law.' Neither the cause 
 nor the necessity can be exposed by any but essential or commen- 
 surate premisses. Accidental premisses, then, will be sophistic. 
 'EweJ 8' ef avdyKrji ini-pyei Ttepl fKaa-rov yivos Sa-a Oku avTo, vTrapxn 
 Koi fj exooTov, (pavfpbv 5ri Tiepl t&v Kad' avTO. VTiap-j^ovrtav al Iwi- 
 (TTrjfioviKal cmobfi^eis Koi Ik t&v toio-utcov fl(rL Ta [xev yap (jvp-^i- 
 ^rjKOTa ovK avayKoia, &rrT ov/c avayKi) to (rujj.irepaa'ij.a eibivai bioTL 
 vTtdpxfi . . . TO 8e biOTi iTtltTTatrdai etxTi to bia toC alTiov iirlaracdai. 
 At' avTb &pa Set koc to p,i(Tov ru rpfru koj. to Ttp&TOV tu jueo-u 
 virApxeiv. An. Post. 1.5. ' Essential attributes furnish the 
 only necessary propositions and must form the premisses and 
 conclusions of scientific demonstration. Accidents are contin- 
 gent and cannot exhibit the reason or cause of a necessary law. 
 Both the major and minor premiss, then, must be essential.'' 
 Ata tovto ovb' &v rts SeifTj /cafl' ^kucttov to Tpiyutvov AiroBetfet tj 
 joitS r\ erepq 8ti bvo dpdas exei ^Kaarov, to icroTikevpov x<Bp'S fat to 
 ffKaX-qpfs KOI TO Z(ro(T(ceXe's, ovttu> otSe to Tptymvov oti b'do opBais, (I 
 jxri rhv (TocfuaTLKOV rpoTtov, ovbi KaSokov Tpiyaivov, ovb' tl fxr\6iv kern 
 Ttapa TavTa Tpiyavov ^T€pov. Ov yap fj rplyavov olbev. An. Post. 
 I. 5. 'If one were to prove in detail of each species of triangle, 
 equilateral, scalene, isosceles, the equality of their interior angles 
 to two right angles, he might exhaust the possible cases, but his 
 predicate would not be essential and commensurate, and he 
 would only have a sophistical science.' 
 
Chap. XL NOTES. 129 
 
 To complete the statement of Aristotle's view, it should be 
 added that essential propositions are* those whose predicate 
 cannot be defined without paming the subject, or whose subject 
 cannot be defined without naming the predicate. KaO' avra be 
 {\4y(i>) oaa vmpxeL re ev rm tL etTTiv, olov Tpiydva ypaixfxri koX 
 ypafxfxrf (TTiynr], r/ yap ovcria avr&v l/c Tovrtav eari, Koi ev 70) K6yio 
 Tm KiyovTi tI ecrriv evvTtAp\ei,' koI o(tols t&v ewnapxovTmv avroii 
 avTCL ev T(p Koyia evvna.p)(pv<Ti t5i tC eort brjXovvTf otov to evdv 
 VTtapxei ypap.p,rj koX to irepLtpepes, koX to -nepiTTOv kw. apriov api9p,S, 
 KM TO TTp&Tov KOI (Tvv&eTov KOl IcTOTTkevpop Kol Ircpo/irjKey KW. TTam 
 ToiiTots h'VTTap\ov<Tiv fv T<5 Koyu) t(^ tC eiTTi kiyovTi evda p,ev ypai^ixri 
 
 ivBa 8' a.pi6p.6i Ta apa \ey6p.eva ein tS>v awAdls e-nLa-TrjToiiv KaO' 
 
 avra ovtios, as evvirdp^^eiv tols KaT-qyopovixevois r] evvnApxecrBai, bC 
 ami. Te lort koX If av6.yKi]s- An. Post. T. 4. 'An attribute is 
 essential that enters into the conception of the subject, as line 
 enters into the conception of triangle and point of line. It helps 
 to compose the essence of the subject, and is found in its defi- 
 nition. Or, it is an attribute in whose definition the subject is 
 contained. Straight and curved are attributes of line ; and even 
 and odd, prime and compound, square and scalene, of number ; 
 and we cannot define them without mentioning the subjects they 
 
 attach to, line and number In the essential premisses, then, 
 
 of absolute science, where the subject is either contained in the 
 definition of the predicate, or contains the- predicate in its own 
 definition, the essence of the terms is the cause of their con- 
 junction and the conjunction is necessary.' A modern logician 
 might admit that, as a condition of science, we must have pro- 
 positions of causation, and that in causal propositions the ante- 
 cedent and consequent terms must bear to one another a certain 
 definite relation ; but he would insist that the test of this rela- 
 tion was not definition, but the inductive methods of agreement 
 and difierence. To reconcile these doctrines it would be neces- 
 sary to assert that these methods are methods of definition. But 
 even then a difierence would remain. For the modern logician 
 would be satisfied by an objective relation, discovered by expe- 
 rience : while Aristotle seems further to require a subjective rela- 
 tion, viz. such that it should be impossible to conceive one of 
 the terms without at the same time conceiving the other. 
 
 3] I do not know what distinction is intended between ^ev- 
 
 e: 
 
130 NOTES. Chap. XL 
 
 boyp6,((>r)na and \}/evboyp6.(f)r]iJ,a itepl &\r)6is, unless it is that of art 
 and science. It is evident that the quadrature of the circle by 
 lunules was not the method of Hippocrates, as is generally 
 supposed. His method was what Aristotle elsewhere calls the 
 method of segments (see Appendix F). The problem of 
 squaring the circle, i. e. of finding a square whose area shall 
 equal that of a given circle, long occupied the scientific world; 
 and, like the problem of perpetual motion, was a favourite arena 
 of the unscientific long after the scientific had pronounced it 
 insoluble. Modern mathematicians are agreed that it cannot 
 be solved by arithmetic or geometry, the only methods of the 
 ancients, and requires the method of infinitesimals. See an 
 article on the quadrature of the circle, by De Morgan, in the 
 National Encyclopedia. Aristotle seems to have suspected it 
 was insoluble from his expression, Et koI TtrpayavC^eTal 6 kvkXos'. 
 in the Categories he asserts that it had not been solved in his 
 day : 'Ert to fiev eTriarrjTov avaipediv crwavaipei ttjv eiriar^jitjji', ^ 
 
 be eincrT'^ixri to ^irtorjjror ov crvvavaipei olov Koi 6 tov kj^kAou 
 
 TeTpaya>vi(Tij,6i el ye i(TTiv, (TtKTTrjfiri fiiv avrov ovk Icruv ovhitco, 
 aMs 6^ fTiKTTTjTov luTiv. Cat. 7. 'Without a knowable there 
 can be no knowledge, but without knowledge there may be a 
 knowable : if, for instance, the quadrature of the circle is pos- 
 sible, it is knowable, though at present it is not known.' 
 
 4] Kara to Ttpayp.a here means morak. than it did in the 
 beginning of the chapter, where its force was limited by the 
 words ret koivL There it meant, necessarily connected with a 
 subject, though not coextensive with it. Here it is equivalent 
 to Kara rqv olKilav jxiOobov, and means coextensive, or commen- 
 surate, with a given sphere. 
 
 5] So read, as the sense requires, for tov yf(afj.eTpr)v. 
 
 6] Here p.iv is followed by no corresponding clause, and the 
 text is doubtless corrupt. We might add, after bijKoi', aKKa Kh 
 ■nepl Th yecoixeTpiKo. etr], or we might read, 6 6' v-nb Tfjv haheKTinTiv. 
 Ufpl (lAvToi TaWa ort ipia-TtKos Icrn, brjKov, or something equivalent. 
 In the first case rSWa would mean to, Kotvd, in the second case it 
 would mean to, tbia, or, rather, to yta/jifTpiKd. In any case the 
 drift is certain, viz. that the same problem, e. g. the quadrature 
 of the circle, may be handled either in a sophism or in a pseudo- 
 grapheme. 
 
Chap. XL NOTES. 
 
 131 
 
 7] 'ApixoTTiLv, or i<j)apix6TT€Lv, is a technical term in describing 
 dialectical proof. 'Earn yap ovtco Seifot So-irep Bpv(r<ov top rerpa- 
 ymvi<Tp.6u. Kara koivov ti yap bftKwiovcnv ol toiovtoi koyoi, b Kal 
 erepo) virdp^ei- 810 Kal en &K\iov ^apixoTTOvcrw 01 Xoyoi ov avyye- 
 v&v. OvKovv oiix ft exewo- enCaraTai, a\Ka Kara a-vpL/Se^riKos- ov 
 yap &v f^ripixoTTev fj aTrdSeifis Kal e-n' aK\o yivos. An. Post. i. 9. 
 'Such a proof, like Bryso's squaring of the circle, as it may 
 conclude by a cause that is not confined to the given subject, 
 but is found in other genera, is transferable to a heterogeneous 
 subject-matter. But if the essence of the subject and not an 
 accident is the cause of knowledge, the demonstration is not 
 transferable to any other genus.' The paraphrast says, "O 8' 07:0' 
 nvatv Koivoripaiv Kal vitepfiaiv6vT<ov Kal ttoAAow app.oC6vTa>v yeveaiv 
 ipKTTiKos. For vuep^awovrmv [transcendent] Aristotle would have 
 said, iXiTa^awovTcav. "D.m'' rj avK&s av&yKT] ro avTo thai yevos ^ 
 mj, ei fiiKKei rj cntobei^Ls i^era^alveiv. An. Post. I. 7. 'Two sub- 
 jects must be the same in species or genus, if a demonstration 
 can be transferred from the one to the other.' 
 
 8] Kadokov must be taken in the sense in which it is de- 
 scribed in the Analytic, as equivalent to KaB" avro, and therefore 
 6 KaOoKov will mean 6 eic r&v lUmv apx&v airobeiKTLKos. Even the 
 philosopher (6 (piXoa-o^os) who has the most comprehensive 
 sphere must deal with his problems commensurately and essen- 
 tially (Ka96\ov, Kad^ avTo), and therefore is limited in his pre- 
 misses and conclusions. Unlike the dialectician, he has nothing 
 to say to geometrical problems. 
 
 9j Tas 6' avTas ap^as anAvrav etvai t&v avWoyio-pMV abvvaTov. 
 
 Erepat yop itokK&v rw yivu al ap^ai Kal ovb' e^app.6TTova-ai.. 
 
 Analytica Posteriora, 1.33. 'The principles of all deduction are 
 not identical They are heterogeneous and vary with the sub- 
 ject, and are inapplicable beyond their respective spheres.' The 
 constitution of philosophy imagined by those who maintained 
 the unity of first principles was probably such as we have in 
 Hegel's system, where the laws of physic and ethic are repe- 
 titions of the laws of the development of reason laid down in 
 the logic : or in Herbert Spencer's philosophy, where tbe theo- 
 rems of ethical and natural science are exemplifications of the 
 general laws of evolution and its component processes of differ- 
 entiation and integration, which themselves are again aflSliated 
 
 K a 
 
132 NOTES. Chap. XI. 
 
 on -a primary axiom of the persistence of force, a principle which 
 very mach resembles, if it is not identical with, the Aristoteliaii 
 axiom. 
 
 In the Metaphysic we are told that though all being" does 
 not belong to a single geiins{Ka66Kov,-Kaff ev), yet as referribleto 
 a common standard (irpos eV) it belongs to a single science, 
 philosophy. To be 6v keyfTai fiiv iioWax&s, aXXa irpas h koI 
 
 IJ-Cav Ttva (pvaiv, /tat ov)^ o/xoivv/icos Ov ixovov 6e [irept] t&v Kaff 
 
 tv Xeyoiihmv e7rtoT?jfi?js i<TT\ deoiprjcrai ixias, aK\.a koi t&v vpbs p.iav 
 
 keyoixivwv (pvcnv ArjXov ovv oti koi to. ovra fj,ia.s Oeaipijfrai rj ovra 
 
 KoX ei jxr\ iCTTi TO Sv 7j TO Iw Ka66\ov Koi TOVTO eirl TrdvTav rj xm- 
 
 puTTov, &<jTtip lams ovK eoTt. Metaphysica, 3 . 2. ' The meanings of 
 being, though heterogeneous, are referred to one standard, and . 
 the word is not equivocal. As not only homogeneous subjects, 
 or those that are denoted by a univocal name, belong to one 
 science, but also all that are related to a common standard, 
 the essential attributes of being will be investigated by a single 
 science, though being may not be a genus or a separate entity.' 
 Dialectic resembles philosophy in the wideness of its range: 
 'Ewei (ocrirep lori koI apidp.ov rj apiOfibs tbia TraOr).... ofwCws ii koI 
 (TTtpeiS.. ..((TTiV erepa Ibia, ovtu) kol tS ovti rj ov lori Tivh ihia, 
 Kot TavT larl Tifpl &v toB <f)ihocr6(j}Ov iTntrKiyj/acrOai, rakrides. Sj/fteioi; 
 bi' ol yap biaKeKTLKol koi (roc[>LcrTal tovtov jjifv vrtobiiovTai (rxwo^ ™ 
 t^iAoird^b)' T] yap (ro<j)L(TTi,Kr] c(>aLvoij.ivri jiovov troipia eori, Kai oi bia- 
 AfKTtitol biaKiyovTai irepl anavTotv koivov bk iraai. to ov €(tti, bia- 
 \iyovTai 8e iiepX tovtcov bfjX.ov on bia to Trjs (l>iX.o(TO(pCas etvat avTa 
 oueia. Uepl pxv yap to avTo yivos ffTpi(peTai fj ao(^itTTiKr\ kw. ?/ bia- 
 KiKTiKTi TTj 0iXo(TO(^^a, oAAa bi.a<l>ep€i t^v fiev ru Tpo-nia r^y bvvi.p£(itii, 
 TTJs be ToC l3Cov ttj Ttpoaipecrei. "Eori be fj biaKeKTinri ireipaanKri irepl 
 Stv r\ (pikoaocjiia yvotpicrTiKri, fj be <TO<^i(TTiKr] ^aivop^evr), ovaa b ov. 
 Metaph. 3. 2. 'As number and solidity have certain essential 
 attributes, which are examined by particular sciences, so being 
 has certain essential attributes, which are investigated by phi- 
 losophy. For dialectic and sophistic assume the garb of phi- 
 losophy. Their range is universal; and being, the theme of 
 philosophy, is universal. The other two deal with the universe 
 •of being because it is the proper sphere of philosophy. For 
 philosophy has the same sphere as sophistic and dialectic; but 
 differs from dialectic in the nature of her power, from sophistic 
 
Chap. XI. NOTES. 133 
 
 in the aim of her life : for she is scientific, while dialectic is 
 pirastic, [or, as Grote would say, she is ^positive and dogmatic, 
 while dialectic is negative and sceptical,] and sophistic a sham/ 
 But philosophy is restricted to scientific methods, and has 
 appropriate prohlems; dialectic is unrestricted in problem and 
 process. Dialectic proof, therefore, difiers not only from 
 scientific, but also from philosophic proof: and the sophism 
 difiers from the philosophic as well as from the scientific pseudo- 
 graph ema. 
 
 10] This seems to be the point of connexion with the pre- 
 ceding chapter. We saw there that some theorist had identified 
 dialectic and didactic. But they must be distinct ; for didactic, 
 ex -vi termini, proves something or other; dialectic is merely 
 pirastic, and proves nothing. It interrogates, that is, is willing 
 to accept a denial of any truth whatever, and therefore cannot 
 prove any single conclusion. If, like the sciences, dialectic 
 proved any theorems, dialectic, like the sciences, whatever other 
 problems it left open, would refuse to allow the truth of its 
 principles to be called in question. Didactic then, though 
 conversational in form, is not, in the true sense of the word, 
 ipcoTrfTiK^. Perhaps for (Sore we should read hi or lirei/ra; 
 for the train of thought seems to be, that even if there were a 
 universal science, it could not be dialectic, because dialectic 
 interrogates. 
 
 11] In the mathematics it is possible not only by synthesis 
 to obtain compound formulas by composition of elementary for- 
 mulas, but also by analysis from formulas respecting the com- 
 pound to obtain by decomposition a knowledge of the elementary 
 factors. But though the pirastic reasoner must possess some 
 derivative propositions respecting the subject-matter; must 
 know, for instance, that the thesis advanced by the respondent 
 is false, and that certain deducible consequences are impossible ; 
 yet these propositions are not such as to enable him to deduce 
 from them by analytical reasoning the primary laws that govern 
 the subjects and attributes in question. Otherwise pirastic 
 would implv science ; for knowledge of a conclusion as deducible 
 from the primary laws is science. Compare, Ei 8' rjv abvvarov 
 SK '^evbovs a\ri0is M^ai, pdbiov iiv rjv to avaXveiv. 'AvTe'irTpec^e 
 yap av ef avdyKrjs. "Koto) yap rb A 3v, tovtov 8' ovtos toBi eorii'. 
 
134 NOTES. Chap. XI. 
 
 h olha OTi 'iaTiv, olov to B' ek TovTb>v &fja bel^a> on ecruv eKilvo. 
 '' AvTi,(TTpe<f>fL be jxaWov to, iv rots iJ,a6riiJ,acnv, oti ovb\v (rt;/ii;3e/3)j){oj 
 XaiipdvovcTLv, &K\a koI Touro) biacpepovai. t&v ev rots biaXoyois, a\K' 
 opiirixovs. Anal. Post. I. la. 'If true conclusions never resulted 
 from false premisses, it would be easy to obtain by analytical 
 reasoning the principles on which any theorem depends. For 
 the principles and theorem would be related to one another 
 as the terms of a convertible proposition. If the antecedent 
 A involves the consequent B, when I knew the existence of B 
 I might infer the existence of A. This reciprocal demonstration 
 is more common in science than in dialectic, for the premisses 
 of science are never' accidents but definitions.' 
 
 12] The introduction of the word nature ((pva-is) may remind 
 us of a negative definition of logic in the pantheistic system of 
 Hegel, where logic is defined to be reason before the creation 
 of the world, or, reason antecedent to nature; the three succes- 
 sive transformations of reason being logical truth, nature, and 
 morality. In the passage before us, however, <^ijiTis jueludes 
 moralities as well as laws of nature. 
 
 13] It appeai-s that a pseudographema would be legitimate 
 in pirastic : for if the respondent could not solve it, it would 
 prove his ignorance of the science (woiet brjKov el Ayvoel, ch. viii). 
 The pseudographema, however, does not belong to pirastic ; for 
 pirastic is not supposed to have sufficient knowledge of scientific 
 principles to construct a pseudographema. 
 
 Pirastic proof is intermediate between sophistic proof and 
 scientific proof. The former has no particularity (Ibiov) ; the 
 latter no universality {kolvov) ; pirastic has both particularity 
 and universality. Scientific proof cannot be extended beyond 
 its private sphere : sophistic confutation proves no ignorance in 
 a particular sphere : pirastic confutation tests knowledge in a 
 particular sphere by principles applicable to every sphere. 
 Kara -ro TTpayfia, i. e. Iblies, deap&v to. koivcl, ■n-eipaori/co's. See 
 above. For a further examination of to, Kotva. see Appendix D. 
 Whately has divided fallacies into lexical and extra-logical. We 
 shall see in Appendix D that this division will not bear exami- 
 nation. Aristotle's division is into dialectical ((Toc/jiV/iara) and 
 extra-dialectical or scientific {\j/fvboypa(l)ripi.ara). If we define 
 dialectic to be opinionative reasoning and logic the science 
 
Chap. XIL NOTES. 135 
 
 of proof, we may divide dialectical fallacies into logical and 
 extra-logical, but logical will include all^that Whately considers 
 extra-logical. 
 
 CHAPTER XII. 
 
 1] EiTi 6 cro<pi(TTiKos TpoTtos, TO &yfLv ets ToiovTov TTpbs evTroprj- 
 aofiev eTtix^iprjiJidTav. Tovto 6' Itrrai ore p,iv avayKoiov, 6t^ be 
 (paivofxevop avayKoiov, or'k he owre (pawonevov ovre avayKOLOV. 
 'AvayKoiov jxev ovv orav, apvr\iTa)i.ivov tov ajnoKpivop.ivov t&v nrpos 
 T^v diaiv n \pr]criij.a>v, irpos tovto tox)s \6yovs woi^tou, TvyxAvrj be 
 
 TOVTO TOIOVTOV &U TipOS & iVTtOpiiv k<TTlV iTtl')(€lp7\p,6,TmV. 'O/XO^CO; hs 
 
 KoX oTav, amaymyriv irpos tl 5to tov Keiiiivov itoiria-dfifvos, dvaiptiv 
 iinxeipfi' TOfiTov yap avaipeOevros Koi to itpoKeCjj.fvov avaipeiTai. 
 f^aivoiievov bk avayKoiov, oTav clyaLvrjrat fjiev XRW^-I^ov ical olKeiov 
 T^s Oe(r€(i>s, p,fi fi be, npos o ylyvovrai oi Koyoi, etre apvr\ua)j,evov tov 
 TOV koyov virixovTOi, elre aitayotyrjs evbo^ov bia Trjs de(re(os irpos 
 avTo ytvoixevris avaipeiv eiti)(eipei avTo' to be Kolttov, otov )M)Te 
 avayKawv ^ jx-qTe (^aiv6p,evov Trpos b ylvovTat ol Xoyoi, dWias bi Tta- 
 pe^e\iyxea-0aL crvii^aivr] tu d-noKpLvofiiva. Aei bi evka^eltrdai tov 
 etryaTov t&v prjOevTcov Tpovcav' irajreAaij yap duripTrijxevos (cai aXKo- 
 Tpios ioiKev eXvai ttjs biaXexTiKrjs. Ato Sei (cai tov ditOKpivofievov fii) 
 bva-KoXaiveiv, dWa Tidevai to, pJri xpi^crtixa -npbs ttjv deinv, ima-rmai- 
 v6p,evov ocra p.7i boKei ixev, TCOrjcn bi. MaWov yhp airopeiv as eTTiTO- 
 Ttokv <Tvp,^aivei toIs fpcoT&triv, OTav ttAvtidv TiOeptevav avTOK t&v 
 ToiovToav p.ri irepaCvaxnv. Topica, a. 5. ' There is also the sophistic 
 method of leading the respondent on to ground where attack 
 is easy. This is sometimes really necessary, sometimes ap- 
 parently necessary, sometimes neither really nor apparently. It 
 is really necessary when a premiss directly bearing on the thesis 
 is denied by the respondent and happens to be easy for the 
 questioner to argue : or when the questioner has deduced a con- 
 sequence from the thesis and argues to prove its absurdity. It 
 is apparently necessary if the proposition only appears to be an 
 appropriate premiss or necessary consequence of the thesis. 
 When neither really nor apparently necessary, it may give an 
 opportunity for a collateral or by-confutation. The last method 
 must be avoided, for it is quite alien to dialectic. When it is 
 practised, the respondent should not be obstructive, but grant 
 
126 NOTES. Chap. XII. 
 
 every proposition that is unconnected with the thesis, observing 
 that he is willing to grant it for the sake of argument, though 
 he knows it to be false. Eor the questioner is the more dis- 
 comfited, if notwithstanding the most liberal admissions he fails 
 to confute the thesis.' The second case, which Aristotle im- 
 plies may be practised by the dialectician, shews the affinity 
 of dialectic and sophistic, for the locus, so far at least as it 
 consists of reductio ad absurdum, is the fallacy of non causa 
 pro causa. 
 
 2] i. e. ev ttj t&v TvpoTAirecav fKKoyfj. See Topica, i . 14. Though 
 dialectic is characterized by its metaphysical principles [koivo), 
 sometimes called forms of thought, yet it must always have 
 special premisses (tSta), which some have called its matter, and 
 Aristotle its materials (Spyava). As they are extraneous to the 
 art of dialectic, they are dismissed in the Topica with the remark 
 that a collection (e/cXoyTj) must be made of them. They are here 
 called pre-eminently premisses {-npordcreis), because the universal 
 maxims, though often treated as premisses, are usually sup- 
 pressed, and are often viewed not as premisses, but as regulative 
 principles, or precepts for the conduct of argument. Sroixetow 
 or TOTTos is elsewhere opposed to the etSr; or special premisses; 
 here the collection of etbri is called a aToixeiov. Thesis is here 
 used not for any tenet defended by the respondent, but in the 
 special sense of paradox. See Topica, i . 1 1 . 
 
 CHAPTER XIII. 
 
 1] I do not see how else to translate the text. But there is 
 no relation of genus and species in the first example : for double 
 and double of half are not so related. We might construct a 
 syllogism respecting duplicity, containing the relation of genus 
 and species, thus : Double is equivalent to multiple of a half; 
 therefore double of a half is multiple of a half of a half. But 
 this would not involve iteration ad infinitum, like the first 
 example. 
 
 2] Perhaps f) ovaCa should be cancelled. It is not a proper 
 term to express the subject of an attribute, and the words &v 
 and TO'6rois shew that the nominative to TrpoabrjkovTai is a plural. 
 Accordingly, Waitz proposes for f] ovaCa to read to, uTroMt/iefo. 
 
Chap. XIV. NOTES. 187 
 
 The predicates described are one of the two classes of essential 
 predicates investigated by science. Seetch. xij note 2. 
 
 3] Aristotle says that double, in the expression double of a 
 half, is not exactly equivalent to double placed independently. 
 The other fallacy consists in falsely defining odd as if it were 
 odd number. 
 
 CHAPTER XIV. 
 
 1] For f] Trrwfris we require, rj S,ppevos rj OriKeos KXrjms, ' the 
 masculine and feminine termination or form.' See below. 
 
 2] For \eyofi,ivois read Ae'yeo-flat, or read yivoji.ivoi^ and after 
 d/io^cos understand XiyeaQai or epixrivevfo-Bai. 
 
 3] In figura dictionis the same form is common to different 
 categories, e. g. the substantive name, nomen substantivum, to 
 substances and accidents : in the fallacy of solecism the same 
 form is common to the nominative and accusative. In figura 
 dictionis we are cheated into an error of fact : in the fallacy of 
 solecism we are cheated into a wrong grammatical construction. 
 The employment of the word solecism, which properly means an 
 impropriety of diction or a violation of grammar, to express an 
 impropriety of action or a violation of some practical science, 
 has become a common metaphor. Referring to ch. iv. we shall 
 see that one of the instances of amphibolia would furnish a fallacy 
 of solecism : ^Apa tovto, h opq Koptcr/cos, opa ; tovto 6e niinv uffre 
 opq 6 KopCaKos, ov Kiova dAAd, klcdv. 
 
 4] In the Rhetoric Aristotle treats of invention, expression, 
 and arrangement. TpCa ea-rlv h 6ei itpayiiaTeuOrivai lapX tov 
 \6yoii, kv fxev ix rlvrnv at irCa-reis ea-ovrai, bevrepov bi nepl tt]V 
 Ae'ftz;, ipCrov be iraJs XPV Ta^ai. to, [Jifpr] tov Koyov. Rhetoric, 3. i. 
 In the Topica he treats of invention and arrangement. Me'xjOi 
 fiev ovv TOV (vpeiu tov tottov oixolcos tov (j)t\o(r6(()OV Kal tov bia\eK- 
 TiKOV T] crKe\j/is. To 8' rjbr) ravTa TOLTTfW kol epaiTr]p.aT((eiv ibiov tov 
 biaKeKTiKOV' 7rpo9 erepov yap Tiav to toloCtov. T<3 be (^lAoad^bi kol 
 C-qTovvTi Kad' kavTov ovbev fieKei, iav aXrj9rj p.ev if kol yvcapiixa bi S>v 
 6 (Tv\\oy(.(Tpi6s, firi dfj 8' avTo. 6 a.TTOKpiv6iJ.evos bia to irvveyyvi elvai 
 TOV e^ djOYTjs Koi Tipoopav to aviJ-firjaoixevov dW' tcrtas Khv (ntovbA(Teiev 
 OTi fxaKuTTa yimpip-a Kal avveyyvs elvai to, dfidJ/^iaTa- e/c TOVTav yap 
 oi em(TTr)p.oviKol crvXKoyuriMoi. Topica, 8. I. ' Invention of the 
 
138 NOTES. Chap. XIV. 
 
 method of argument belongs to philosophy and dialectic alike : 
 the arrangement and shaping of the questions to dialectic alone. 
 The philosopher and solitary inquirer, when he has discovered 
 true and evident premisses, has no trouble from the refusal of 
 the respondent to grant them, because they bear immediately on 
 the problem, and manifestly confute his thesis. He is glad to 
 have them connected as closely and evidently as possible with 
 the problem ; for so they must be in scientific proof.' From 
 the contents of the following chapter it appears that ra£ts ex- 
 presses rather tactics than simply arrangement. 
 
 CHAPTER XV. 
 
 1] For ikeyxfiv read kavOauuv. 
 
 2] It seems that Aristotle was capable of giving precepts for 
 lengthiness, but they are not extant, unless he refers to what he 
 said about unnecessary propositions in the Topica, 8. i. 
 
 3] Various methods of concealment are given in the Topica, 
 8. 1. E. g. to keep back till the last moment the conclusions of 
 the inductions and prosyllogisms that furnish the premisses of 
 confutation [fjJq biapOpotdivToiv t&v irpoTepav (rvWoyia-fi&i)) ; to leave 
 the subject of dispute and obtain concessions respecting its cor- 
 relatives or pai'onyms {to. (rvm-oixd) ; to smuggle in the important 
 premiss with a quantity of irrelevant matter (iv ■napapmrif 
 '}TpO(TTi9evTes KaOatap ol v^enSoypac^oCires) ; &c. 
 
 4] "En 8ia rrj? opioiorijTOS ■nvvddvea-daf Koi yap itiOavov km 
 XavdAvei fxaWov ro KaOokov. Olov on Sxmep eirio-T77fXj; km ayvoia 
 r&v evavrCiav f] alrri, ovTot Koi ata-drjcns t&v evavriuin r] avrr\, rj 
 avairakiv, l7ret8^ aiudr^ais fi avTrj, kolL eTnaT-qjxrj. Tovto 8' icrnv 
 Sp,oiop iiiaycayfj, ov fxijv tomtov ye. 'Exet p-iv yap airo t&v 
 Kaff exacrra to KaOokov kap^dveTai, iiri be t&v ofioiav ovk hri 
 TO kajX^avoiievov to Kadokov v(j) & ttAvtu to ofwid ia-n. Topica, 
 8. I. 'Another method of concealment is to reason by simi- 
 litude, that is, to reason directly from particulars to similar 
 particulars. The reasoning is persuasive and the immediate 
 premiss is not disclosed. For instance, as the intellectual 
 appreciation or non-appreciation of contraries is identical and 
 simultaneous, so is the sensational, and vice versa. The 
 mode of proof resembles induction, but differs, because it does 
 
Chap. XV. NOTES. 13y 
 
 not express the universal proposition, but passes at once to the 
 particular conclusion.^ This mode of raasoning has lately risen 
 to distinction. Mill considers it the true or natural type of all 
 reasoning, induction and syllogism being artificial. Grote finds 
 here the long-sought criterion between true opinion and know- 
 ledge : true opinion, so far as it is not merely a lucky guess 
 but founded on evidence, passing immediately from particulars 
 to particulars without recognizing the intermediate law. See 
 his comment on the Meno. After aK\a in the text perhaps we 
 should add avavvnov. 
 
 5] Kal TO. oKiydKis oKiya, so read, comparing ch. xxiv, for /cat 
 TO TtoWaKis TioWd. 
 
 6] In the Rhetoric this artifice is given as the fallacy figura 
 dictionis. Tottoi 8' eial t&v (^Mvofiivtav ivdvjxrjjx&Tiaiv its fiiv o 
 ■napa Tr\v Xl^iv, kol to^tov kv ijt,ev /xepos coo-irep fv rot? biaXeKTiKois 
 TO JUT) (TvWoyKTaiJievov o'vixTTepQ.criJ.aTiK&s to TfXfvToiov eraety, ovk 
 &.[ta TO Kol TO, avdyKY] apa to koL to. Kal to tois ivOvp,T]y.a(nv 
 \_olKiiovT\ TO avve(TTpap.p.H>ii>s icai avTiKeifxivms ilniiv (paCveTai (vdv- 
 p.rj\xa. 'H yap ToiavTr] \efis X'^P" ^''''''i' ivdv^-f]p.aTos. KaJ lotKe to 
 toioCtoi' ilvai napa to cF)(rnj.a t^s A^fews. Rhet. a. 24- ' One 
 locus of seeming oratorical proof is diction. One division of this 
 is, as in dialectic, without proving to conclude in the language 
 of proof: "It follows, then, that this- must be true:" "It 
 follows, then, that that must be false." For crowded and anti- 
 thetical propositions look like proof, because such diction is the 
 vehicle of proof : and the fallacy is figura dictionis.^ 
 
 7] *Ai' 8' iT^pov bo^av bia(j)v\dTTrj 6 d.-nOKpivofj.fvo's, brj\ov oti 
 Ttpos Tr\v, (Kelvov bidvoLav a,7ro/3Ae7rovTa 6(Teov (Kaara Kal apvrf f.ov. 
 Aio Koi 01 KopiCCovTis okKoTpCas bo^as, olov dyaObv Kal KaKOV etvuL 
 ravTov, Kaddirfp 'Hp(iKAetTo's <^7](ri,v, ov biboaa-i, p.ri Tiapdvai &p,a ru 
 avTio TavavTia, oi^ ^s ov boKovv avTols tovto, aAA on Kad' Upa- 
 K\fiToi> ovToi KiKTtov. Topica, 8. 5. ' When the respondent de- 
 fends the tenet of another person, the opinions of that person 
 are the standard of what he ought or ought not to admit. 
 Accordingly, the advocate of a dogma which he himself does 
 not hold, — for instance, that good and evil are identical, as Hera- 
 clitus said, — will not grant that contraries cannot coexist; not 
 because he disbelieves it, but because it is inconsistent with the 
 system of Heraclitus.' In the text ■npoKuiiivov seems to signify, 
 
140 NOTES. Chap. XV. 
 
 not, as usually, the thesis, but the conclusion of the argument, 
 i. e. the contradictory of the thesis. So in Topica, 8. 5 : 'ASo'fot) 
 yap ovaris rfji Oicreas ^I'bo^ov to (rviXTtepacriJia' (Sore bei to. Xap,fiav6- 
 [jL€va evbo^a ti&vt etvai Koi p,a\\ov evbo^a roC irpoKeiiJtivov, ei p,eK\ei 
 81a r&v yv<opift,(OTep(av to fJTTov yvdpifjLOV iiepaLveadai. ' If the 
 thesis is improbable, the conclusion of the disproof is originally 
 probable ; therefore all the premisses ought to be probable in a 
 still higher degree, in order to fulfil the conditions of proof.'' 
 
 8] "A^Aos (toti-os ivQv\t,-f\p.aToi) Ik Kpia-eas itepl tov avTov rj Sfwiov 
 fi ivavrCov, fidKiara p,ev el irdvTes kol au, el h\ p,rj, aXK' ot ye TrAei- 
 oTot, ^ (Tocpol rj TtAvm 7j 01 TrAfioTot, fj ayadoC, jj et avTol oi Kpivov- 
 T€s, rj ois aTtobe\ovTai ol Kpivovres, rj oh jxij owv re-evavTiov aplvuv, 
 olov roTs KVpiois, rj oIs ti-Ti koKov to, ivavrCa KpCveiv, olov deois r) iiaTpl 
 rt 8i8a(TK(i\ois. Rhet. a. 23. 'Another topic of argument is 
 authority, or the decision on an identical, similar, or opposite 
 question, either of all the world, or of the majority of the world, 
 or of all philosophers, or of the majority of philosophers, or of the 
 good, or of the judges, or of those whom the judges accept as 
 authorities, or of those whose decision cannot be rescinded, as of 
 a superior tribunal, or of those whom it is immoral to disregard, 
 as the gods, or parents, or teachers.' 
 
 9] Ta i-nixfiprjp.aTa eiii.Tift.veiv is to cut down the propositions 
 {eT!i.\eipr\jj,aTa) so as to disarm the respondent of his enstasis. 
 Dpos 6^ Tovs evicnap-ivovi ru KaOoKov, p,ri kv avTa be ttiv evaraaiv 
 (jjepovTas a.K\ ev roJ 6p.aiVvp,tD, bieKofxevov epatTTfriov. . . . 'Eav b\ jutj 
 ev Tu diMCiiVvpia a\\' ev airu evicrTaixevos KwK'iri ttiv epdr-qaiv, cupai- 
 povvra Set ev Z rj eva-TCKns ispoTelveiv to \ovnov KadoXov TToiovvra. . . 
 Oi) jxavov 8' evi(TTap.ivov tovto 7rot)jre'oi', dAA.a kolv 6.vev iva-ria-eas 
 apvfJTai bia to irpoopav n t&v Toiovrav a^aipedevTos yap ev <a r] 
 eva-Tacrii, avayKacrdrjiTeTai TiOevai bia to puq irpoopav ev to! koiir£ em 
 Ttvos ov\ ovTuis. Eav be fxri Tidfj, anaiTovfievos evaraa-iv ov p.r] Ixj? 
 aiTobovvat,. Topica, 8. a. ' If the respondent opposes a premiss 
 by an enstasis, availing himself of an equivocation, the questioner 
 must distinguish. If the enstasis is not founded on equivoca- 
 tion, he must cut ofi" from the proposition the portion open to 
 enstasis, and propose what remains as a universal. He must do 
 this even when the answerer adduces no enstasis, but simply 
 denies the proposition, because he perceives the possibility of 
 an enstasis. When the exceptionable portion has been excluded, 
 
Chap. XVII. NOTES. 141 
 
 the proposition must be granted, for the answerer can no longer 
 adduce an enstasis/ • 
 
 10] So read for T:p6s ri iTrixeips'iv. Compare AiratroCz'Tat yap, 
 Tt TovTo Ttpos TO iv &px,fj } ch. viii. 
 
 CHAPTER XVI. 
 
 1] For biaXvirai read KiaXvaai. The former would be a very 
 ill chosen term to express a process opposite to analysis and 
 analogous to synthesis. 
 
 CHAPTER XVn. 
 
 1] At first sight opar&v seems to be a false reading for opuavv- 
 fjMi). But opar&v may stand. Aristotle is not speaking of all 
 equivocation (he would hardly say that all involved inevitable 
 confutation) but of a particular species, i. e. when one proper 
 name belongs to several individuals. These individuals, accord- 
 ing to Aristotle, cannot be distinguished by any artifice of 
 nomenclature. 
 
 2] To TovTov TOP KopCcTKOV. So read for to tov KopCcrKov. 
 3] The formulas of dialectic, now obsolete, were not long ago 
 household terms, as the following quotation may shew : — 
 ' Mais le quadrille aussi. Monsieur de la Garonne, 
 Est un jeu du hasard.' — 
 
 ' Madame, distinguo : 
 Pour I'honnete personne. 
 Oh 1 vraiment, concedo ; 
 Mais pour la gent friponne, 
 Nego.' 
 Le Sage, L'Esperance (acted 1730). 
 4] For wotci rts read eiro^et tis, or eiroietro. It seems that 
 some logician had maintained that a single answer should be 
 given to an equivocal question if it is true in both interpreta- 
 tions, though he also held that a single answer should never be 
 returned to several questions. Against this logician Aristotle 
 says that every fallacy of homonymia or amphibolia may be 
 regarded as a fallacy plurium interrogationum. 
 
 5] Aristotle asserted thi^ before in the beginning of the 
 
142 NOTES. Chap. XVIl'. 
 
 chapter, but he has not justified it, unless we take what was 
 said about t&v opar&v to be a justification. But this, if it proved 
 anything, proved that sometimes there is no true solution, not 
 that a false solution is to be preferred to the true. It is not 
 easy to see how he could justify it, except on the ground that a 
 fallacious solution is often cleverer than the true one, and there- 
 fore to be preferred in a trial of skill. See however ch. xxxiv, 
 note 3. 
 
 6J Read orav 6^. 
 
 7] 'Ecrn 5e eir' iviuiv y.\v iiidyovTa bwarbv epa)T^(rai to KaOoKov. 
 'Ett' ivCuv 8e ov pabiov bia to fir] Keia-dai rats oixoLOT-qmv 6vop.a 
 ■n&dais Kowov, aAA' oral' hhj to KadoKov kapiiv, Ovrcos eirl -navTrnv 
 T&v TOWUTUtv, (fiadi' tovto be btopi(Tai t&v xaAeiKordrcoi', ottoTo t&v 
 TTpocpepo^ivaiv ToiavTa koI oiroia ov. Kal Tra/M tovto ToAAaxts aXhrj- 
 \ovs TrapaKpovovTai Kara tovs Xdyovs oi piv (J)6.(tkovt€s opoia nvai 
 TO jii^ ovTa op.oia, ot 5^ ap,(^i<T^r}TovvTes to. ojj.oi,a /lit/ elvai opoia. 
 Ato TseipaTeov iitl -navTrnv t&v Toio{iTa)v ovoixaToiioLelv avTov, ottios 
 fxijre TIB airoKpivop-iva e$fj ap,(jji,(Tl3r]Tew cbs ovx 6p,o((DS to firicfiepo- 
 p.iVov Aeyerat, \x-qTi tu epa>T&VTi trvKOCpavTeHv as bp.oiij>s K(yop,hov 
 eweiSTJ woAAa t&v ovx_ op-oices \eyop.iva>v o/xotioj (fmlveTai. Xfyeadai. 
 Topica, 8. 1. 'In induction it is sometimes difficult to word the 
 generalization, because the point of similarity in the particulars 
 has not been denoted in popular language by a common name. 
 In generalizing we say. And so in all like eases, or, And so in 
 all the members of the class. But it is excessively difiicult 
 to define the class or determine what particulars are like : and 
 hence many fallacies arise, one party maintaining the likeness 
 of what is unlike, the other the unlikeness of what is like. We 
 ought therefore ourselves to invent a name for the class, that 
 the answerer may be unable to pretend the unlikeness of what 
 is like, or the questioner the likeness of what is unlike, for what 
 is really unlike often appeai-s to be like.^ It is curious to see 
 the fundamental problem of induction treated so incidentally 
 and perfunctorily. The definition of the antecedent term of a 
 generalization is spoken of as if it were merely the process of 
 inventing a name. It is really the problem, which Aristotle 
 would allow to be all-important in science, of distinguishing 
 essential (/cofl' avTo) and accidental propositions, or, as we should 
 now say with Mill, of eliminating chance from causal conjunc- 
 
Chap. XVII. NOTES. 143 
 
 tions, and can only be solved by the methods of agreement and 
 difference. • 
 
 8] 'ATio(t>dva-€Ls. So read for aTTo^direis, the perpetual error of 
 the scribes. 
 
 ■ 9] Perhaps for itoTipass ixei TaXrjdis, we should read ■noTspo}'} 
 exet TO (riivrjdes, i.e. Ttorepas ftmOi keyedOai. But toA?j0€s, though 
 an ill-selected word, may be the right reading, for it may refer 
 to TCLS a\r)9fis boias, which occurs above. It would denote the 
 real or symbolized meaning as opposed to the figure or imagery. 
 The theorem that the side and diagonal of a square are incom- 
 mensurate is demonstrated by Euclid, lo. 97, and is alluded to 
 by Aristotle : Flept 6e t&v aCbCaiv ovhels fiovkeuerai, otov Trepl rov 
 Koa-fiov, fi TTJs biajxiTpov Kol rrjs irXevpas on i.(nip\xiTpoi. Eth. Nic. 
 3. 3. We might suppose there was an allusion to the ambiguity 
 of the terms, f) biApifTpos aaijp,p.iTpos, which may express either 
 that the diagonal and side of a square, or that the diameter and 
 circumference of a circle, are incommensurate. The latter pro- 
 position was probably stnmbled on by those who were seeking 
 a method of squaring the ciixjle; for they discovered that the 
 area of the circle equals half the rectangle of the radius and 
 circumference. But the interpretation given in the text seems 
 better. 
 
 There is a similarly constructed period in Topica, 8. 3 : T&v be 
 opwp bvaeTti^fiprjTOTaToi -navTatv etcrtv oaoi Ki\privTai toiovtois ovo- 
 Ixaa-LV h TTp&Tov ptiv 6,br]kA (ariv etre aiikm the -nokXax&s keyirai, 
 ■npos be toutois /liijS^ yvd>piyt.a voTtpov Kupicos ^ Kara p,iTa^opav vtto 
 Tov 6pia-ap.evov kiyeraf bia fiev yap to aa-a^rj thai ovk ex^' ^ '" 
 XeLprip,aTa, bia be to ayvoelcrOai el itapa to Kara p.eTa(j)opav keyecrdai. 
 tomvt' ecTTlv, ovK e^ei eiiiTLp.r](nv. ' Of all definitions the most 
 diflScult to attack are those whose terms raise a doubt, firstly, 
 whether they are ambiguous or unambiguous, and secondly, 
 whether they bear their proper sense or are metaphors. The 
 doubt whether they are ambiguous saves the definition from 
 confutation as false, and the doubt whether they bear their 
 proper sense saves it from condemnation as metaphorical.' 
 
144 NOTES. Chap. XVIII. 
 
 CHAPTER XVIII. 
 
 1] 'I'eiiSTjj 8e \dyos KaXeirai TfTpa)(&s' fva jjiev Tpoirov orav (pai- 
 vrjTai trvjjL-nepaCvfaOai fxri a-vixiTepaivoixevos, 6s Ko\eiTat crv\\oyiiTp,6s 
 ipicTTiKos- "AWov 8e oTav (ivp.T,epaivr\Tai jiiv, pifi p,ivToi irpoi to ttpo- 
 KeCfxevov, oirep (Tvp,^alv€i p.akiaTa rois ets to ahvvaTov S,yov<ni>. *H 
 Tipbs TO TTpoKiCp.evov ij,ev (Tvp,T!ipaivr]Tai,, yjfi fiivToi Kara rfiv oUdav 
 ixedobov TOVTO Se ^cttiv eav 6 fXTj 5)v loTpiKos 6ok^ iarpiKos eivaf, fj 
 yewjuerpiKos p.ri S)V yeaifj.eTpLK6s, rj biaXeKTiKos p.fi &>v 6ia\eKTuo's, &v 
 Te -^j/fvbos av re aXrjdes s ''o crvixj3aivov. 'A\kov be Tpoirov iav 8ia 
 •^revb&v (TVfjmepaCi'riTai' tovtov be earai wore piev to avun^paa-na 
 \jffvbos wore 6e a\ri9es. Topica, 8. lo. 'False proof is of four 
 kinds : firstly, inconclusive or eristic proof: secondly, conclusive 
 but irrelevant proof, which chiefly occurs in reductio ad absur- 
 dum : thirdly, relevant proof by an inappropriate method, i. e. 
 proof that has a false pretence of being physiological or geo- 
 metrical or dialectical, though it has a true conclusion : fourthly, 
 proof from false premisses, whether the conclusion is true or 
 false/ The first class is inconclusive syllogism. The second 
 class is inconclusive confutation, including non causa pro causa 
 and ignoratio elenchi (see ch. x, note 4<). The third class is 
 simulated pirastic proof or simulated scientific proof, and may 
 be identified with one of the significations of accidental or in- 
 commensurate proof (ch. vi, note 5). The exposure of this 
 class of fallacy is beyond the competence of pirastic, and de- 
 mands science or at least education (see Appendix E). The 
 fourth class is dialectic, sophistic, or pseudographic, according 
 as the false premiss is a special opinion, a general maxim, or a 
 special theorem. Perhaps Aristotle would also call it dialectic, 
 if the general maxim was a really probable hypothesis. The 
 first two classes exhaust the thirteen paralogisms. All the 
 classes are sophistic, though the fourth class includes some mem- 
 bers which are not. The sophistic members of the fourth class 
 are discussed in chap, viii, where, however, they are not distm- 
 guished from the fallacies of the third class. Are there any 
 confutations which fall under the third class and not also under 
 the fourth, that is, which are sophistic and yet conclusive and 
 constructed of true premisses ? It is difiicult to conceive any 
 
Chap. XVIII. NOTES. 145 
 
 thing that fulfils these conditions except the confutation of a 
 geometer, who is seduced into advaaeing an ungeometrical 
 thesis. He would scarcely do this deliberately, but he might 
 in the heat of a discursive debate, and would then expose him- 
 self to a by-confutation (irapef Aeyxoy). We might, however, 
 regard this as a case of non causa pro causa, that is, of the 
 second class. See the mention of by-eonfutation in ch. xii, 
 note 1. 
 
 2] Here the disproof of a conclusion is called counterproof, 
 and spoken of as a solution of the argument in support of that 
 conclusion. This is not only ijaanifestly inadmissible, but is 
 flatly contradicted by Aristotle himself in ch. xxiv. ' Something 
 more than the exposure of a fault is required in solution, for the 
 falsity of the conclusion may be demonstrated without explain- 
 ing why the reasoning is fallacious. To solve Zeno's proof of 
 the impossibility of motion, we ought not to try to prove the 
 opposite, for though we gave ten thousand valid proofs, this 
 would be no solution, for it would not expose where the falsity 
 of his argument Kes.' Elsewhere Aristotle clearly implies that 
 antisyllogism or counterproof (he uses the synonymous term 
 avTi-niyeipilv) is directed not against the conclusion but against 
 a premiss. 'E'ffei h\ -naa-a TtpoTacns crvXkoy io-tikt] ?j ToijTOiv rk lariv 
 ff &v 6 (rvWoyi(Tjj,os, -tj tivos Tovrmv evsKa {bfj\ov 8' orav eripov 
 )(({pti; \ap.^avr)Tai tu irKeCo) to, of/,oia kparav ?j yap 8i' eiroymyTjs -q 
 hi 6p,oi6Tr)Tos bis eiil to ttoXv to Ka66\ov Xap,^&vov(ny to jj.tv KaOe- 
 Kaara navra Oeriov, hv fj aKrjdrj Kol evbo^a, irpos 8e to KadoKov iret- 
 paTiov fva-raaiv (j)fpeiv. To yap &vfv evffTda-eois rj ovarjs ri boKOwris 
 KUiKvfiv Tov Xoyov bv<TKo\aCveiv eariv. Ei oSv ewt noW&v (paivo- 
 p,iv(ov oil 8t6o>crt to Kadokov fi^ ex"" evcrracnv, ipavepov oti bva-KO- 
 Xaivii. "En b\ d p.7]b' avTeTiix^ipeiv exoi on ovk aXrides, p.aX\ov &v 
 b6$fie bviTKohaCvdv. Kakoi oibe rovd' havov -noXXovs yap Xoyovs 
 ivavrCovs i-)(pp,iv Tais,- So'^ais ofis xaXt-nov Xi'juv KuOdirtp tov Zrjvoi- 
 vos OTi OVK fvbexeTai Kiveia-dai ovbe to aTAbwv buXBelv dX\' ov bia 
 TovTO TO. avTiKdjxiva TovTOLs ov Oeriov. El ovv fiTjre drTeirixetpf tv 
 lx<t>J' /nijre kvioTatrdai ov TCOrjai, bijXov ort 8i;£rKoXaii'€t. 'Eo-n yap f) 
 fv X6yoLS bva-KoXCa AwoKptcrts ■napa tovs dpy}p.ivovi Tponovs a-vXXo- 
 yio-juoi; ^OapTiKr). Topica, 8. 7. 'AH propositions are premisses of 
 the final proof, or premisses of these premisses, as the particulars 
 adduced in induction and simihtude. These particulars must 
 
146 NOTES. Chap. XVIII. 
 
 be admitted if they are true, and the universal inference opposed 
 by enstasis. To resist an inference without adducing an enstasis, 
 real or apparent, is perversity, or irrational obstructiveness. To 
 resist without even adducing a counterproof, is still greater per- 
 versity. Yet even this would be insufficient, for many proofs of 
 paradoxes are hard to solve, like Zeno's about motion, and yet 
 the respondent (in arguing on a different question) is bound to 
 admit the opposite. If, then, the respondent refuses to admit a 
 premiss without adducing either enstasis or counterproof, he is 
 undeniably perverse. For logical perversity is withstanding 
 proof without one of these modes of justification.^ The same is 
 implied in the- Rhetoric : Ta be -Kpos tov avrChKov ovx erepov n 
 «i8os, aWa Tmv Tiiarfoov i<TTi to, fj.iv \vaai, fvcrraaei to, 8e (tuAAo- 
 
 yio-fj.^ icTTepov Se kiyovra np&Tov to. irpbi tov evavTiov \6yov 
 
 \fKTeov, Kvovra /cot avTia-vWoyi^ofievov, Koi fictAtora &v ewSo/ct/aTj- 
 KOTa fj. wcnep yap S.vdpwTiov T:pobM^i^kr)}xivov ov S^erot ^ ^XV) 
 TOV avTOv TpoTTOv ovbl koyov, eav 6 ivavTios ev boKrj elprjKivaL. Sei 
 ovv \wpav iroteti/ ev t(3 aKpoaTrj tu ixiWovTi Aoyu • eorat be, hv 
 avekris. Rhetoric, 2. 17. 'The portion of a speech which answers 
 an opponent is not a separate kind of proof, but is a solution of 
 
 his argument by enstasis and antisyllogism The orator who 
 
 speaks second should first encounter his opponent's argument by 
 enstasis and antisyllogism, at least if it was eflfeetive. For as a 
 person against whom we are prepossessed finds our mind closed 
 against him, so does an argument after an effective speech of 
 the adversary. Room therefore must be made in the hearer's 
 mind for the coming proof, and this can only be by upsetting 
 the adversary's argument.' Here avTiarvWoyiaixos is contrasted 
 with 6 fjieWoiV Xoyos. It therefore can only signify opposition 
 to the opponent's premisses : for if it was opposition to his con- 
 clusion it would be identical with 6 /^eAAmv Ao'yos. This ques- 
 tion is continued in the following note. 
 
 3] 'As was said before' must refer, not to Topica, 8. 8, quoted 
 in last note, but to what immediately precedes. *H S8e ri &he, 
 therefore, means that the ^vaipeais applies either to the premiss 
 or to the conclusion. Here, then, we are in a difficulty ; for no 
 logician could suppose that an argument is solved by another 
 argument in support of an opposite conclusion. The following 
 seems to be the explanation. The disproof of the conclusion of 
 
Chap. XIX. NOTES. 147 
 
 a prosyllogisirij though no solution of that prosyllogism^ is a 
 solution of any subsequent syllogism in^hich the conclusion of 
 that prosyllogism figures as a premiss. In fact, every premiss 
 that the questioner wishes to obtain must be supported by 
 induction, therefore every refusal of the answerer to admit a 
 premiss is the rejection of an inductive conclusion. "Orav 8' eTrd- 
 yovTOi em tioW&v ixtj 8t8(o to KaOdXov, Tore biKaiov cntaLTfiv evara- 
 (Tiv. Mr) flirovTa 6' aiiTov em rCvtov ovrms, ov bCxaiov airaiTeiv em 
 Tivaiv ou)( oijTuis' 8ei yap iirAyovra Trporepov oiirai ttjv ^varaoiv 
 
 anaiTilv 'Eaf 6' eiii TtoXX&v irpoTeCvovTos p/fj (jiepr) evcrranv, djto)- 
 
 riov TiQivav hidKeKTiKT) y&p ecm irpoTacns irpos fjv oSrcos fTrl tioW&v 
 exovcrav p.r] fo-Tiv evcrTacris. Topica, 8.2. ' When 'the questioner 
 has made an induction by many particular instances, if the uni- 
 versal is not admitted, he has a right to ask for an enstasis or 
 contradictory instance. Before he himself has adduced -sup^ 
 porting instances he has no right to ask for contradictory in- 
 stances. The induction must be made before the enstasis can 
 be demanded. When many particulars can be alleged in support 
 of a premiss and no contradictory ones against it, the universal 
 proposition must be granted. For in dialectic that is a good 
 proposition which is supported by many examples, and to which 
 no exception can be alleged.^ It appears, then, that enstasis and 
 antisyllogism do not differ because one attacks a premiss and 
 the other a conclusion, but because they attack the same premiss 
 in a different manner. For more on the nature of enstasis see 
 Appendix D. 
 
 CHAPTER XIX. 
 
 1] Thus : to speak of stones is possible, to speak of stones is 
 speech of the speechless, therefore speech of the speechless is 
 possible. 
 
 2] ^vveTrCa-Taa-dai is not explained by the lexicons, and we 
 have no means of conjecturing the nature of the fallacy. But 
 we may observe that it did not depend on any double meaning 
 of eiriorrao-flai, i. e. on homonymia, as we might imagine from what 
 is said below, for we are here told it was a case of amphibolia. 
 
 3] Suppose Appius to be blind : then, to see Appius is pos- 
 sible, to see Appius is sight of the blind, therefore sight of the 
 blind is possible. 
 
 L 2 
 
148 NOTES. Chap. XIX. 
 
 When the conclusion is ambiguous, the sophist must take 
 care to get it denied hefore he proves it, or it will be admitted 
 and ridiculed as a truism. E. g. Tldrepov be op&criv, e^yf 6 Ei9u- 
 brjixos, KoX ^KvOat Kol oi aA\o( avOpoairoi ra bwara opav r) to oM- 
 vara ; Ta bwara Stjttoi;. OiiKovv koI (tu, ^(pir]. K&yd. 'Opas ovv to, 
 rnxirepa IfxaTLa; Noi. AvvaTo, ovv'opav iarl ravTa ; 'Ttt e p(j>v&s, fcjiri 
 6 KTTjo-Mnros. T^ be; rj 8' os. Mrjbiv. 2i 6' Itreos ovk otei aiiTa opav. 
 OfiTcoy 178^1? ei. 'AXAci /xot boKUi, 'EvO'ibriiJ.e, ov Ka0e6b(ov irnKSKOi- 
 iJ.Ti<T6ai. Euthydemus, § 67. 'Is what the Scythians and other 
 people see able to be seen (able to see) or unable ? — Able.— And 
 what you see too ? — What I see too. — Do you see our dress ? — 
 Yes. — Is our dress able to see (able to be seen)? — Certainly. — 
 Why you don't mean to say — Yes I do. Did you think it was 
 not able to be seen ? What a noodle you are ! Why, Euthy- 
 demus, you must be sleeping with your eyes open.' 
 
 4] A proposition or proof is said to be addressed to a term 
 <T7pos TovTo) when that term is the subject of the proposition or 
 of the conclusion. Ewat p.\v avWoyiffiwv ovbev Kco\i;et, -npos fxivToi 
 
 TO B OVK. ea-rai bia t&v elXriiJ,fji.4vaiv 'O jn^i/ yap o-uWoyto-juos avkSs 
 
 €K irpordcreoiv eariv, 6 b\ Trpos robe orv\Koyi(TiJ,o9 Ik t&v irpbs robe 
 •itpoT&tTeuiv, 6 b\ Tovbe Trpbs robe bia r&v rovbe irpoi robe irpordaecov. 
 Abwarov be Trpos to B kafie'iv irpoTaarip ij,rjbiv ixrire KarriyopovvTas 
 avTov fxrJT' airapvovp-evovs. Analytica Priora, I. 23. 'We may 
 prove something, but not respecting this term, from these pre- 
 misses. For all proof is from premisses, proof respecting a 
 given term from premisses addressed to that term, proof con- 
 necting a given predicate with a given term from premisses 
 addressed to that term, and relating to that predicate. When a 
 premiss is addressed to a term, that term must be a subject on 
 which the premiss imposes, or from which it removes, some pre- 
 dicate.' "OAms 8^ TTiv Trpos ru ft,e!.^ovi, &Kpif Trporacnv ouk Iotu' 
 ai'a(rKevd(rai KaOokov bia ttjs avTKTTpocjifjs, ael yap dvaipelTai 810 
 Tov TpiTov <r>(rjp.aTos, dvayKr] yap irpos to i(r){aTov aKpov hp,^OTtpa% 
 Xa/Selv Tas TrpoT&ireis. Anal. Priora, 2. 8. 'The contrary of the 
 major premiss cannot be proved by the minor premiss and the 
 contrary of the conclusion, for the proof is in the third figure, 
 the minor term becoming the middle and being made the sub- 
 ject of both premisses.' AryAov 8e /cat on ev Unacn toXs o-xtjVc"^"' 
 •OTav pjj yivrfrai avWoyicrfios, KarriyopiK&v {/.kv ^ a-TeprjTlk&v diJ,<pO' 
 
Chap. XIX. NOTES. 149 
 
 riprnv ovTtov t&v opcov, ov5\v oXoas yiverai avayKoiov, Karrj-yopiKov 
 Be /cat orepjjriKou, KaOoKov X.ri(})divTos tov» aTeprjTiKov, ael yiverai 
 cvk\oyi<riJi.oi tov fXArrovos &Kpov irpos to fie'iCov, olov eJ ro fj-iv A 
 Tiavrl ™ B 77 TwC, to bk B ixrjbevl tu F. 'AvTicrTpe(f>ofiivu>v yap t&v 
 TipoTAcreatv avdyKr] to F tlvI t£ A fx-q vTrdpxeiv. Anal. Priora, 1.7' 
 ' In all the figures, when the premisses are ineonclusivCj if one 
 is afiirmative and the other universal negative, we get a con- 
 clusion by making the major term the subject and the minor the 
 predicate. E. g. 
 
 Some M is P, 
 
 No S is M, 
 . • . Some F is not S, 
 for conversion of both premisses gives us the first figure.' [Ari- 
 stotle employs conversion because he did not recognize the fourth 
 figure. Conclusions in which the relation of the major and minor 
 terms is inverted were called by the Schoolmen Indirect moods.] 
 Sometimes, however, the opos Tipos 6v designates the predicate 
 of the conclusion. 'Ev fiiratri yap tois els to dh'ivaTov crvXkoyifyp.o'is 
 avdyKrj kowov Tiva Xa^ilv Spov dXXov t&v VTiOKeifxivav, Trpos hv icTTai 
 Tcni x^eiiSovs 6 m)XXoyia-p,6s, Si(tt avTiiTTpacpeicrris TavTr]S ttjs Trpord- 
 (Ticos, Trji 8' er^pas ofioicos ixov<Tris, heiKTLKOs earai 6 (rv\Xoyi(Tij,bs 8to 
 T&v avT&v Spmv. Anal. Priora, i. 29. 'In reductio ad absurdum 
 we must take a third term distinct from those of the problem, 
 and of this third term prove what is absurd. The contradictory 
 of this conclusion and the other premiss of the reductio are the 
 J>remisses of ostensive proof.' I. e. supposing no 5 is P to be 
 proved ostensively thus. 
 
 No M is P, 
 
 All 5 is M, 
 .-. No/S- is P, 
 we may prove it indirectly by combining its contradictory. 
 Some S is P, with either of the ostensive premisses, thus : 
 
 No M is P, 
 
 Some S is P, 
 
 . ■ . Some S is not M. 
 
 Or Some S is P, 
 
 All S is M, 
 . • . Some M is P. 
 In the former case, which is that which Aristotle examines, the 
 
150 NOTES. Chap. XIX, 
 
 new term, M, is the predicate of the false conclusion : in the se- 
 cond ease it is the subject. We may observe that in the first of 
 the passages which we have quoted^ Aristotle seems for the mo- 
 ment to have overlooked the third figure, for there the minor term 
 (irpo9 6v) is the predicate, not the subject, of the minor premiss. 
 
 A proof is said to be addressed to a proposition (irpos tovto) 
 when that proposition is the conclusion or contradictory of the 
 conclusion. 'Ev Sjta<n yap rots sf vi^odecreais 6 ijiev cri/AAoyttr/ios 
 yiviTai irpbs to ixeTakafi^avoufVOv, to 8' e£ apx')^ irepaiveTai 6i' oixo- 
 Aoyia? ^ Tivos a\Kr}s vvoOecreais. An. Pr. 1 . 23. ' In hypotheticals 
 the categorical reasoning is directed to prove the subsumption 
 or condition (the antecedent or contradictory of the consequent) 
 and the original problem is decided by an agreement or hypo- 
 thesis making the problem depend on the subsumption.' "Orav 
 6' 17 Tipoy TO aiiOifJM Koi TTjV TTpoTaa-iv fjiei^ov epyov biaXeyrjvai rj t^v 
 dicnv, hiaTioprta-eifv ai> ns, noTfpov OeTeov to, Toiavra r] ov. Topica, 
 8. 3. 'When a premiss or proposition is harder to prove than 
 the thesis to disprove, it may be doubted whether the respondent 
 ought or ought not to concede the proposition.' 
 
 It appears, then, that wpos 3, when it denotes a term in a syl- 
 logism, excludes the middle ; when it denotes a proposition, ex- 
 cludes the premisses. In the Analytica wepl o denotes the sub- 
 ject of demonstration, or minor term ; a the predicates, or major 
 terms; ^f &i>, not the middle terms, but sometimes the pre- 
 misses, sometimes the axioms or syllogistic canons, 
 
 0] No English word expresses the ambiguity of biovra. For 
 want of a better let us take the word necessary, then we have 
 the syllogism : What is evil ought not to be done, what is evil 
 is necessary, therefore what is necessary ought not to he done. 
 
 6] I. e. TTiv 6e<nv biopOareov. 'EpaJrijo-ts at other times denotes 
 a premiss : herg it denotes the thesis, or the question by which 
 it is elicited. So in ch. xxii, 'O ixev yap ibmKev ipmTrjOeis, 'Epa- 
 TTjcras oSj' 6 «X*'j (Tvvdyei im tov ocra, OJ 6' eiflis ttjv eparqffiv 
 avaipovirres, and in ch. xxiv, Avovcri 6e Tives avaipovvrti Tr\v 
 ipdrtjcrtv. There is the same ambiguity about to KeCptevov. In 
 Topica, 1 . 4, Aristotle says that a premiss is properly introduced 
 by the formula S.pa, and a thesis by the formula -noTtpov, but he 
 himself \aolates the rule shortly afterwards. 
 
 7] For lo-Ti read, or after eorti' insert, abvvaTov. 
 
Chap. XX. NOTES. 151 
 
 CHAPTER XX. 
 
 1] Therefore he was beaten with eyes and you saw him with 
 a stick. One syllogism will stand thus : What he was beaten 
 with was what you saw him beaten with; what you saw him 
 beaten with was your eyes ; therefore he was beaten with your 
 eyes. This we should call an ambiguous middle^ if Aristotle in 
 the text had not objected to the term. The other syllogism may 
 stand thus : He was beaten with that with which you saw him ; 
 what he was beaten with was a stick ; therefore that Asnth which 
 you saw him was a stick. Here the minor is ambiguous. 
 
 2] After (T-qixaCvei trepov we may supply or understand, tu 
 fiimoL TrveviiaTi erepov a-r]p,aivii.. Ae^^ev a-qixaivei erepov is equiv- 
 alent to ipOoyyov (Trip.aivu erepov. The passage shews that written 
 signs of accentuation and breathing were an innovation when 
 this treatise was composed. * 
 
 8] The logician, who reduced all fallacies to equivocation, is 
 probably the person criticized in ch. x, and very likely a Pla- 
 tonist. 
 
 4] This fallacy is alluded to in the Rhetoric, but is not ex- 
 plained. 'AWos TOTtos TO hirjpr]fj,evov avvTiQevTa Xeyeiv ri to avy- 
 keCixevov biaipovvra. 'ETret yap ravTov boKel eivai ovk ov tovtov ttoA- 
 XctKi;, oTTOTepov yfiT\(rni.(LTepov, tovto hei -Koieiv. Eori 8c tovto Y.v6v- 
 br]p.ov Xoyos, oXov to elhevai on Tpvqpi}^ ev Yleipaiei ea-Tiv, eKacrrov 
 yap oibev. Rhet. 2. 34. 'Another source of fallacy is compo- 
 sition and division. As a proposition often seems the same when 
 its parts are differently combined, we may combine them as suits 
 our convenience. So Euthydemus argues : You know the fact 
 that there is a trireme in the Pirseus, for you know every sepa- 
 - i-ate-element of the fact.^ 
 
 5] This is no syllogism, as Aristotle seems to have thought ; 
 it is merely a pretence of stating in one sentence what had pre- 
 viously been stated in two. S is good, ;iS' is a shoemaker, there- 
 fore Sis a. good shoemaker. Here all the three terms reappear 
 in the quasi conclusion. The same may be said of the next 
 example. Evil is bad, evil is a thing to learn, therefore evil is 
 a bad thing to learn. 
 
 6] For (T-novbaiov to jxadrjixa read a-novbaCa fi eiricm/joiij. Mcidr^ixa 
 = T0 ixadrjTOV or to eTTtcTTtjroV. 
 
152 NOTES. Chap. XXII. 
 
 CHAPTER XXII. 
 
 1] Energy or function (thought, sensation) is distinguished 
 from production ((ciVrjo-ts) because the former is complete in 
 character at every moment of its existence, whereas the latter 
 has not its complete character till it ceases. Pleasure, for in- 
 stance, is pleasure at every moment, and the sum of a pleasant 
 emotion only differs from the component parts in quantity. The 
 parts are homogeneous to one another and to the whole. But 
 the process called housebuilding is not completely housebuilding 
 till it is finished. Before that time it is foundation-laying, wall- 
 building, roof-constructing, and these stages differ in nature 
 from one another and from the total operation. If the architect 
 has built a house, he is not still building it ; but the owner may 
 have used it, and be still using it. 
 
 2] For h 6x«t ^kafiev read 6 eXa^iv ^x^i, or, eyei h ika^ev, and 
 below for h ij.fi i\a^fv ex^iv read nfj h f\a^ev ex^iv. 
 
 3] 'EpciTri(ns here signifies the thesis. It is rather an abuse 
 of language to speak of solving a fallacy by contradicting the 
 thesis. To contradict the thesis is not to solve the fallacy, but 
 to admit that the confutation is valid. We were told in eh. xix. 
 that we might, by way of solution, remodel the thesis, when the 
 reasoning disclosed an ambiguity, but here the thesis is not 
 remodelled, it is abandoned. 
 
 4] Solution points out the cause of a fallacy, and the cause 
 "ought to stand the criteria of causation. The solution ought to 
 satisfy what Mill calls the method of difference. If the state 
 of circumstances indicated by the solution deprives the elenehus 
 of its cogency, the reversal of those circumstances ought to 
 make it vahd. No solution, therefore, is true, unless the elenehus 
 becomes sound as soon as we correct the vices the solution indi- 
 cates. But, in the above cases, we may concede the truth of 
 what the solution alleges to be false, and yet the elenehus 
 remains inconclusive. 
 
 5] 'EypA(t)eTo. So read for iypa<j)4 tis. A truth was written; 
 what is written is what was written ; therefore what is written 
 is a truth. Here we may place the fallacy : What is bought in 
 the market is eaten ; raw meat is bought in the market; there- 
 
Chap. XXII. NOTES. 153 
 
 fore raw meat is eaten. Or^ better in Latin : Quod emisti, eome- 
 disti J crudum emisti ; ergo crudum comgiisti. 
 
 6J *A 86 ovx Unavra. So read with one of the MSS. for r^ 8' 
 &T:avTa. The construction is, & fxiv otbev, &Trav rj jxaObtv rj evplitti 
 oihev h be oibev, ov)^ Stvavra f; jiaOav rj tvptav otbev. , 
 
 Similar to this- is the reasoning : Food is necessary to life, 
 corn is food, therefore corn is necessary to life. Food is taken 
 collectively in the major premiss, distributively in the minor. 
 The major does not mean, as Whately says, that some food is 
 necessary to life, i. e. taking some in its logical sense, some 
 particular food; for this would be false, as all food has its 
 substitute. 
 
 7] 'O Tphos &vdp(OTTos is the name of an argument directed 
 aganst the doctrine of Ideas. If, wherever there are similar 
 individuals, we require an idea to account for their common 
 nature, we can set no limit to the multiplication of hypothetical 
 existences. If the likeness of individual men to one another 
 must be explained by an ideal man, then the likeness of the 
 individual men to the ideal man must be explained by a second 
 ideal, and so on, ad infinitum. 
 
 8] 'EKde(ns is used in different senses. In the Analytica it 
 means separating part of the denotation of a term, some of the 
 members of a class, from the rest, and giving them a name. 
 This is one way of reducing Baroko and Bokardo. For instance, 
 let P represent the predicate or major, Jf the middle, and S the 
 subject or minor j then in Baroko we have the following propo- 
 sitions : 
 
 All P is M, 
 Some S is not M, 
 . • . Some S is not P. 
 Separate the portion of S which is not M and call it ^: we then 
 have the following : 
 
 ' All P is M, 
 No Z is M, 
 .-. No.^ is P; 
 which is reduced as Camestres. This Aristotle describes as 
 follows : 'AvAyicr] eKdefxevovi <o Tivl eKorepov irfi vvApxei, Kara tiovtov 
 ■noieiv Tov <Tv\\oyi,crp.6v. "Eorat yap avayKalai em tovtwv. El be 
 Kara tov exTeOevTos ea-rlv avayKoios, Koi /car' eKeCvov twos, to yap 
 
154. NOTES. Chap. XXII. 
 
 iKTfdev 5-nep ineTvo tL iariv. An. Pr. I. 8. 'We must isolate 
 that portion of the minor of which the middle and major are 
 denied and make it a new minor. Then the premisses are neces- 
 sary propositions ; and whatever is universally true of the new 
 minor is partially true of the old ; for the old is the genus of 
 the new.' 
 
 In the present passage enOea-n signifies separating part of the 
 connotation of a term from the rest, the specific from the indi- 
 vidual or the generic from the specific j and we are reminded 
 that this may be a purely mental or logical separation, not 
 physical or real. 
 
 In the Metaphysica fKdfcris is used for real separation. Tovto 
 8' eKivjjo-e ixev "EwKpdTtj's bia roiii bpUTjxovs, ov p-riv f^wpwi ye rfiy 
 KaO eKacTTov. Kal tovto dpScSs evoijcrev ov ^tapLcas. A-qXoi bi ex 
 T&v ipyiov &vev jJikv yap tov kuOoKov ovk iarw einvT'^ixrjv Xa^eiv, 
 TO be ^(liplQiiv aiTLOV T&v (Tvp,paiv6vTu>v bv(Txep&i> irepl tos ibeas 
 €(TtCv. Ot S' d)S avayKOLOV etwep ecrovTai rivis ovaiai Trapa ras 
 ala-Orirai Kal piovcras, xt<>/3tf ray eXvai, ahXas p-iv ovk ftx"") '"owas 
 8e Tas KadoKov Keyop,4vas eiidiaav. Met. I3. 9. 'Attention to 
 universals received an impulse from the Socratic definitions : but 
 Socrates did not separate them from particulars, and he did well, 
 as the result shewed. For universals are indispensable to 
 science, but their separation from the objects of sense produces 
 the difficulties of idealism. The idealists saw that substances, if 
 there were any besides the objects of sense, must have a separate 
 existence, and not knowing what else to assign, hypostatized 
 universals.' Compare, 'A\X' 6 ixev SaiicpiiTjjs to, Ka66\ov ov x<fl- 
 ptora eTTotei o^Se tovs opiaixovs' ol 8' ex^pi-a-av, kol to. Totavra t&v 
 8vTmv Ibias irpoarjyopevaav. Met. 12. 4. 'Socrates assigned no 
 independent existence to universals and the objects of definition. 
 The Platonists separated them from the world of sense and 
 called them ideas.' 
 
 9] The idealists supposed that the existence of ideas was an 
 indispensable logical hypothesis. It was to them what the uni- 
 formity of nature is to modern logic. No ideas, no science, was 
 their notion. Aristotle contradicts this in the Analytica : EJ61) 
 piiv ovv itvai, T] ev ti Trapa to. itokXh, ovk avdyKT], ei diro'Seifis iO-TM' 
 tlvaL fx4vToi ^v Kara ttoKK&v aXrjOes eiTreif, dvayKt]. Ov yap icrrai 
 TO KadoXov, hv p.1} TOVTO ^' lav 8e to KadoKov p.ri ■p, to p,i(TOV ovk 
 
Chap. XXII. NOTES. 155 
 
 iurai, &<TT ovb airohn^is. Aet apa rt ev kol to airo em ■n'Kiwvmv 
 ftvai ij.ri oixdvvixov. An. Post. i. ii. ' Th# existence of ideas or 
 substantive unities independent of the world of sense, is not 
 indispensable to demonstration : the existence of classes, or uni- 
 form relations (attributes) declarable of many individuals, is. Un- 
 less one and the same thing were predicable univocally of many, 
 there could be no demonstration, for there could be no middle 
 term to comprehend the minor.' In the text Tiaph. is used in an 
 unusual sense. In Aristotle to €v itapa, to, ttoWo, usually denotes 
 the idea : here it denotes the universal. The doctrine that Aristotle 
 here enunciates is Nominalism, i. e. that the similarity of uni- 
 versals to substances is merely grammatical (evrfj A.efet), the only 
 point they have in common being their name, nomen substan- 
 tivum. The words eirl Trairiv imply an exception, which, I sup- 
 pose, refers to the active or objective reason {vovs irottjri/co's). 
 
 10] Whately considers that the fallacy of figura dictionis con- 
 sists in taking for granted that paronyms, i. e. nouns, verbs, 
 adverbs, adjectives, derived from the same root, like design, 
 designing, art, artful, project, projector, have a precisely corre- 
 spondent meaning. In English this is not so, and the fallacy 
 thence arising may be fairly classed under fignra dictionis. But 
 this was not Aristotle's view. In Greek, a more regularly con- 
 structed language, the meaning of paronyms, with very few 
 exceptions, does exactly correspond; and paronyms {to, avaToixa) 
 were a locus of dialectic, i. e. valid reasoning. MdXtara 8' eirt- 
 Kaipoi Kal KOivol t5>v Toncav o'i t e/c t&v avTiKeifxivaiV Koi t&v crvcrroi- 
 Xav KOL r&v TTTma-ecav o/nottos yap evbo^ov to dftSo-at. Topica, 3. 6, 
 ' The most effective and universally applicable topics are those 
 from opposites and those from paronyms, for a proposition 
 transferred to an opposite or a paronym is just as probable as in 
 its original form.' This is another instance of the proximity 
 (yetrvtao-ts) of dialectic and sophistry. 
 
 Paronymous words (irapdwixa.) are different modifications of 
 the same root ; like-figured words {oixoiocrxruxova) are similar mo- 
 difications of different roots. Homonymous words appear to 
 denote things entirely identical; like-figured words appear to 
 denote things belonging to the same class, order, or category ; 
 paronymous words appear to denote things variously correlated 
 to the same standard of reference {irpos ev) . In Greek the things 
 
156 NOTES. Chap. XXII. 
 
 not the words are called 6iJi.(avviJ,a and isapt&vviw., so that these 
 definitions would require modification. 
 
 CHAPTER XXIII. 
 
 1] For ffx^vxpv read a^vxpv. ^ ATTotfiria-avTa fir] elvai {a\jfV)(ov) 
 denotes the thesis, and is equivalent to (jj-rja-avTa etvai fjxijfvj^ov 
 Su/njSaii'ei denotes the conclusion of the confutation. 
 
 CHAPTER XXIV. 
 
 1] Prom this it might seem that every solution by fitajpeo-ts, 
 as well as every solution by avaipeuis, and every proposition of 
 the questioner, was to be supported by induction : but Aristotle 
 does not impose this obligation when speaking of any other 
 fallacy. 
 
 2] Here the attribute (unknown) of the accident (about to be 
 asked) is transferred to the subject (the summum bonum). It 
 would be easy to state any of these fallacies so that the attribute 
 of the subject should be transferred to the accident ; e. g. if we 
 inferred that because the summum bonum was known, therefore 
 the question about to be asked was known. [The fallacy seems 
 really to be amphibolia. The premiss, nescis quid sim te roga- 
 turus, is employed as if it were, non novisti quod sum te roga- 
 turus.] 
 
 3] The fallacy seems really equivocation, a confiision between 
 the two senses of knowledge, old acquaintance, and recognition 
 on a particular occasion. 
 
 4] In these two examples there is no syllogism, for all the 
 three terms appear in the quasi conclusion. There is only a 
 pretence of expressing in one sentence what had previously been 
 expressed in two. The principle of the fallacy seems the same 
 as that of the good shoemaker, which was put under the head 
 of composition and division. 
 
 5] This excentric syllogism may be illustrated by the follow- 
 ing : Oxygen combined with hydrogen is water ; oxygen com- 
 bined with hydrogen is oxygen, therefore oxygen is water. Or : 
 Oxygen is gaseous j oxygen combined with hydrogen is oxygen ; 
 therefore oxygen combined with hydrogen is gaseous. The 
 fallacy may be regarded as equivocation. In one premiss, four 
 
Chap. XXIV. NOTES. 157 
 
 multiplied by four means the product of the factors, in the 
 other, only the first-named factor. 
 
 6] For avaipovvTes read btaipovvres. 'Eptorrjo-ts here, as in ch. 
 xxii, is the thesis. But when we point out an ignoratio elenchi, 
 it is not necessary to remodel or abandon the thesis [avaipelv) . 
 It is sufficient to shew that it is not contradicted {biaipe'iv). 
 One MS. reads ov biaipovvTes. This seems to be the query of 
 an intelligent reader. 
 7] See ch. xx. 
 
 8] Here again (see ch. xxii, note 3) we have by implication 
 the strange expression of solving a fallacy by contradicting the 
 thesis. The syllogism seems to have been : A four is a small 
 number ; a four multiplied by a four is a four ; therefore a four 
 multiplied by a four is a small number. 
 
 9] Aristotle does not speak very accurately. He said in 
 ch. iv. that a term is ambiguous whether the plurality of signi- 
 fication is (i) proper^ or (a) customary, or (3) merely arises in 
 combination. 
 
 10] From this expression it might seem that Aristotle con- 
 sidered the fallacy to belong equally to per accidens and to 
 composition. 
 
 11] The pui-port of the passage seems to require a mark of 
 interrogation after KaK&v. 
 
 12] Aristotle seems to mean that there would be a fallacy of 
 composition. But if Davus is good and belongs to bad masters, 
 the conclusion that something of the bad is good follows without 
 any fallacy of composition. Aristotle is in difficulties from re- 
 fusing to admit that the genitive is ambiguous, at least has a 
 partitive and relative as well as a possessive force. Yet he repu- 
 diates as an impossibility the proposition, elvai r&v kuk&v ti 
 ayaOov. But what is there paradoxical in this unless its first 
 and most obvious, i. e. proper, meaning is, that some evil, is 
 good, in other words, unless the genitive is partitive ? This was 
 recognised by subsequent grammarians as its original meaning, 
 when they called it the genus-predicating case (yevurj ■nT&aris). 
 
 13] If the expression is not ambiguous, how would Aristotle 
 solve the fallacy. What is of the animals is the property of the 
 animals, man is of the animals, therefore man is the property of 
 the animals ? He could not refer it to any of the heads of fallacy. 
 
158 NOTES. Chap. XXIV. 
 
 but apparently would be obliged to deny the minor (see eli. xvii, 
 A^kov ovv fv oh a(ra(t>es to TipoTfivoixevov ov avyx<i>P'nTiov awAws), 
 which would be a very unsatisfactory mode of solution. 
 
 14] The fallacy per accidens has been generally misunder- 
 stood, which seems to shew that it is an ill-defined species. We 
 might do well to drop it from the list and distribute its contents 
 among the other classes. The principle which, in order to solve 
 it, Aristotle brings to bear against the sophist, namely that the 
 predicate of a predicate cannot be inferred of the subject, unless 
 one of the premisses is an essential proposition or even a defini- 
 tion, is far too sweeping; and if admitted would upset nine- 
 tenths of the syllogisms ever constructed. If we retain the class 
 in order to comprehend the instances given in ch. v, i. e. all the 
 cases of illicit process and undistributed middle that are not 
 comprehended in eonsequens, it would be well to give the class 
 a more appropriate name than accidens, and make one class 
 represent both accidens and eonsequens. 
 
 CHAPTER XXV. 
 
 1] Whately, followed by Mill and De Morgan, makes per 
 accidens the converse of secundum quid. He confines the second 
 to the ease where a term is first used with a limitation and 
 afterwards without, and per accidens to the opposite ease, where 
 a term is first used without and afterwards with a limitation. 
 But it is plain that with Aristotle secundum quid included both 
 the case where a term has a limitation in the premisses and not 
 in the conclusion, and vice versa ; and both the case where the 
 limitation is in the conclusion but not in the thesis, and that 
 where it is in the thesis but not in the conclusion. 
 
 2] For vyiaCveiv read apxuv. 
 
 3] So we must read with one of the MSS. : the others give 
 TO yap Xa^iiv aya6bv ayadov. 
 
 4] NiKai'. So read, in spite of MSS., for KpLvuv. Perhaps 
 too, below, for hUaiov ea-riv iKav&s Xiyfiv, we should read bUaiov 
 f(TTi viKCLV \eyovTa, or biKai,6i> eerri vLKav os \iyei. 
 
Chap. XXVIII. NOTES. 159 
 
 CHAPTER XXYI. 
 
 1] See eh. v. 
 
 CHAPTER XXVn. 
 
 1] 'Eiret TO y epu>Tav afx^ilioKa xai to. napa ttjv oyL(iiwp.iav, oaai. 
 T aX\aL TOLavrai •napaKpova-eis, koI tov aXi^dwov eXeyxov ac{>aviCei, 
 KOI TOV iXeyxpixevov koX pH] iXeyj^opevov tiSrjAov Troiei. . . "ASjjXov 
 yap d a\ri6rj Ae'yet vvv. . . Nvv be, ha to /xtj KaX&s eptoTav tovs 
 T!vvdavop.ivovs, avdyK-q Trpo(Ta-noKp[ve(r9aC tl tov €poiTcap,evov, biop- 
 dovvTa TT]V pL0)(6ripCav rfjs irpoTdaftos. Ch. xvii. 
 
 CHAPTER XXVm. 
 
 1] For avTiOea-eis read avTicjida-eis. The generic term dvTiKei- 
 p.evov which foUowSj and which caused the false readings is only- 
 used because avTL(pr]p,i, has no perfect passive participle. If A 
 and B are related as antecedent and consequent, that is, if all 
 A is £, one form of fallacy is to assume that all £ is A. This 
 in hypothetical reasoning is to infer the truth of the antecedent 
 from the truth of the consequent. Another form is to assume 
 that all noi-A is not-_B. This is to infer the falsehood of the 
 consequent from the falsehood of the antecedent. ArjXov ovv otl 
 Ttpbs afKpoi a.VTi,(TTpe(fiei r) Kara Trjv avT[(l>acriv anoKovBrjcns avairaKiv 
 yivofiivT]. Topica, a. 8. ' Whether the original terms are aflBrma- 
 tive or negative, in both cases the contradictories of the original 
 terms have their sequence in an inverted order.^ The false read- 
 ing is probably the origin of the name of the famous conversion 
 by contra-position. The logicians who used the name used it 
 without a m^eaning, and were not troubled by the fact that in 
 the rest of their system avrCOeais had been translated opposition, 
 not contra-position. In the above-quoted passage wpos ap.(j)ia 
 avTHTTpicjiei yivop,ivr] = en aiJ.<poiv 6p,oLa>s yiviTai. 
 
IGO NOTES. Chap. XXX. 
 
 CHAPTER XXX. 
 
 1] TavTa, so read for ravra. In the preceding line, after 
 ■naXiv, add, or understand, avAyK-r] avii-ftaivnv {ntevavTiaiiia. 
 
 2] For eirel b" read ^iretdrj. 
 
 33 Read, ei to jjlIv dyaOov yiverai, to 5e KaKov, hvo yivovr hv 
 ayada 7] hvo koku, or something similar. 
 
 4] Whately, forgetting that the names of the fallacies are 
 taken from a treatise on Eristic, i. e. catechetical disputation, 
 thinks that the questioning in plurium interrogationum is 
 merely a rhetorical figure, and that this fallacy merely differs 
 from homonymia because the orator, to give animation to his 
 discourse, puts his assertions into the form of interrogations, 
 making believe that he expects an answer. But the examples 
 given shew that the peculiarity of plurium interrogationum is, 
 that the premisses are in the form, A and B are X and T, and 
 that there is no ambiguity in the principal terms A, B, X, Y, but 
 only in pronouns and syncategorematic words, such as they, 
 themselves, both, all. 
 
 The error of treating two questions as one is independent of 
 diction, and therefore Aristotle has placed this class among the 
 fallacies extra dictionem : but as after this error has been com- 
 mitted no fallacy arises unless the questioner takes advantage 
 of an ambiguity, it seems it ought to be classed with the fallacies 
 in dictione. But throughout this treatise Aristotle seems in- 
 clined to differ from the logician, perhaps the theorist criticized 
 in ch. X, who reduced all fallacies to equivocation. 
 
 CHAPTER XXXI. 
 
 1] Perhaps we should read, otov StirA.dcnoi' &vev tov fmiatos h 
 Tu hvn\A<nov fjixCa-eos. 
 
 2] To €v TTJ &Tro^A<Tei. So read for rb h tm rjixia-fi. 
 
 3] Tavro. So read for tovto, 
 
 4] 21/.10S and paifios lose part of their connotation when joined 
 to substantives. Taken separately they mean something more 
 than Koi\6s ; but (xijxq pis and paifiov (TKfKos mean no more than 
 Koi\ri pCs and koi\ov (XKiKos. This must be the gist of the 
 
Chap. XXXI. NOTES. 161 
 
 passage, but it is not easy to get it from the text. If, with 
 some MSS.j we omit the words ev6a /jikv yap t6 cifiov, hOa 6^ to 
 paipov (rr\iiaivu, we may read, ■npoa-Tidijj.evov 8' ovb^v KooXvei &Kko 
 TO ijiev Ttj pivl TO 8e rm o-iceAei (TTjjua&eij'. Bekker's reading, avfj.- 
 paivfi. instead of the first oTjjotaiVet, is merely a conjecture of 
 Pacius, and does not make the passage more intelligible. 
 
 5] The sophistic locus of tautology may be considered as a 
 caricature of a dialectic locus. One fault which dialectic criti- 
 cism finds with a definition is the introduction of superfluous 
 words. OvK ^<TTi be to 5tj (pQiy^acrdai toutov ovofxa r&v aTOTimv, 
 a\ka TO TtkeovaKis irepl tivos rb ovto KaTriyopfjaai, olov us Bevo- 
 Kp6.Tr]s Triv (ppovrjcnv bpi(TTiKT\v KOi 6fa)pr\TiKr]V t&v SvTav ^rjcrlv 
 ftvcu. 'H yap opKTTiKrj OecoprjTiKrj tis kdTiv, &(rTe his to ovto Aeyet 
 Ttpoo'Bih ir(i\ii; xai deoapriTiKi^v. TldMv el tov Ka66\ov eiprnxivov 
 ttpoaOeir) koX em /xipovs, olov el rfjv iTneUeiav eXaTTCotriv t&v (rvfi- 
 ^epovTutv Koi hiKaimv to yap hUaiov avp-K^epov ti, &aTe Tiepie^eTai 
 ev Tu crvp,<t)^povTr itepiTTov ovv to hiKaiov. Kot el Tr\v laTpiKrjv 
 eTTKTTijjiijji' T&v vyiew&v C4'9 ""^ avOpcoTra, ?) tov v6\wv ehova t&v 
 <f>Tu<reL Ka\&v koI biKaiav to yap bCKaiov Kakov ti, (Sore ir)\.eov&Ki,s to 
 avTo Xeyei. Topiea, 6. ^. 'It is not the recurrence of a word 
 in a sentence that is to be condemned, but the reiteration of 
 an identical predicate. Xenocrates is guilty of this when he 
 says that wisdom defines and inyestigates truth, for to define 
 is to investigate. The following definitions, which assert the 
 particular after asserting the universal, are tautological. An 
 equitable spirit is a willingness to have one's interests and 
 rights reduced. Rights are included in interests and the word 
 is superfluous. Medicine is the science of what is wholesome 
 to animals and men. Law is the copy of the naturally beautiful 
 and right. Right is included in beautiful.' noWdxis yap \av- 
 Bdvova-i TOVTo TTOiovvTes (wA.eoi'd/cts XeyovTes to aino) Kai iv TOis 
 IbCois Kadd-nep koi ev roTs opoK. Ouk eorai 8e Kak&s Keifxevov to 
 TOVTO ■neTTOvBos Ibiov. Tapdrret yap tov aKOvovra to TikeovAKis 
 ke^Bev. 'Acraipes ovv avayKalov icrri yLvecrBai, koL irphs toiJtois 
 abokeaxelv boKovinv. Topica, 5. a. 'There is often a latent 
 tautology in statements of property as weU as in definitions. It 
 is a fault, for it obscures the meaning, perplexes the hearer, and 
 shows an incontinence of words.' 
 
 M 
 
162 NOTES. Chap. XXXII. 
 
 CHAPTER XXXIL 
 
 1] If for the neuter tovto we substitute the masculine, which 
 distingnishes the nominative and accusative, we find there is an 
 ambiguous middle; and that the solecistic conclusion does not 
 legitimately follow unless we substitute a false major or false 
 minor premiss. Adopting the English collocation of the subject 
 and predicate we have the following as the true syllogism : 
 
 Minor : To vTSOKeiiLSVov la-riv oiros hv Xe'yeis awo etvai. 
 
 Major : OSros hv kiyeis avrh elvai i<m KLQos. 
 
 Conclusion : T^ vwo/cei/xeroi> apa ^crri kCdos. 
 The solecistic conclusion requires either the false and solecistic 
 minor. 
 
 To viioKil.p.evov ia-Ti tovtov hv Xiyen avTO flvai, 
 which with the true major. 
 
 To TOVTOV hv K^yeis ovto etvcu, arniaivii to \(,6ov, 
 gives the conclusion, 
 
 To VTroiceCfievov &pa ea-n \l9ov : 
 or the false major. 
 
 To oSros hv kiy (IS ovto eivai arjfiaCvei to \iQov. 
 
 2] F.lT!iiv. So read with one of the MSS. for Hiriv. After 
 oSros add ^ tovtov. Then the complete sentence is, "SvKov 8' 
 ehteiv oiroi t) tovtov ovbev bt,a(j}4pei, where oSros and tovtov merely 
 represent cases, their gender being disregarded. 
 
 3] For Tov Kldov (rrip,alv€iv oSroy, read Kldov o-r/jnofoeu; to oStos. 
 Here Aristotle assumes that the conclusion depends on a false 
 major premiss ; above he assumed that it depended on a false 
 minor. As the reasoning relates not to things but to words, 
 the realistic copula eanv is replaced by the nominalistic copula 
 aT]p,aCveL. 
 
 4] We have MS. authority for omitting the article before 
 \l6ov. In the infancy of grammar Aristotle could not give a 
 very lucid explanation from the want of technical terms : but 
 he has sufficiently shewn that no solecism can enter a valid con- 
 clusion unless there was already a solecism in the premisses; 
 and that the paralogism of solecism depends on the ambiguity 
 of the neuter pronoun, which has the same form for the nomina- 
 tive and the accusative. 
 
Chap. XXXIII. NOTES. 163 
 
 CHAPTER XXXftl. 
 
 1] M€Ta(j>epe(Tdai. is the characteristic of a dialectical as opposed 
 to a scientific principle^ or, within the limits of scieneCj of an 
 axiom [kolvti ap)(fi) as opposed to a thesis {ibCa apxfi), that is, of 
 a method as opposed to a doctrine. It is an ontolog^cal proposi- 
 tion, and has no relation to any one object of thought more than 
 to any other. [TSj" TSTpay<ovi(Ty.5)v'\ tov fj-lv ovk ecru ixerevfyKeXv 
 bia TO SK T&v i&Caiv tlvai apx&v, tov 6e irpos itokXovi, dpjuotret y&p. 
 Ch. xi. Kant would explain its universality by making it sub- 
 jective, i. e. part of the framework of the logical faculty, only 
 regarding as objective truths those which are specific and 
 limited in range. The falsifications of dialectic maxims may be 
 regarded as the Kowai apxai of eristic. The character of trans- 
 ferability, therefore, is common to dialectic and eristic principles. 
 
 2] This was Dugald Stewart's opinion. He thinks the book 
 of Sophisms the most useful part of the Organon, and that it 
 supplies a very convenient phraseology for marking concisely 
 some of the principal fallacies which are apt to impose on the 
 understanding in the heat of viva voce disputes. However, he 
 expressly excepts the fallacies in dictione as too contemptible to 
 be deserving of any notice. Philosophy of the Human Mind, %, 3. 
 On the other hand, see the examples accumulated by Mill under 
 the head of Ambiguity. 
 
 S] This idea, expanded by Wallis, is somewhat overpraised by 
 Dugald Stewart, who was ignorant of its parentage. He tran- 
 scribes the words of Wallis " for the benefit of those who may 
 hereafter speculate upon the theory of wit." Philosophi/ of the 
 Human Mind, Note M. 
 
 4] Head, rts 6 avoijfievos ; 
 
 5] Bead, oixoCais 8e koI iiapa to crvpi,fiePriKbs koI irapa tSv &\X.a)v 
 
 €Ka(TTOV. 
 
 6] KlTre'iv usually denotes rather the substance than the words 
 of a speech : but in the Rhetoric, as here, it is used to designate 
 diction. Ov yap dTro'xpjj to sx^lv h SeT kiyeiv, aAA' avAyKYj Kal 
 TavTa d)S 8ei direlv, Koi crvuPiWeTai ttoWo, irpos to (pavrjvM ■no'iov 
 nva TOV \6yov. Rhetoric, 3. i. 
 
 7] The meaning of f*erari0e/xe//ijs appears from the Analytica. 
 
 M a 
 
104 NOTES. Chap. XXXIII. 
 
 To 8' avTKTTpe^eLV lorl to niraTidivra to crviJLiTipaa-ixa iroieiv tov 
 crvWoyia-iJMV ori ^ Tb &Kpov t& ii.i(Tio ovx vTrdp^ei fj tovto t£ Tekev- 
 Toift). 'AvdyKTi yap rov crvimepAcrixaTos kvTicnpa(^ivTOi koL t^s 
 kTipas pievo-ucrris TrpoTourecos avaipeta-Qai ttiv Xonrrjv. An. Priora, a. 8. 
 ' Conversion here means the employment of the contradictory 
 of the conclusion as a premiss to disprove the original major or 
 minor premiss. For the contradictory of the conclusion com- 
 bined with either of the premisses will upset the other.' Thus 
 we shall have three syllogisms all equally probable and im- 
 probable. 
 
 All M is P, 
 
 All S is M, 
 . • . All S is P. 
 
 All if is . P, 
 
 Some S is not P, 
 
 . • . Some S is not M. 
 
 Some S is not P, 
 
 All S is M, 
 
 .-. SomeifisnotP. 
 
 8] We have observed, before that a syllogism with a false 
 premiss may be either dialectic (ei yap « \jrevb&v p-ev kvbo^cov 
 b4, Xoyoco's. Topica, 8. 12), or sophistic^ or pseudographie. See ch. 
 xviii, note 1. Grote has pointed out that under these circum- 
 stances it must be excessively difficult, not to say impossible, 
 to draw a line between sophistic and dialectic proof. Certainly 
 there is nothing here like extinction of species to establish a 
 gulf between the genera, and the boundary, if there is one, can 
 only be fixed somewhat roughly, as between right and wrong 
 in morals, by the arbitration of common sense, — as &v 6 ^povip^s 
 opla-€iev, 
 
 9] Th b\ yvp-va^icrQai hvv6,p,iias X^P'^j "<*' p.a\urTa irfpl tos irpo- 
 Td(T€is Koi kvoT&aeK. "'Eort yap is anrXSs eJiretf StdXeKrtKos 6 upo- 
 TOTLKos Kal eva-rauKOi. 'Eort bi to piv ■npoTeive<rOai Iv ■noniv ra 
 irXeto), bei yap iv 8A&) krjtpdrjvai, Trpos & 6 \6yos, to 6' kviaTatrQai to 
 If 'KoXXA' fl yap biaipei rj avaipei, to p,ev StSoiis to b' ot t&v vpo- 
 T€tvopi,4va)v. Topica, 8. 14. 'Facility comes by practice, and is 
 chiefly shewn in proposition and enstasis. For dialectic power 
 is the power of putting propositions and raising enstases. Pro- 
 
Chap. XXXIII. NOTES. 165 
 
 position reduces plurality to unity; for the subject in dispute 
 must be referred to a class. Enstasis reSblves unity into plu- 
 rality; for it distinguishes inconclusive from conclusive proofj 
 or divides a universal proposition into particulars, of whicli 
 some are granted and others denied.' 
 
 10] There is a similar statement in Topica, 8. ii. E^tj 6' av 
 •noTe X6yos Koi, (m/xTreTrepacrjueVos juitj (Tv^imenepadfj.evov yjsipwv, otav 6 
 liev If evri8&v avixTiepalvryrai nr\ toiovtov tov irpojSAijpiaros ovros, 6 
 8^ •npo(Ther\Tai TOw{ira>v & iartv evbo^a Kal aXrjdil], koI p/f) ev Tois 
 "npoa-kap.^avop.ivois j) 6 Ao'yos. 'A complete proof is of inferior 
 merit to an incomplete proof, if the premisses of the former are 
 more improbable than the conclusion requires, and the premisses 
 to be supplied for the latter are both probable and true and only 
 remotely related to the conclusion.' 
 
 11] 'Eo-Ti 81 \6yov KOjXCorat (Tvp,TTepdva<70ai Terpax&s. *H yap ave- 
 kovra -nap' o yivexai to \|feSSos, rj irpbs tov epa>T&VTa evcTTatnv 
 eVnovTa' TtoKk&Kis yap ovbk kikvKev, 6 p-ivToi Ttvv6av6fievos oil bvva- 
 Tai -noppaTepm irpoayayeiv rptrov he irpos to, ripa)Tr]p,4va' avp,^aCri 
 yap &v ex piev t&v fipa>TriiJ^v<ov p,ri yCvecrOai b j3oi;Xerat 8j^ to kuk&s 
 ■^pwTjja-Oai, Trpoo'TeddvTos bi tivos yCvea-dai to <n)p,nsipa<Tp.a. Ei p.\v 
 ovv p.r]KeTi dvvaTUL -npodyeiv 6 epaT&v, trpbs tov epatT&vTa eftj h.v f) 
 ivaratris, el 8^ bvvarai, irpos to, ■qpcoTrjp^va. TeTdpTrj 6e Kal yeipiarrf 
 T&v kvffT&crewv fi -irpos tov \p6vov ^vioi yap Toiavra ivCa-TavTat irpbs 
 h hia\e)(6rjvai irXetovos eari yjpovov t^s ■napo'6(rr]s biaTpi^^s. Ai p,iv 
 ovv evirrda-fis KaOincep eiirap,ev Terpax&s yivovrav kuais 6' eort t&v 
 elprndvwv f] irpatTri p.6vov, oi bk \on:al KaiXva-eis Tivh kuI ep,Trobi(rnol 
 T&v o'vixTrepaa-p.a.Tav. Topica, 8. lo. 'There are four modes of 
 preventing proof: first, the repudiation of a false premiss; se- 
 condly, an objection that silences the prover, for he is sometimes 
 silenced by an objection not really fatal; thirdly, an objection 
 that meets the premisses ; for though the premisses are at first 
 inadequate, some further addition might make them adequate. 
 K the prover cannot complete the proof, he is silenced; if he 
 c^n, only the original premisses are met. The fourth and worst 
 enstasis is addressed to the time. For an objection may require 
 a longer rejoinder than the time permits. Only the first of 
 these enstases is solution, the rest are merely evasions and hin- 
 drances of proof.' The argumentum ad hominem of the school- 
 men seems a translation of Aristotle's avWoyLapbs vpbs rbv duo- 
 
166 NOTES. , Chap. XXXIII. 
 
 Kpivofxevov, but it does not mean the same thing, for the latter, 
 it appears, is not addressed to the opinions but to the powers of 
 the disputant. Argumentum ad hominem corresponds better 
 with pirastic proof, the premisses of which are the opinions of 
 the respondent. The argumentum ad verecundiam may refer 
 to the locus of authority or to the locus for entrapping in para- 
 dox, the discrepancies of secret and avowed opinion (eh. xii) . 
 
 CHAPTER XXXIV. 
 
 1] SoXoiKtcr/iios. So read for avkkoyiaiioi, and o-oAoiKKr/uois for 
 (TvkKoyLtTiwv'i below. For this excellent emendation we are in- 
 debted to Pacius. 
 
 2] H i/lkv TipoOtdis T7JS TipayiJ,6.TiLas jXiOohov fvpiiv, a<f rjs bwrj- 
 aopieOa avWoyC^eadai Ttepi wazros tov tipoTedevroi TipoPKrjpiaTos ef 
 ivho^av, Koi avTol Xoyov vvixovTes firjOev fpovfifv virevavTiov. To- 
 pica, I.I. ' The aim of our inquiry is the invention of a method 
 that shall enable us to reason with probable premisses on every 
 problem that may be proposed, and to maintain any theses 
 against attacks without self-contradiction.'' ITept 6' cmoKpiafbis 
 TTp&Tov p.(v hiopicrriov ri icrriv epyov tov Ka\&s airoKpivop.evov KadS.- 
 •nep TOV Ka\d>9 ep<DT&VTos. Eort be tov kuX&s epcoT&vros ovtoos fna- 
 yaytlv tov \6yoi> ojcrre Tioirj(Tai tov anoKpivdixevov to. dSoforara 
 \iyeiv T&v bia ttjv Oiaiv avayKaiuiv, tov 8' emoKpwoixivov to pr/ bi 
 aiiTov (patvea-Oai avpfiaivnv to abvvaTov rj rb irapAbo^ov aWa 8ia 
 Trjv decriv fTfpa yap taws apapTia to OicrOai vp&Tov o pr] Set km to 
 6ipivov pj\ (f>v\6.^ai Kara TpoTiov. Topica, 8. 4. ' To determine rules 
 for the answerer, we must first define the aims of the questioner 
 and answerer. The aim of the questioner is so to conduct the 
 reasoning as to force the answerer to the most improbable pro- 
 positions necessitated by the thesis : the aim of the answerer to 
 make the impossible or paradoxical propositions appear due not 
 to himself but to the thesis. For it is a difierent fault to ad- 
 vance a wrong thesis, and after advancing it not to defend it as 
 well as one might.' KaTh Tpo-nov here, and opoTpo-nuts in the 
 text, seem to mean, not consistently or without self-contradic- 
 tion but, with a degree of probability that varies with the 
 thesis. 'Etici 6' 6 koAus cruAXoytfo'/iiei'os ef ivbo^oTepaiv koI yvapir 
 poiTepiov TO ■npo^Xr)d\v aTrobeiKvvcn, (pavfpbv ws &b6^ov pev ovtos 
 
Chap. XXXIV. NOTES. . 167 
 
 ciirX&s Tov KeijXivov ov horiov tu aiTOKpLVO[i,iv(a ovff h fxri boxet 
 av\&s, ovff o boKsi fjLev tjttov 8^ tov criz/iiTreociir^aros Soxet. Topica, 
 8. 5. ' As premisses should be more probable and certain than 
 •conclusions, when the thesis is improbable, the answerer may 
 refuse both all improbable premisses and all which though pro- 
 bable are less probable than the contradictory of the thesis.' 
 Aoyov vitiyi'-v seems nearly the same as diaiv (pvXarTeiv. 'Tirix^iv 
 hk KoX Oidw Kol opiajixiv avTov aiJru Set Trpoey)(eipri(TavTa. . . ^Abo^ov 
 8' VTrodeaiv evXa^rjTiov vnexuv. Topica, 8. 9. 
 
 S] Throughout this treatise the questioner has represented the 
 sophist ; so that we were hardly prepared for the announcement 
 that answering is the sophistic side of dialectic. The rest of the 
 Topica, however, is written more from the point of view of the 
 questioner; and the answerer appears as a sophist. 'Ewtr^/xjjirts 
 6e \6yov kut ovtov re tov \6yov Kat orav epioToxai o^x V o'^''^- 
 rioXXd/cts yap tov pifj Kah&i hieikexOai tov koyov 6 kpuiT^jxevos atnos 
 ha TO p,fi avyxapfiv ef &v ^v bLa\e\drivai Ka\&s irphs ttjv 6f<nv. Ov 
 yap ea-Tiv i-nl OaTepa p,6vov to KakSn einTekea-B^vai rb koivov epyov. 
 'AvayKaiov ovv eviOTe irpos tov KeyovTa Koi jutj irpos ttji' decriv ewt- 
 Xetpeiv, orav 6 anoKpLvojXfVos TavavTla ru kpu>T&VTi TiapaTrjpfj ir/aocr- 
 (TtripeACaiV. AvffKokaivovTes ovv ayavia-TiKhs Koi ov SiaXeKrtKOS tiol- 
 
 ovvTai Tas Starpt/Sds 'Eirel be (jyavkos Koivoovbs 6 ipLTTobCCav to 
 
 KOIVOV epyov, brjKov oti koi ev Ao'yu. Koivbv yip tl koI kv to^tols 
 •npoKelixevov ecrTi, Ttkriv t&v aycaviCofievoov. TovTots 8' o£k e<TTiv ap^ 
 0OTep(Jts Tvxe'iv tov aiiTov rekovs. Aia<})ipei 6' ovbev av re bia tov 
 aitoKpivtcrBai av Te bia tov kp<oTav -noi^ tovto. "O re yap ipicrTiK&s 
 epmT&v (f)avka>i biakiyeTai, o t iv t(3 &moKpi,ve<T6aL p.r\ bibovs to (pai- 
 v6p,evov p,r}b' inbexpixevoi o tC -nore ^ovXerai 6 kpa>T&v ■nvdecOai. 
 Topica, 8. II. "In criticising we must distinguish between the 
 argument and the arguer. The badness of an argument is often 
 imputable to the answerer who refuses to grant the premisses 
 which would fairly confute the thesis. For it is not in the 
 power of one of the disputants without the co-operation of the 
 other to accomplish successfully their joint task. Accordingly, 
 the questioner is sometimes forced to argue against the answerer 
 instead of against the thesis, if the answerer takes every means 
 of thwarting him with unscrupulous effrontery. This perversity 
 
 makts the argumentation eristic He is a bad associate who 
 
 impedes the common work in reasoning as in any other occu- 
 
168 NOTES. Chap. XXXIV. 
 
 pation. Both disputants attain their object in well-conducted 
 argument, though not in eristic, for both cannot be victorious. It 
 is equally reprehensible to spoil the common business by captious 
 questions, and by refusing to admit what one really believes or 
 pretending to misunderstand the questions.' Dpos yap top -nav- 
 Tus ipia-Tajxevov TtAvrws avTiraKTeov kariv. Topica, 5. 4. 'The un- 
 serupulousness of the respondent forces the questioner to be 
 unscrupulous.' 
 
 It is not solely in the province of the answerer, however, that 
 we may see the contiguity [yeiTvlatris) of eristic and dialectic. 
 A conclusive dialectic proof may be formed of false premisses. 
 "EiTi 8' Ivti yv^xvaalas koL ireCpas yapiv aXK ov SiSatrxaXtas 01 toiov- 
 Toi T&v Koywv, bfjKov &i ov jxavov Ta\r]6ri (rvWoyurreov aWa Kal 
 \j/€vbos, ovbe fit' a\r]6&v cLel dW' ej^iore koI ^evb&v. HoWaKis yap 
 a\r]6ovs reOevTos avaipeiv avdyKr] tov biaXeyojievov, (Sore irpoTareov 
 TO, ^evb-q, 'Evfore be Kal \jfevbovs re^e'iros avaiperiov bia ^evh&v. 
 Oiibev yap Kmkvei tlvI boKelv to. ixfi ovra \mKXov t&v akrjd&v, &(tt, 
 l/c T&v fKeivio boKovvTav tov Xoyov yivofxevov, p-aWov eorai ireireto-- 
 lJ,f.voi 7) &<l>e\rjixivos. Aei 8e tov koXms jxtTa^i^&QovTa biaXiKTiK&i Kai 
 fiT] €pi(TTLK&s lierapi^dCeLV, KaOdvep tov yeutfiiTpriv yecojxeTpiK&s, av 
 re \j/fvbos av t dXTj^es jj to iyvp/nepaiv6p,ivov. Topica, 8. 11. 'As 
 practice and mutual examination, not instruction, are the object 
 of these argumentations, the dialectician must often prove a false 
 conclusion, and employ false premisses : for if the thesis is true, 
 the premisses of the confutation must be false. Even a false 
 thesis must sometimes be confuted by false premisses : for the 
 answerer may disbelieve the true premisses, and as the proof 
 must be composed of his beliefs, he will be convinced but hardly 
 enlightened. The proof, however, must be dialectic, not eristic, 
 whether the conclusion is true or false : just as a proof by a 
 geometer should be geometrical.' But dialectic proof may also 
 be inconclusive or fallacious. We saw (ch. v, note 4) that the 
 locus a dicto secundum quid is the common property of eristic 
 and dialectic : we saw (ch. xii, note 1) that' the dialectician does 
 not abstain from the locus non causa pro causa : we saw (ch. xxii, 
 note \0\ that paronyms are in Greek a locus of dialectic, in 
 English a locus of sophisms. It appears also that ambiguity is 
 common ground to the dialectician and sophist. Xp^o-t/ioi' 6e to 
 ■noa-ax&s XeyfTai ivevni^dai. . . , Kal wpos to TrapaXoyliraa-Qai. Elba- 
 
Chap. XXXIV. NOTES. 169 
 
 res yap iroa-ax&s X^yeroi, avroi epaiT&VTes bvvr](r6iJ,s6a napaXoyl- 
 aaaBai, eav jxr] Tvy^Avrj eiScos 6 aTioKpivauevos Tioaax&s Xeyeroi. 
 "EoTt 6e owK piKeTos 6 rpoTios oSros rrjs biaXeKTiKrjs' hib navreX&s eiika- 
 fitfiov roTs 8taX€KriKoTs to towvtov, to Trpos roUrojua 8ia\^yecr9at, 
 eaf fHj ns bXS.uis e^abwaTrj irepl tov ■npoKup.ivov biaKiyeardai. Topiea, 
 1. 1 8. 'A knowledge of the various meanings of a term is 
 useful, because it enables us when questioning to construct falla- 
 cies, if the answerer has not the same knowledge. This mode of 
 reasoning is not characteristic of dialectic, and should be utterly 
 avoided, unless there is no other possible means of attacking the 
 thesis.^ Elsewhere the locus is recommended without even this 
 slight admonition. "En eav iroWaxw XeyrjTai, Keip.evov he jj us 
 vTiapyii 7] MS o^x vvApxn, Barepov beiKVvvai t&v TT\eova)(&s Aeyo- 
 jxivai', eav p-r] &p<f)(o evbixTT''ai- KpriaTeov b' eTrl t&v KavdavovTtav. 
 'Eav yap pr] Xavdavrj TroXKax&s \ey6p.evov, evaTrjaeTai, on ov bieiKe- 
 KTot OTtep avTO'i '^Ttopei aXXa Bdrepov. Topica, a. 3. ' If a predi- 
 cate is ambiguous, prove it in the wrong sense if you cannot in 
 the right. This is only practicable when the answerer fails to 
 detect the ambiguity : otherwise he will object that the term is 
 not used in the confutation in the same sense as in the thesis.' 
 Knally, the advice to the geometer (ch. v, note 5), to decline 
 answering before any but a geometrical tribunal, looks very like 
 an admission that all pirastic is sophistic (see Appendix E) , 
 
 4] This refers to ch. i. 'ETrel 8' ea-rl ncn paXXov Ttpo epyov to 
 boKelv etvai ao<fiois ^ to etvai Kal prj boneiv, b^Xov on uvayKoiov 
 tctCtols Kal rb tov aocjiov epyov boKelv iroLelv ixaXXov ?j voiew Kal p,7i 
 boKe'iv. "Ecrn b\ ws ^v irpos kv elneZv, epyov irepl ^kucttov tov elboTos 
 a^evbeXv pev avrbv Trepl S>v oibe, tov be \j/evb6pevov ep(f>avi^eiv 
 blivacrdai. TaCro 8' ((ttI to p,iv ev to b-6va(r6ai bovvai Xoyov, Tb 8' 
 kv TO Kafieiv. 
 
 5] The Topica begins with a classification of propositions and 
 problems (theses). Y\p5>Tov oSv Oeaiprp-eov e/c tCviov f) pAOobos. Ei 6?j 
 Xd^oipev Tipbs ■noaa Kal iroia Kal l/c rtVcoj; 01 XoyoL Kal ttSs To-ircav 
 etmoprfio'opev, eyoipev hv iKav&s ro irpoKeipevov. Eort 8' apidp£ icra 
 Kal TO, avTa, e^ &v Te ol Xoyoi koI -aepl &v oi (TvXXoyia-poi. TLvovrai 
 p\v yap ol Aoyot J/c t&v TiporAo-ecoV Tiepl &v be ol avXXoyicrpx>l, to, 
 'npopXripaT6. eort. Ylatra be Ttporacns Kal vav irpo^Xripa rj yevos rj 
 Xbwv ^ avp.pel3riKbs brjXoi. Topica, 1.4. ' We have first to ex- 
 amine the elements of the method, that is, the number and 
 
170 NOTES. Chap. XXXIV. 
 
 nature of the points to vvhicli arguments are addressed, and of 
 the elements of which they are composed, and how they are 
 ohtained. The two questions are identical : for arguments are 
 composed of propositions, and addressed to problems ; and every 
 proposition and problem is a genus, definition, property, or 
 accident.'' 
 
 6] The sources of proof are pointed out partly by describing 
 the Spyava and partly by enumerating the loci. Ta fxev ovv yivri 
 irepl S)v re oi Ao'yot koX ef Siv, biMpCirOaf to. 6' opyava, hi' &v tviro- 
 pri(Jop,iv tS>v a-vKKoyia-^&v, etTrl Terrapa, ev fj,ev to TrporAa-eis Xa^eiv, 
 bevTepov 8^ TTO(rax&s e/caoroi' XdyeraL bvvatrdai heXeiv, rpiTov ras 
 bia<f)opas evpsLV, TerapTov 8e fj tov ofiolov o-xe'i/riy. "Eort 6e Tpoitov two, 
 KoX TO, rpCa TovTav Trpordcreis. Topica, i. 13. 'So much for the 
 classification of problems and premisses. Operations subsidiary 
 or instrumental to proof are four : the collection of propositions, 
 the definition of equivocal terms, the discovery of similarities, 
 the discovery of dissimilarities : and all four may be regarded as 
 the collection of propositions/ Ta /jikv ovv Spy ana bi &v 01 avX- 
 XoyKTjuot rai;r' eariv ol bi tottoi TTpos ots xP'Jf'/'ia ''a Aex^eVra otbe 
 elaCv. Topica, i. 18. 'Such are the materials of proof: the 
 maxims which will enable us to apply them have now to be 
 enumerated.' 
 
 7] Arrangement and answering are treated of in the 8th book. 
 Some of the precepts relating to solution appear to be lost. 
 
 8] Aristotle's desire to give an appearance of amplitude or 
 development {irXrjdos) to his system has been very injurious to 
 it. This has led him, with astonishing naivete, to -pretend to 
 multiply the loci by repeating them for each of the predicables 
 in a different order. He professes to do this for the sake of clear- 
 ness J but it is difficult to conceive anything less luminous than 
 the mode of exposition he has adopted. M^ XavOavera 8' ^ims 
 OTi TO, Ttpos TO ibiov Koi TO yivos Kal TO (7ii/x/3e;3)jK6s Tt&VTa Kal wpos 
 rovs 6pt,afi,ovs apptoa-ei, kiyea-Oai. . . 'AW' ov bia tovto piCav inl iiAvTatv 
 KaOokov p,idobov ^rjTrfiov. Oiire yap pqbiov evpeiv tovt ea-Tiv, eW 
 evpedeb], TravTeX&s &a-a(l)ris Kot 8i5(7XpjjoTos &v eh] irpos TrjV irpoKei- 
 Hevriv Tipayp,aTiiav, 'I8ta? b'k Kaff ^KacTTOv tSv biopurdiVTotv yevav 
 AnoboOeCarji lieOobov paov €k t&v irepl eKanrov oheCwv rj fiiefoSos 
 TOV TtpoKSLptevov yivoiT av. Topica, i. 6. 'It should be observed, 
 that the rules for proving property and genus and accident are 
 
Chap. XXXIV. NOTES. 171 
 
 all applicable to the proof of definition : yet we must not try to 
 establish a single body of rules of univ^sal application. Such 
 rules would be difficult to invent, and, if invented, woidd be very 
 obscure and hard of application. By giving separate rules and 
 appropriate methods for each predicable, we facilitate the ex- 
 amination of the different problems.^ According to Alexander 
 Aphrodisiensis, Theophrastus attempted to unite the canons of 
 proof in a single system, and verified Aristotle's prediction : but 
 against the failure of Theophrastus we may set the exposition of 
 the methods of induction by Mill. 
 
 9] It is difficult to reconcile Aristotle's assertion with what 
 we know had been done by Plato and Socrates and the Eleatics 
 and Megarians. What he really performed in his dialectical 
 treatise was to indicate a number of methodic principles or 
 elements of method {to. koivA.) ; and it is probable that none of 
 his predecessors had separated and extricated these from the 
 specific propositions [ra iSta), or what some would call the mate- 
 rial, as opposed to the formal, elements in which they are 
 imbedded in actual ratiocination. 
 
 10] What the rhetoricians gave their pupils to learn by heart 
 were, doubtless, not complete speeches, but finished portions of 
 speeches, i. e. what Quintilian would have called loci communes, 
 and the later Greek rhetoricians to'ttoi. Aristotle might have 
 used the word here, and we may even suspect that he originally 
 used it, for as the sentence now stands there is an awkward 
 repetition of koyovs. But he was forced to use the latter word 
 to distinguish the method of his predecessors from his own. For 
 his own system is merely a list of loci. He has erred nearly as 
 much by the omission of examples as his forerunners by the 
 omission of rules. He has not even given us the maxims that 
 group themselves about the different loci, although he admits 
 that the exact form of these propositions is of the utmost im- 
 portance to the disputant. YipoTaa-iv re koivt)V jxaWov fj \6yov us 
 IJ,VTJiJ,r]v Oereov, dpx'js yo.p Kal viTo9fa-eu>s einToprja-ai /.lerptus, x<^^f- 
 wdv. Topica, 8. 14. 'A universal proposition is better worth 
 remembering than a chain of proof : for a moderate command of 
 principles and premisses is difficult to obtain.' He recommends 
 however, like his predecessors, that whole arguments should be 
 committed to memory. Opo's re to, ■nXfLCTTd.Kis ipraTtTovTa t&v 
 
172 NOTES. Chap. XXXIV. 
 
 TTpo^krjiA&TOiv ^evltTTaaOai Sei \6yovi, mi jxAXurra Ttepl rmv irpdrm 
 diaeiav kv tovtois yap a-nobva-jreTova-iv ol a-noKpiv6\xevoi ttoWokis. 
 'We should get by heart arguments on the problems that 
 oftenest arise, particularly on the elementary theses j for here 
 chance often makes the answers take an unlucky turn.^ 'Airo- 
 bvaireTovcnv is a metaphor from dice. First principles are so 
 difficult to elicit by questioning that the questioner may be 
 baffled without any skill on the part of the answerer. [Compare 
 the use of evTrer^s. Kat yap iSeiv aiirbv Kal Ka^fiv napa t&v Ipco- 
 Twp,iv(ov Tas Toiairai upoTd-a-m qvk. evveres. Topieaj 7- 5-3 ^'^' 
 8e Kal ■neTtoirjp.ivovs ^X^tv \6yovs irpos ra Toiavra t&v irpo^krjfWTmv, 
 ev o?s ika^Cn-Taiv evitopi^cravTes irpbs irXeicrTa xpi7<''tM0DS ^^op-tv, oSrot 
 6' ela-lv ol KadoKov, Kal irpos ots -nopl^etrdai xakeTtdrepov e/c t&v irapa 
 ■nobas. Topica, 8. 14. ' We should have ready-made arguments 
 for the conclusions that depend on the fewest premisses and yet 
 are oftenest wanted, namely, the most ahstraet, and for those 
 problems whose proof is difficult to extemporize.'' 
 11] Read aWa Tpi^fj. 
 
ADDENDA. 
 
 Ch. VIIj note 2. ^Etiicnraadai was a common term in the schools. 
 E. g. 'H p.'kv afwSpa nal eKkvroi (l)avTacria om hv et?j KpiTqpiov ru 
 yap firjTe aw^y ju^re to Tsoir\(Tav rpav&s evheinwdOai ov Trecfiviiev 
 fjiMS TTfCdeiv oid' ell <TvyKaTdde(7iv eTna-jTcurBai. Sextus Empiricus, 
 Ad versus Logicos, i. 'A faint and weak sensation, according 
 to Carneades, cannot be a criterion or ultimate evidence of truth : 
 for, not clearly revealing either itself or its cause, it is not apt to 
 persuade us or induce our assent/ 
 
 Ch. VIII, note 6. ^aivop-ivovs 5^ ov\ oraovv aWa rois roioiabe. 
 For the meaning of rots Toioto-6e, compare, Ovbe fj p-qropiKr) to KaO' 
 iKoarov ^vho^ov deaprjirei., oXov Sftj/cpdTet rj 'lirTrta, aXka to toTs tol- 
 ourhe, KaOAmep koI r) bLaKeKTUcq. Kot yap iKeivrj crvXXoyCCfTai o^x ^i 
 &v ervxe, <f>a(veTai yap Stto Kal tois Ttapak-qpovaiv, a\A.' eKeivq ixev 
 e/c T&v Koyov beoiJ-ivcav, fj be prjTopiKrj Ik t&v ^8)j ^ovXevecrBai elcoOo- 
 Toov. Rhetoric, i. a. 'Rhetoric, like dialectic, examines what is 
 probable, not to any individuals, but to certain classes. Dia- 
 lectical proof appeals, not to any opinions, for madmen have 
 opinions, but to the opinions of those who want not understand- 
 ing but evidence ; and rhetorical proof to the opinions of those 
 who are accustomed to deliberate.^ 'Ek t&v Xoyov beop.h<(ov=:eK 
 T&v evho^av tols \6yov beop.evoi.'s, and Ik t&v -ijbrj PovkeveaOai eto>66- 
 T<i>v=:eii T&v irWav&v tois jjSjj fiovKeviaBai elmBocrLV. For the mean- 
 ing of T&v \6yov beoixevav, compare, Ov beX be irav ■npofiXrjixa aibe 
 iraa-av 6e<nv eTriaKOTreiv, a\\' fjv anoprjcieiev av tis t&v Xoyov b€op,evav 
 KoH firj KoXda-eas fj ala-di^a-eas' ol p-ev yap airopovvTes iroTepov Sei 
 Toiis Oeoiis TipRv Kol tovs yovels dya-nav r) ov KoXdo-fcos beovTai, ol be 
 ■noTepov fi xtmv XevKri ^ ov aWBrjtTem. Topica, I. 1 1. 'We should 
 not examine every problem or thesis, but only such as may be 
 doubtful to a person who wants not intelligence but proof, not 
 those which are doubtful to a person who wants castigation or 
 
174 ADDENDA. 
 
 to a person who is defective in a sense. He who questions 
 whether we should reverence the gods or love our parents wants 
 punishment, he who does not know that snow is white wants 
 an organ of sense.'' 
 
 Ch. XI, note a. Aristotle seems to have thought that, if we 
 were in full possession of the ultimate conceptions, that is, the 
 definitions of the ultimate terms, we should be able to predict 
 the special propositions which are the ultimate basis of deduc- 
 tive science : that the conjunction of the terms A, B, C, &c. in 
 all the primary objective theorems, Ais B, B is C, C is D, is, to 
 use the words of Kant, not synthetical but analytical, just as 
 in geometrical theorems. Brown, in his celebrated treatise on 
 Causation, has attempted to shew that, in the natural sciences 
 at least, that is, in those that deal with changes or events, i. e. 
 successions of phenomena, the ultimate immediate conjunctions 
 are unpredictable, i. e. though constant juxtapositions, are inex- 
 plicable and mysterious. It is not quite clear what Aristotle 
 considered to be the logical relation of the cause and effect in his 
 causal definitions of natural phenomena ; but, if we may judge 
 from his expression, Aia yap ro BavixdCeiv ot &v0pa>Troi km vvv Kot 
 
 TO TTpWTOP ffp^avro (fnXocTo^tiv, bei be els to evavriov /cal to a)j.ei- 
 
 vov Kara ttiv irapoifxCav airoTekevTrja-ai, Met. 1.2,' Men began to 
 philosophize because they wondered, but the end of philoso- 
 phizing should be something better, the cessation of wonder,' he 
 seems to have expected that, in any province of inquiry what- 
 ever, if we carried the analysis far enough, when we arrived at 
 the ultimate immediate conjunctions, whether of coexistent or of 
 successive terms, we should find them neither inexplicable nor 
 mysterious, but the evidently necessary result of determinate 
 relations. 
 
 Kara expresses causation (oAtos he to Kad' h l(Tax&s Koi to alnov 
 VTiap^ei, uxTTe Koi to xa^' avTo itoKKax&s avdyKtj XeyeaOai.. Met. 4. 
 18). Accordingly the proposition, to A vitdpxei ™ B Ka6' avro, 
 means that all the conditions of the conjunction of A and B are 
 contained in A and B themselves : that we are not to look for 
 its cause in the interposition of any third independent term. 
 The conclusions of science, as well as the first principles, are 
 KaO' avTo, v-ndpx^ovTa, that is, ro xad' avro v-ndp^eiv is not confined' 
 to immediate conjunctions except so far as it excludes the inter- 
 
ADDENDA. 175 
 
 ference of any foreign cause. We may add that in the expres- 
 sion, TO A virapxei t£ B ko^' ovto, avTo is either the subject or 
 the predicate, i. e. KaQ'' ovto means, as appears from Aristotle's 
 definition of the two classes of ko9' awo vv&pxovTa, either Kar 
 avTO TO A, or kot ovto to B '. e. g. ypa/xjUTJ vrrdp\ii rpiydvio Kar 
 . aiiTo TO TpCytavov, but to evdv wtipx^' VP^l^l^fi '"'^' o'^to to evOv. 
 
 Ch. xXj note 3. Eudemus, the disciple of Aristotle, informs us 
 more than once that the theory of ambiguity {to bLo-crov) was 
 invented by Plato. napp,evLbov pikv ovv ayaa-deCr] hv tis ava^io- 
 TTioTOis aKo\ov&il]<ravTos \6yois koI vtio Toio^Tutv anaTrjOivTos h odiro) 
 Tore 'Steo'eo-di^TjTO ; Ovre yap to T:oK\a\&s iX.ey€v ovieCs, aWa YlXd- 
 Tmv irp&Tos TO dicro'ov eliri^yayev, ovre to Kad' avTO koI to Kara o-ujli- 
 /3e/3j;Kos' 0aiVeTat 6e vtto TovTtav bia^evcrdrjvai. Eudemus, quoted by 
 Simplicius on Phys. Ausc. i. 3. 'We ought not to be surprised 
 that Parmenides was misled by inconclusive reasonings and 
 fallacies which in his time had not been exposed. For in his 
 days no one had heard of equivocation, a method of solution first 
 introduced by Plato, or of the distinction of subject and attri- 
 bute which he overlooks.' See also eh. x, note 1 . 
 
 Ch. XXXIV, note 3. 'Eirel hi vpoa-KaTaa-Keva^eraL irpos avTTjv as 
 ov jJLOvov Tteipav hvvaTai Ka^eiv biakiKTiK&s aA\' &s ilbds. This 
 should have been translated, ' Since it claims the power of 
 catechizing or cross-examining not only dialectically but also 
 scientifically.' 
 
APPENDIX A. 
 
 PETITIO PRINCIPII. 
 
 To 8e kv dp)(fj alriiaOai koX Xafi^dveiv iari fuv, ms h 
 yivfi Xa^etv, kv t& firj dwoSeiKvdvai to irpoKiifievov. Tovto 
 Se kniavii^aivei iroWay^ws. Kal yhp el oXcas fir) avKkoyi^erai, 
 Kal el Sl dyvm<TTOTep(ov i} ojioims dyvdxTTCav, Kal el Sia twv 
 iiarepcov to nporepov 17 ydcp diroSei^is e/c irioToreprnv 76 Kal 
 TrpoTepcov kcTTi. Tovtcov jiev ovv ovSiv kcrTL to alreiaOai to e^ 
 dpyrj^. '/4XX' knel toi. jiev St avrmv neipvKe yvmpi^eardai tA 
 Se St dXXcov (at /xev yhp dpyal Si eavTwv, t& Se irirb rAy 
 dp^ds Sl dXXmv^ oTav Th jii] 81 aiiTov yvmo'Tov Sl eavTov tls 
 kwL'yeLpfj SeLKVvvai, Tore alTeiTUL to k^ dp-)(rjs. 
 
 Tovto Si ka-TL jiev ovTm voLetv &<tt evOds d^imaaL to irpoKei- 
 jxevov, kvSeyeTai Se Kal fieTa^dvTas eir dXXa aTTa tS>v Tretjyv- 
 KOTCoy Sl kKeivov SeiKvvcrOaL, Sid tovtodv dnoSeiKvivai to e^ 
 dp^fjs. OTov, el TO A SeiKvvoiTo Sid tov B, to Se B Sid tov /", 
 TO Se r ne^vKos eir] SeiKwa-QaL Sid tov A- avfi^aiyei yap 
 avTo Sl iavTov to A SeiKVVvai Tois ovrco (TvXXoyL^ojievavs, 
 "Oirep TTOiovcrLV ol Tds TrapaXXi]Xovs olojievoi ypd(peiv. Aav6d- 
 fovcri yap avrol eavToiis ToiavTa Xaji^dvovTes d ov\ oeov Te 
 dTToSei^ai firj ovcr&y t&v irapaXX'tjXav, "DaTe toTs oStco avXXo- 
 yi^ojikvois crv/j.^aivei eKaaTOV Xeyeiv etvai el ecTTiv 'eKa<nov 
 oUtco Se dirav ecTTai Si aiiTOV yvaxTTov oirep dSvvaTOv. 
 
 El OVV Tis, dSijXov ovTOS oti to A vnapyei Tm F, Sfioiwi Sl 
 Kai OTL Tm B, ahoiTo rS B indpyeiv to A' ovttco SfjXov el to 
 kv dpxfi alTeiTai- dXX' otl ovk dnoSeiKvvai, S^Xov ov yap 
 ka-Tiv dp)(fi diroSei^eoos to ofxoims dSrjXov. El fiev tol to B 
 
177 
 
 APPENDIX A. 
 
 PETITIO PEINCIPII. 
 
 Begging the question ij or, assuming the point to he proved, 
 is a specific case of failing to demonstrate a theorem. This 
 occurs in various ways, either when the reasoning is inconclu- 
 sive, or when the premisses are less evident than the conclusion, 
 or equally devoid of evidence with the conclusion, or when they 
 are its consequents rather than its antecedents. For demonstra- 
 tive premisses must be antecedent to the conclusion and more 
 evident. None of these eases is begging the question. But 
 some propositions being self-evident, others having a derivative 
 evidence (for principles have their evidence in themselves, con- 
 elusions derive their evidence from other propositions), to 
 attempt to make a proposition that is not self-evident evidence 
 of itself is to beg the question. 
 
 This may either be done by directly assuming the conclusion 
 or by assuming what is properly a conclusion from a proposition 
 as a premiss to prove that proposii^on, proving, for instance, A 
 by B and Bhj G when C can only be proved by A. For this 
 amounts to proving A by A. An example of this is the pre- 
 tended method of constructing parallels. Here the prover un- 
 consciously assumes an operation which cannot be performed 
 unless parallels have been consti-ucted^. The proof therefore 
 asserts a thing to be true if it is true, and if it were valid, all 
 propositions would be self-evident, which cannot be. 
 
 When the conclusion, C is A, and the major, B is A, are 
 equally deficient in evidence, there is not of necessity a begging 
 of the question, but there is clearly no demonstration ; for that 
 cannot be a premiss of demonstration which is no more evident 
 than the conclusion. But if the middle and minor, G and B, 
 are so related as to be identical, either because they are con- 
 
 N 
 
178 APPENDIX A. 
 
 Trpbs TO r ovTCos ex^' &<m ravTov itvai, fj SrjXov 8ri^ dvTKrrpi- 
 ^ova-iv, fj imdpy(ii Qdrepov Oarepm- to iv dp)(rj ahetTai. Kal 
 yap dv oTi t& B to A virdp\€i Si tKeii/cav SeiKi/voi, el dvn- 
 <TTpe<fiiL. Nvv Se TovTo KwXvei aAX' ou^ d Tponos. El Sk 
 TOVTO iToteT, TO upriiiivov &v noLoi Kal dvTKTTpe^oi ws Si& 
 Tpmv*. 
 
 DeravTtos Se Kav el to B t& T Xafifidvoi virdpyeiv, ojioim^ 
 dSrjXov ov Kal el to A rS T* o^<o to e| dp)(rjs alTeiTai, dXX' 
 OVK diroSeiKwanv. ' Edv Se TaiiTOV ^ to A Kal to B rj ra 
 dvTi<TTpe<j>eiv fj r£ errea-Oat to A t& B- to e| dp^rji ahehai 
 Slit. TTjv aiTrji/ ahiav. To yap t| dpyrjs Ti SvvaTai, nporepov 
 e'iprjTai fffiiv, Sri to Si' eavTOv SeiKvvyac to jxri Si' afiTOv 
 SfjXoy. 
 
 El oSv e<7Ti to kv dp)(fj ahelaQai to Si aiiTov SeiKvvvai to 
 fifj Si avTov SfjXov, TOVTO Si eaTi to fifi SeiKvwai, oTav 6/ioim 
 dSrjXmv ovTmv tov SeiKvvfievov Kal Si' o5 SeiKvvTai ®, jj r^ Tairra 
 Tm aiiTw fj Tffl TavTov Toli avToTs {mdp-)(eiv''- ev [lev tZ jjiia-a 
 ayrjuaTi oiiSeTepcos^ &v evSeypiTO to ev dpy^^ alTeTa6ai, ev Se 
 KUTr/yopiKw avXXoyi<r/j.& ev re tw TpiTW Kal tw npwTto. 
 
 ' AnotpaTiKws Se, oTav to. airr^ dno tov avTov- Kal o^X 
 Sfioims dpKJiOTepai at npoTdaeit. 
 
 i2<ravTcos Se Kal ev tS /*€<?■», Sia to jirj dvTiaTpe^eiv^^ tovs 
 Spovs KaTh Tods d7ro(paTiKois avXXoyia/iovs. J 
 
 EffTi Se TO ev dpy^fj alTeiaOai ev (tev Tals diroSei^ecri to, 
 KaT dX'qOeiav ovtcos e^ovTa, ev Se toTs SiaXeKTiKoTs to. KaTO. 
 So^av. Anal. Prior. 2. 1 6. 
 
APPENDIX A. 179 
 
 vertible or because the middle involves the minor, the argument 
 is a begging of the question. For the i»ajor premiss, B is A, 
 might be proved by the minor premiss and conclusion if the 
 middle and minor are convertible. If it cannot be, it is only 
 from the comparative extension of the terms, not from any other 
 relation. If they are convertible, we might, as was stated, 
 prove the major premiss from the minor and conclusion, and we 
 should have a circular proof of three propositions in which each 
 would be alternately premiss and conclusion. 
 
 Similarly if the minor premiss, G is B, is no more evident 
 than the conclusion, C is A, we have not necessarily a begging 
 of the question, but we have a failure of demonstration. If, 
 however, the major and middle terms are identical, because they 
 are convertible or because the major is involved in the middle, 
 then we have a begging of the question as before^. For begging 
 the question arises, as was explained, when a proposition not 
 self-evident is made to prove itself. 
 
 If then begg^g the question is making a proposition not 
 self-evident prove itself, and this is a failure of proof, from the 
 premiss being no more evident than the conclusion, because the 
 premiss and conclusion either affirm two identical predicates of 
 an identical subject or an identical predicate of two identical 
 subjects, the question cannot be begged in the second figure 
 in either of these ways, but only in the figures that give an 
 affirmative conclusion, namely, the first and third'. 
 
 In negative syllogisms there is a begging of the question in 
 the first and third figures when an identical predicate is denied 
 of two identical subjects, and it is not either premiss indifierently 
 that begs the question but only the major^". 
 
 In the second figure there is a begging of the question when 
 two identical predicates are denied of an identical subject, and 
 it is not either premiss indifferently that begs the question but 
 only the minor, because the position of terms in the other pre- 
 miss of negative syllogisms is not homologous to the position 
 of terms in the conclusion. 
 
 Begging the question in scientific discussion is what really 
 satisfies these conditions, in dialectic what has the appearance 
 of doing so. 
 
 We have some further remarks in the Topica ; — 
 
 N 2 
 
180 APPENDIX A. 
 
 To 8' kv dpxfj TcBs aireirai 6 kpan&v Kaff d\i]6eiav /lev kv 
 Tois 'AvaXvTiKoTs eipriTai, Kara So^av Se vvv XeKTeov. Ahei- 
 a-dai Se ^aivovrai to ki> dpxfj irei/raxaJs. <t>avepa)TaTa fih 
 Kal nprnrov d ris avrb to SeiKwaOai 8kov ah^aer tovto S' kit 
 avToO fj-eu ov paSiov \av6dvew, kv 8e toTs avvcavvfiois Kal kv 
 oa-ois TO ovofia Kal 6 \6yos to avTo a-ri/iaii/ei fidXXov. Aev- 
 Tepov 8e oTOAi KCLTo. fiEpos 8iov dTToSeT^UL KadoXov TIS aiTTJoTj- 
 olou el kTn-)(iip3>v otl tS>v kvavTicov jxiw kiricrTrjiir], oXws t&v 
 dpTiKeifievcoy d^idxreie jiiav eivai' 8oKel yhp h e8ei KaB' aiiTO 
 SeT^ai fjLeT aXXcav aheTa-OaL wXeiovcov. TpiTov e'l tis, to KaOoXov 
 SeT^ai TTpoKeifievov, kutcc fiepos ahrjcreiev oiov el iravTcov tS>v 
 kvavTioDV irpoKeijievov, T<bv8e tlvSiv d^iScreie' SoKec yap Kal 
 ovTos, o fieTO, irXei6v(cv eSei SeT^ai, Ka$ avTo Kal )(copls alrei- 
 aOai. ridXiv e'i tis SlsXwv ahelTai to Trpo^Xrjdev oIov ei Skov 
 SeT^ai TTjv laTpiKrjv vyteivov Kal voacoSovs, X'^P'-^ eKaTepov d^iw- 
 aeiev. *H ei tis tSiv eTro/ikpcov dXXrjXois k^ dvdyKris ddrepov 
 aiTtjcreiev, oIov Trjv irXevpav davfifieTpov Trj SiafieTptp^ S4ov 
 dnoSe'i^ai otl 77 SidjieTpos Trj irXevpa. Topica, 8. 1 1 . 
 
APPENDIX A. 181 
 
 What begging of the question is to the philosopher we have 
 examined in the Analytics : what it is to the dialectician we 
 will now explain. It appears to occur m iive ways. The first 
 and most manifest way is when the very thing that should be 
 proved is assumed. This cannot easily pass undetected when 
 the terms are the same, but when synonyms are used, or a name 
 and a circumlocution, it may escape detection. A second'way 
 is when a particular ought to be proved and the universal is 
 assumed : as, for instance, if we have to prove that contraries 
 are objects of a single science, and assume that opposites, their 
 genus, are objects of a single science. It appears that what 
 should be proved alone is assumed in company with other pro- 
 positions. A third way is when a universal ought to be proved 
 and the particular is assumed ; as when what ought to be proved 
 of all contraries is assumed of some. Here too it appears that 
 what ought to be proved in company with other propositions is 
 assumed alone. A fourth way is when we divide the problem 
 to be proved and assume it in detail ; as if we have to prove 
 that medicine is the science of health and disease and succes- 
 sively assume it to be the science of each. A fifth way is when 
 two facts are reciprocally involved and we assume the one to 
 prove the other; as if we assume that the side of a square is 
 incommensurate to the diagonal when we have to prove that 
 the diagonal is incommensurate to the side. 
 
182 NOTES TO 
 
 NOTES TO APPENDIX A. 
 
 1] Aristotle examines the relation of the terms in a syllogism 
 containing a petitio principii, and determines which premiss in 
 each of the figures may be the petitio. In the first figure, if 
 the principium, or conclusion assumed, is afiirmative, either the 
 major or minor premiss may be a petitio, and the middle term 
 will be identical with the minor or major. If the principiimi is 
 negative, the major premiss is the petitio, and the middle is 
 identical with the minor. In the second figure the prineipium 
 must be negative, only the minor premiss can be a petitio, and 
 the middle term will be identical with the major. In the third 
 figure, whether the prineipium is afiirmative or negative, the 
 major premiss is the petitio, and the middle is identical with 
 the minor. All this is obvious from an inspection of the sym- 
 bols of the figures. It does not throw much light on the nature 
 of petitio principii, but for the satisfaction of the reader we give 
 it in Aristotle^s own words. AiTrma, petition, is the assuijaption 
 without proof of a proposition which ought to be proved. It 
 may or may not be opposed to the belief of the respondent. 
 Hypothesis is, properly, an indemonstrable proposition. A rela- 
 tive hypothesis is a proposition which ought to be proved, but 
 which is believed by the respondent and is assumed without 
 proof. "Oo-ffl jLiev ovv beiKra ovtol Kaixfidvei avros fJifi Sei'fas, ravr , 
 fhv iJiiv boKovvra Kaix^dm) t^ jxavddvovrL, VTrorideTai, Koi tcrTiv ov^ 
 ottASs vTr66e(ns aWa -npbs iKeivov \wvov hv 8e rt fijjSepiias ewoutrijs 
 8o^?7S r] Koi IvavHas evova-rji Kafi^dvri to avTo, atreirot. Kai rovr^ 
 bia<l)epei vv6d{(ris koi, atrrjua' ea-Ti yap alrrnxa to inrevavTiov tou 
 fxavdavovTos rfj 6ofn, jj h S.V Tis aTtobeiKTov Sv \ap,^dvr) km xP^''"' 
 firj bs[$as. An. Post. X. lo. 'What is capable of proof, but 
 assumed without proof, if believed by the learner, is, relatively 
 to the learner, though not absolutely, an hypothesis; if the 
 learner has no belief or a disbelief, it is a petition ; and this is 
 the difference. Petition is an assumption opposed to the belief 
 of the learner : or, still wider, a demonstrable proposition as- 
 sumed without demonstration.' Ahrjms tov h> dpxfi is an atTrjyta 
 
APPENDIX A. 183 
 
 where the proposition assumed is the ebnclusion which ought to 
 be proved. 
 
 2] It is not easy to say what is the vicious construction that 
 Aristotle contemplates. Euclid postulates the power of drawing 
 any circle from a given centre with a given radius, that is, the 
 use of the compasses as well as of the ruler. Some geometer 
 may have attempted the impracticable feat of solving the pro- 
 blem without the help of this postulate. 
 
 3] Perhaps for tj trjXov on we should read bion ^. Compare 
 below, fj ru avrurrpe^nv r) ru S-neadai. Or we might read, el 
 hrjXovoTi, except that brjkovoTi in the sense of ' that is to say' 
 belongs to a later period of Greek. 
 
 4] The meaning of rpoVos is not obvious. 
 
 5] Assuming the conclusion to be affirmative, let us examine 
 a syllogism in Barbara : — 
 
 All S is A, 
 
 All C is S, 
 
 .-. Ml C is A. 
 
 And let us first suppose that the major premiss is a petitio prin- 
 cipii, i. e. that the proposition All B is A is identical with the 
 proposition All Gis A. This can only be because the terms B 
 and G are identical. 
 
 Next let us suppose that the minor premiss is a petitio prin- 
 cipii, i. e. that the proposition All C is 5 is identical with the 
 conclusion All Cis ^. This can only be because B and A are 
 identical. 
 
 The identity of the terms is their convertibility or their 
 sequence {vTiapx^h ?wcTat). This, however, requires some limi- 
 tation, for as the major is always predicated {vTidpxei, iireTai) of 
 the middle and the middle of the minor, if this were enough to 
 constitute petitio principii, every syllogism with a problematical 
 premiss would be a petitio principii. 
 
 6] Perhaps for beUvvrai we should read bemvvriTai, which must 
 otherwise be understood. 
 
 7] When the major premiss is the petitio, i. e. when 
 B is A, and 
 C is A, 
 are identical, we may apply the formula ravro rots ovrois virdpxtij 
 
184 NOTES TO 
 
 A being rawo, and B and C to. aird. When the minor premiss 
 is the petitio, i. e. when 
 
 C is B, and 
 
 C is A, 
 
 are identical, we may apply the formula Tavra t<5 a-Jru vitapxei, 
 B and A being TavTo. and G to avro. 
 
 8] Ovberepias. So read, disregarding the MSS., for koL rpha 
 &IJ.(j)0T4pa)s. As the conclusion of the second figure is always 
 negative, it can never be begged by an affirmative premiss, such 
 as the above-cited formulas imply. 
 
 9] In the third figure in Disamis, 
 
 Some £ is A, 
 
 All ^ is C, 
 
 . ■ . Some C is A, 
 
 the major premiss may be a petitio principii, and we may apply 
 the formula to ovto tois aiiTois virdpxei- The minor premiss can 
 never be an assumption of the conclusiouj for their terms are 
 dissimilar [ovk avrCa-Tpotpoi. See below]. 
 
 10] If the conclusion is negative, in Celarent of the first figure. 
 No B is A, 
 All C is B, 
 .-. 'No C is A, 
 
 and Bokardo of the third, 
 
 Some B is not A, 
 
 All B is G, 
 
 . • . Some G is not A, 
 
 the major premiss may be a petitio principii. The minor premiss 
 cannot, because in these figures it is always affirmative ; besides 
 which, in the third figure the minor premiss and conclusion are 
 not composed of similar terms in similar positions (ovk hirri- 
 orpo^oi) . We may here notice an inaccuracy of Aristotle, if the 
 text is correct. An inspection of the symbols given above shews 
 that the first and third figures require the formula &rh,v to avro 
 knh T&v aiiT&v (diropf^Tai) , whereas the formula oTctv to, avTo, &.m 
 rov aiiTov only applies to the second figure. 
 
 11] 'AvTUTTpe^iiv, i. e. &vTi(TTp6^(as ^x^iv. In the second 
 

 APPENDIX 
 
 A. 185 
 
 figure the only possible petitio principii is in the minor premiss 
 of Camestres : 
 
 All A is B, ' 
 
 t 
 
 No C is B, 
 
 
 
 .-. No C is A. 
 
 
 In Csesare, 
 
 No A is B, 
 All C is B, 
 
 • 
 
 .-.No C is A, 
 no petitio principii is possible. Why not ? Because the major 
 premiss and conclusion are not composed of analogous or corre- 
 sponding terms [ovk avTLaTpo(j)OL oi opoi). For diroc^artKovs we 
 should probably read some word expressing the mood which the 
 moderns call Csesare. 
 
186 
 
 APPENDIX B. 
 
 NON CAUSA PRO CAUSA. 
 
 To 8e /irj naph, tovto av/x^aiveiv rb ■\jrevSos, b TToWdiKLS kv 
 Toh Xoyots elcoOa/jiey Xkyeiv, trpoarrov jikv kcrriv kv rofs eh to dSv- 
 varov avWoyiafiots, orav irpos avri^aa-iv ff tovtov, b eSeiKwro 
 rfj eis TO dSvuaTov^. O^re yap fir] dvTL(f>'^(7ayT0S^ epei to ov 
 napa tovto, aXX &tl yjrevSos Ti eTeOr] tZv TrpoTepov ovt kv ttj 
 SeiKWOva-T), ov yhp TiOrjai Tr]V avTi^acnv. " Etl 8e, OTav dvai- 
 pe6^ TL SfiKTiK&s Slu t5>v a B r, ovK eoTiv eiiTf.iv oas ov iraph 
 TO Keifievov yeykvr)Tai 6 o'vWoyia/ios. To yap fir/ irapit tovto 
 yiveaQai Tore Xkyojiev, &Tav dvaipeOkvTOS ToiJTOv fir/Sev ^ttov 
 Trepaivr/Tai 6 av\Xoyia/i6s. ' Otrep ovk ea-Tiv kv toTs SeiKTiKoir 
 dvaipe6eca-r}s yap Trjs Okaeats ovS" 6 vpos TavTT]v e<TTai avWo- 
 yia/ios. 
 
 4>avepov ovv Sti kv tois els to dSvvaTov XkyeTai to firj 
 irapb, tovto Kal, oTav ovtcds exTj npos to dSvvaTov tj k^ dp)(rj? 
 iiiroOecris, &<TTe Kal ova-qs Kal fir) oila-rjs TavTTjs ovSkv tjttov 
 uvfi^aiveiv to dSvvaTov. 
 
 /lev ovv (f>avepa)TaT0S TpoTTOS ka-rl tov /ifj wapa Trjv iiro- 
 6eaiv elvai to -^jrevSos, oTav dirb Trjs iinoOkaecos davvatrTOS jj 
 dirb tS>v fieacov npbs Tb dSvvaTOv 6 avWoyia-iibs, wcrrrep eipr/Tai 
 Kal kv ToTs ToTTiKoTs. Tb yhp rb dvaiTiov cos aiTiov TiBkvai 
 TOVTO ka-Tiv. OIov, el ^ovXofievos SeT^ai otl doTJ/iiieTpos fj 
 ■SidfieTpos, kiriyeipoir} Tbv Zrjveovos \6yov SeiKvvvai, d)S ovk ecn 
 KLveicrBai, Kal els tovto drrdyoi Tb dSvvaTov oiiSafi&s yap 
 ovSafifj avveyks^ ka-Ti. rb yjrevSos Trj (f)d<Tei Tfj k§ dpyrjs. 
 
 AWos Se Tpoiros, el avve^es /lev eir] to dSvvaTov Trj iiiro- 
 6kaei, fifi fikvToi Si' kKeivr)v av/i^aivor tovto ycLp kyx<iDpf1 
 
187 
 
 APPENDIX B. 
 
 NON CAUSA PRO CAUSA. 
 
 The objection that a proposition is not the cause of a false 
 conckisionj a formula often heard in controversy^ is made in 
 reply to a reduetio ad impossibile in defence of the proposition 
 contradicted by the framer of the reduetio. For unless the 
 opponent has contradicted the proposition the respondent will 
 not deny that it is responsible for the conclusion, but will object 
 to some other proposition ; nor will he use the formula against 
 direct disproof, for here the thesis is not employed as a premiss. 
 Moreover in direct disproof by three terms, it cannot be said 
 that the confuted thesis is irrelevant to the syllogism. This can 
 only be said when a proposition may be eliminated without 
 annihilating the syllogism, which cannot be the ease in direct 
 disproof, for without a thesis to be confuted there can be no 
 confutation''. 
 
 It is clear then that the formula can only be employed against 
 reduetio ad impossibile, when the thesis impugned is so related 
 to the conclusion that it may be suppressed without destroying 
 the conclusion. 
 
 The most obvious case of the irrelevance of the thesis to the 
 conclusion is when the thesis is not connected by any middle 
 terms with the conclusion, as we said in the Topica* in discuss- 
 ing the fallacy of non causa pro causa. We should exemplify 
 this if, to disprove the commensurateness of the side of the 
 square to the diagonal, we appended aji argument for Zeno-'s 
 theorem that there is no such thing as locomotion, pretending 
 thereby to establish a reduetio ad absurdum, for there is abso- 
 lutely no connexion between this theorem and the thesis. 
 
 Another case is when the conclusion is connected with the 
 thesis but is not its consequence. The connexion may be traced 
 
188 APPENDIX B. 
 
 yevea-Oai Kal eTTi to dvoa Kal kirl to kcctco Xajx^dvovTi. to 
 <Tvve\es. OTov, el to A tZ B k^itoll {nrdp\oi/, to Se B tZ T, 
 TO Se r TO) A- TOVTO Se e'lrj ■ylrevSos, to B tZ A indpyiiv. 
 Ei yhp, d(f)aipe6evTos tov A, /j-tjSIp ?]ttov vvdpyii to B tw F 
 Kal TO r tZ a, oiiK Siv eirj to flrevSos Sia tt]v k^ dp^fjs virodeffLv. 
 *H TrdXiy, ei tis evi to di/m Xafj-jBduoL to a-vve-)(^is. Oiov, d 
 TO jxev A T& B, Tw Se A to E, kul tZ E to Z- -^evSos Se eirj 
 TO {indp-^eiv tZ A to Z- Kal yap ovtcos ovSev av ^ttov e'lrj to 
 dSvvaTov dvaipeOeia-qs Ttjs e^ dp-^rj^ iiroOea-ecof. 'AXXa Set 
 irpbs To^s e^ dp-^f}s^ opovs o-vvdirTeiv to dSvvaTov ovt(o yhp 
 ea-Tai Sid ttjv vwoOeaiv. OTov, knl fiev to KdTco Xap-^dvovri 
 TO (Tvveyes, Trpbs tov KaTrjyopovjievov tZv opmv. Ei yap dSv- 
 vaTov TO A tZ A vnap^eiv d^aipeQevTos tov A, ovk en ea-rai 
 TO ylrevSos. Eirl Se to dvw, Ka6' of) KaTrjyopeiTai. Ei yap 
 tZ B firj ey^copei to Z inrdp)(^eiv, d<paipe6evT0S tov B, ovKen 
 ecTTai TO dSvvaTOv. '0[J,oia>s Se Kal a-TeprjTiKwv tZv avXXo- 
 yicTfiZv ovTcov. 'Pavepbv ovv, on tov dSwdTov fifj npos Totbs 
 k^ dpyji^ opovs oi'TOS, ov irapd ttjv Oeaiv a-vfi^aivei to fjrevSos. 
 H ovS OVTCOS del Sid ttjv vTr66e<nv ea-Tat to yjrevSos ; Kal yhp 
 ei fitj tZ B dXXd tZ K kTeQrj Tb A imdpyeiv, rb Se K tZ F, 
 Kal TOVTO tZ A' Kal ovtco jievei to dSvvaTov. 'Ofioioas Se Kal 
 evl Tb dvoa Xaji^dvovTi Totis opovs. " QarT kirel Kal Svtos Kal 
 fifj ovTos TOVTOv avji^aivei to dSvvaTOv ovk dv eirj napd Trju 
 6e<nv. *H Tb [irj ovtos tovtov /irjSev ^ttov yiveaOai Tb ■<^evSos, 
 ov)(^ o6tco XrjTTTeov, &(tt dXXov Tidefievov avfi^aiveiv to dSv- 
 vaTOV dXX oTav, d(f>aipe6evTos tovtov, Sid tZv XolttZv wpord- 
 crecov to aiiTb TrepaivrjTai dSvvaTov kwel Tb avTo ye '^evSos 
 irvfi^aiveLv Sid wXeiovmv vtrodeaewv ovSev lercos dTonov oTov to 
 Tas irapaXXrjXovs avuniiTTeiv, Kal ei' fiei^oov kaTlv^ij kvTos Trjs 
 eKTos, Kal ei Tb Tpiyatvov e^ei rrXeiovs 6p6ds SveTv. Anal. 
 Prior, a. 19. 
 
APPENDIX B. 189 
 
 either from the attribute or superior term of the thesis, or from its 
 subject or inferior term. As an illustration of a connexion with 
 the inferior term, suppose the thesis to be, All B is A, the pre- 
 misses, All D is C, All G is B, and the false conclusion, All B'lsB^. 
 If, eliminating the superior term A, we can retain the premisses. 
 All D is C, All G is B, the conclusion. All B is B, is independent 
 of the thesis. Again, let us trace the connexion to the superior 
 term, and suppose the thesis to be. All B is A, the premisses. All 
 A is E, All E is F, and the conclusion, All A is F'^. Here, too, 
 the conclusion is unaifected by the suppression of the thesis. 
 But when the impossibility is connected with the more remote 
 of the two terms of the thesis, it will be the consequence of the 
 thesis. When, that is to say, an inferior series of terms com- 
 posing the ratiocination is linked on to the superior term of the 
 thesis, so that the first impossible conclusion is. All JD is A, the 
 elimination of A eliminates the imjiossibility ; and when a 
 superior series is linked on to the inferior term of the thesis, so 
 that the first impossible conclusion is, All B is F, the elimination 
 of B eliminates the conclusion. Similarly when the proposi- 
 tions are negative. It is clear, then, that when the impossibility 
 is not enchained to the remotest term of the thesis it is inde- 
 pendent of the thesis, and when it so enchained it is dependent. 
 Or may it not even then be independent? For if, instead of 
 the thesis. All B is A, we had a thesis. All X is A, and the 
 premisses. All JD is G, All G is X, the impossible conclusion. All 
 I) is A, would still I'esult; and similarly if the ratiocination con- 
 sisted of a superior series of terms. As, then, in spite of the 
 suppression of the first thesis the impossibility remains, is not 
 the first thesis irresponsible for the conclusion ? No. The 
 independence of the conclusion and thesis does not mean that a 
 different thesis might lead to the same conclusion, but that, if 
 the first thesis were suppressed, the remaining existing premisses 
 would of themselves involve the conclusion'. Por the same 
 impossibility may easily result from various theses : for instance, 
 parallels may be proved to meet both from the thesis that if a 
 straight line fall upon two parallel straight lines it makes the 
 exterior angle greater than the interior and opposite angle upon 
 the same side^°, and from the thesis that a triangle contains 
 angles equal to more than two right angles". 
 
190 NOTES TO 
 
 NOTES TO APPENDIX B. 
 
 1] This is oddly worded. Perhaps we should read Srav 
 TTpoaiTocli'qa-r] tovto 6 Bet/criis to &bvvaTov, or, orav ■npbi avTl(j>amv 
 TovTov beiKv6r]TaL to abvvaTov. 
 
 2] ' AvTicjyrjtravTos, So read for avTuprjo-as. One MS. gives 
 avTi<f)'qa-as rts. 
 
 3] In a direct disproof of a thesis if we cancel the thesisj or 
 rather the terms of which it is composed, we cancel an essential 
 part of the syllogism. 
 
 4] This refers apparently to ch. v. of Sophistici Elenchi. If 
 so, this passage must be a later addition, as we have seen (note 
 to ch. ii) that the Analytica was written before the Sophistici 
 Elenchi. 
 
 5] Things are said to be awtxH) continuous, when the hmit 
 which separates them is common to both. To bi avvex^ onep 
 exofievov ti rj a-nToy-ivov. Aiyoo be <Tvve\es orav tuvto yevrjrai kcu 
 kv TO eKaTepov iitpas oXs aitTovrai Koi avvexovrai, &(tt€ bfjXov on to 
 avvexii ev tovtois e^ &v ^v ti Tret^WKe yCyvecrdai Kara tt/v avva^iv, 
 Metaphysica, lo. la. ' Continuity is a species of holding on or 
 touching. Two things are continuous when the two extremities 
 by which they touch and hold together are one and the same. 
 Continuity, therefore, is between things united at the point of 
 contact.'' SuiJexes 8e KiyeTai ov ri Klvr)(ns p.ia xaff' aiiTo kcH fi^ 
 olov re 8.\\ms- fxla 8' ov abialperos. Metaph. 4. 6. ' Two parts are 
 continuous whose motion is essentially and necessarily one and 
 indivisible.'' If we gave Kwrjcns a logical sense, in which sense 
 Kweiadai is sometimes used, two propositions would be (Tvvix^ 
 which must stand or fall together. We shall see however that 
 Aristotle calls a thesis and conclusion avvixr) when their destinies 
 are not thus implicated. 
 
 6] For example : suppose the thesis to be. Every animal lives ; 
 the premisses. All snow is white. All that is white is an animal; 
 the conclusion. All snow is an animal. Here the subject of the 
 thesis is a part of the conclusion. 
 
 7] Suppose the thesis to be, as before. Every animal lives; 
 the premisses. All that lives is a plant, Every plant is insensible; 
 
APPENDIX B. 191 
 
 the conclusion, All that lives is insensible. Here the predicate 
 of the thesis is a part of the conclusion. 
 
 8] 'Apxijs is emphatic. When we take an inferior series, 6 e^ 
 apxrjs Spos, the extreme or remotest term, is the superior term 
 of the thesis. When we take a superior series, 6 e^ apx')* °P°^ 
 is the inferior term of the thesis. Let the thesis be represented 
 by MN, where Jf is the subject and iVthe predicate. The in- 
 ferior series will be represented hy K L M, the superior hy NOP. 
 For the validity of a reductio ad absm-dum of the thesis M N, a 
 ratiocination composed of the inferior series of terms must pro- 
 duce no absurdity until it embraces the superior term of the 
 thesis, N: and a ratiocination composed of the superior series 
 must produce no absurdity until it embraces the inferior term 
 of the thesis, M. In the previous examples by combining the 
 thesis with the conclusions we might obtain the further absurd 
 conclusions. All snow lives, and Every animal is insensible, and 
 the ratiocinations embrace the extreme terms of the thesis. But 
 the reductio is not valid, because these are not the first ab- 
 surdities that arise, for before introducing the thesis we had 
 previously arrived at the same, or rather, equal absurdities. All 
 snow is an animal, and All that lives is insensible. 
 
 9] We should add, ' or an equally impossible conclusion ;' for, 
 as we saw in the last note, it is not exactly the same conclusion. 
 
 A reductio ad absurdum, being an assignation of cause, should 
 stand the test of the method of difference. The impossibility 
 that is found in the presence of the thesis should disappear in 
 its absence. A similar consideration should guide us in deter- 
 mining to what class a fallacy should be referred. See ch. xxii. 
 
 10] I have assumed that in speaking of exterior and interior 
 angles Aristotle uses these terms in the sense in which they are 
 used by Euclid, i. 39. A scruple as to his meaning is suggested 
 by his saying that the lines will meet if the exterior angle is 
 greater than the interior, when it is clear that they will equally 
 meet if it is less: but this scruple vanishes when we observe 
 that in the next hypothesis he says, that they will meet if the 
 angles of the triangle are greater than two right angles, when 
 he might just as well have said, unless they are equal. 
 
 11] Euclid, X. 3a. 
 
192 
 
 APPENDIX C. 
 
 ENSTASIS, OR OBJECTION. 
 
 Eva-raaris Se eatL TrpoTacris npoTdaei kvavria. Aia^epei Se 
 rfjs TTporda-eoas, on rfjy fiev iva-raaiv evSey^erai ehai Kal eirt 
 fiepovs, TTjv Se irporaa-iv ^ oXcos ovk evSix^rai, ^ ovk ev tok 
 Ka66Xov avXXoyia-fioTs. ^iperai Se f] eva-racns 5tx«y re koi 
 Sia Svo (TXV/^dTCOv, Six<os jAv otl f\ KaOoXov rj ev p-epei wdca 
 evaraa-is, Sia Svo Se crxvfJ-dTcoi/ on di/nKeifievai ^epovrai Trj 
 irpoTaaeij to, Se avTiKeifieva ev rm •trpdiTco Kal ev tw rpiTW 
 <TxfilJ.a-rL TrepaivovTai /lovois. "Orav yhp d^Lwa-rj Travrl imdpr 
 Xf', eviardfieOa rj on ovSevl fj on nvl ovx inrdp^ei, rovrmv Sk 
 TO fiev p,T}Sevl eK tov npdoTov (rxvf^aTOS, to Se tlvl jir) e/c tov 
 eaxdrav. Oiov ecTTCO to A, fiiav etvai eina-TrjfirjV e(p' w to B, 
 evavna' npoTeivavTos Srj /liav eTvai toiv evavncov eniaTriiirjv, rj 
 on oXeos ov^ ^ ouirrj twv avTiKeifMevcov eviaTaTai, Th Se evavTia 
 dvTLKeifjLevar &crTe ytveaOai to npaiTOv axvfia' V on tov yvco- 
 (TTov Kal dyvdxTTOV ov fiia- tovto Se to /". Kard ydp tov F, 
 TOV yvcooTOV Kal dyvdxTTOv, to fiev evavTia eTvai dXriOh, to SI 
 jiiav avTwv evurTTJ/irjv eivai ifrevSos. fldXiv eirl rfjs areprjriKfjs 
 TrpoTaaeoDS dxravTCos. A^iovvTOS yap to fifj eivai fiiav eirKTTTj- 
 fj-rjv T&v evavncov, ^ on Trdvrcov t5>v dvTiKeifievwv fj on tlvS>v 
 tSiv evavTicov rj avTrj Xeyojiev, oTov vyieivov Kal vocrwSovs. To 
 fiev ovv TrdvTCov eK tov 7rpd>T0V, to Se tivcbv eK rov rpirov (^XV' 
 fiaTos. AttX&s ydp ev nda-i, kuOoXov fiev eviardjievov, dvdyKr} 
 rrpos TO KaOoXov tS>v TrpoTeLvo/ievoov ttjv, dvTi^acnv eiireiv. Oiov, 
 el (irj T-qv aiiTTjv d^ioi tcov evavncav irdvTcov, elwovra rwv dvTi- 
 Keifievcov jiiav. OCtco S' dvdyKr] to irpwrov etvai axv/^i^' l^fo'ov 
 
193 
 
 APPENDIX C. 
 
 ENSTASIS, OK OBJECTION. 
 
 An enstasis^, or objection, is a proposition proving the contra- 
 dictory or contrary of a premiss. It differs from a premiss be- 
 cause it may be particular, while a premiss must be universal, at 
 least for univeral conclusions. An objection has two degrees, 
 and is urged in two figures : it has two degrees because it proves 
 either the contrary or the contradictory of the premiss ; and it 
 has two figures, because it proves the opposite of the premiss, 
 and the opposite (at least if the premiss is negative) can only be 
 proved in the first and third figure. If the premiss is a uni- 
 versal afiirmative, the objection proves a universal negative or 
 particular negative; in the first case the proof is in the first 
 figure, in the second case in the third. Let A represent objects 
 of the same knowledge, or simultaneously known, B contraries, 
 C the knowable and unknowable, I) opposites, E health and dis- 
 ease. If the premiss objected to is. All contraries are objects of 
 the same knowledge, the objection may be either that no oppo- 
 sites are objects of the same knowledge, and the proof will be in 
 the first figure. 
 
 No B is A, 
 
 All B is B, 
 .-. No -B is ^2. 
 
 or it may be that the knowable and unknowable are not objects 
 x)f the same knowledge, and the proof will be in the third figure : 
 
 No C is A, 
 
 All C is B, 
 
 - • . Some B is not A '^- 
 Similarly if the premiss objected to is negative. For if it asserts 
 thg,t no contraries are objects of the same -knowledge, we may 
 
194 APPENDIX C. 
 
 yotp ytviTai to kuOoXov wpos to k^ ap^rji. ' Ev fiepei Si, npos 
 6 kvTi KaOoXov Kuff o5 XiyeraL rj irp&raa-ii, oTov yvaxTTOv Kal 
 dyvwcTTOv fif] TTjv avTrjv T& yap kvavTia KaOoXov rrpbs Tavrv 
 Kal yiveTai to TpiTov a-)(r)(JLa- fieaov yap to kv fiepei Xajx^a^ 
 v6[iivov, oTov TO yvcccTTov Kal TO dyvcoa-TOv. E^ d>v yap kari 
 (TvXXoyicTaaOaL TovvavTiov, kK tovtwv Kal t^s kyaTaaeis kiri- 
 )^eipovfj.ev XkyeLv. Aib Kal kK fiovcov t&v axtjuaTaiv tovtodv 
 (f>epofj,ev. Ev fiovois yhp tovtols ol avTiKiifUvoL avXXoyurjioi- 
 Sik yhp Tov fiea-ov ovk ^v KaracpaTiKms. "En Se Kav Xoyov 
 SeoLTO irXeiovos rj Sia tov fikaov (r)(^/j,aTOS' o?ov, ei [i^ Soirj to 
 A tS B indpyeiv Sia to /J,fj aKoXovdeiv avT& to /". Tovto yap 
 Si dXXoav vpoTcicremv SfjXov oii Set 5e els dXXa kKTpkirnrQai 
 TTji' evcTTacnv, dXX evOvs <f>auepav ex^"' "^^^ kTepav TrpoTacriv. 
 Alb Kal Tb arjjif.'iov kK fiovov tovtov tov cr)(^iMaTos ovk ecrnv. 
 ' EiriaKenTkov Se Kal irepl tSiv dXXmv kvcrTaaecov oiov nepl tS>v 
 kK TOV kvavTiov, Kal tov o/ioiov, Kal tov KaTci, So^av Kal et Trjv 
 kv fiepei e/c tov irpmTov ^ ttjv (rTfprjTiKfjv kK tov fikaov Swarov 
 Xa^eTv. Anal. Prior, a. z8. 
 
 flepl Se. Xvcrewv k)(6/j.ev6u kaTi twv elprjfievayv einelv. EiTTi 
 Se Xveiy fj dvTC<rvXXoyi(rdfj.evov ^ evaTaaiv kveyKovTa, To iitv 
 
APPENDIX C. 195 
 
 either object that all opposites are objects of the same know- 
 ledge, and then the proof is in the first figftre : 
 
 AU B is A, 
 
 All B is B, 
 .•• All ^ is ^: 
 or we may object that some contraries, say, health and disease, 
 are objects of the same knowledge, and then the proof is in the 
 third figure : 
 
 All ^ is A, 
 
 All E is B, 
 . • . Some B is A. 
 If the objection has to prove th6 contrary of the premiss, the 
 genus comprehending the subject of the premiss must be made 
 the subject of the objection and receive a contradictory predicate. 
 If the premiss is that no contraries are known together, the 
 objection says that all opposites are known together, and we 
 have the first figure, for the genus of the original subject is the 
 middle term and the original subject the minor. If the objection 
 has to prove the contradictory of the premiss, a species com- 
 prehended under the subject or the premiss must be made the 
 subject of the objection, as knoWable and unknowable are com- 
 prehended under contraries. Then we have the third figure, for 
 the middle term is an inferior species comprehended under the 
 minor. A premiss that gives an opposite conclusion is an objec- 
 tion, and such can only be applied in the first and third figures, 
 for the second cannot give an affirmative conclusion. Besides, 
 in the second figure more premisses would be necessary. If we 
 objected to the proposition. All B is A, that No A is C, a second 
 premiss must be expressed to make the disproof evident. But 
 objection should be complete in itself and require no further 
 premiss to be expressed *. For the same reason the second figure 
 is the only one unfitted for proof by signs. We must at some 
 future time examine the remaining modes of objection, namely, 
 the objection of contraries, of similars, and of authority j and 
 inquire whether an objection proving a contradictory cannot be 
 raised in the first figure^, or an objection proving a negative in 
 the second. 
 
 Next to enthymeme (oratorical proof) real and apparent, 
 solution remains to be explained. Solution is enstasis or counter- 
 
 a 
 
196 APPENDIX C. 
 
 oSv avTurvWoyi^eadai SfjXov on eK tZv avT&v Toncav kvSex^Tcu 
 iroieiy oi jjikv yap avWoyia-fiol €K tZv evSo^cav, SoKowfa Se 
 TToXXa kvavTia aXX'^Xois kaTLV. Ai S evaTaa-eis (f>ipovTai, KaOd- 
 Trep Kal kv roTs tottikoTs, rerpax^y fj yap k^ eavrov, fj kK rod 
 ofioLov, fj kK Tov kvavTiov, ^ e/c rmv KeKpifievmv. Aeyco Se a^ 
 iavrov fikv olov, ei vepl eponTos eir] kvOv/xruia ws a-novSaios, 17 
 eva-racris Si^ms, ■?] yhp KaOoXov eiTTOvra on nacra evSeia novrj- 
 pov, ^ Kara fiipos on oiiK &v kXeyero Kavvios epcoy el fifj ■rjo'av 
 Kal irovrjpol epcores. E-rrl Se tov kvavnov evarairis (f>epeTai 
 oiov, el TO evOvfiriiia rjv on 6 dyaObs dvrjp iravTas Tois <f>iXovs 
 ev TToie?, aXX' ov^ 6 iioyQTjpos kukcos. 'Ewi Se twv o/ioiav, el 
 riv TO evdvfn]/jia on at KaKms iretrovBores alel /iiaovcnv, oti aXX' 
 ovSe ol eS ireTTOvOoTes alel <piXovcnv, Ai'Se Kpiaeis at dirb tSiv 
 yvcopi/jLcov dvSpStv olov, ei ns kvdv/irjfia ehrev oti toI^ jieGvauffi 
 Set avyyva>[ir]v e^eiv, dyvoovfTes yap afiapTavoxxnv, evaraiTii 
 on, ovKovv 6 HiTTaKos alveTos' ov yap dv fiei^ovs (rijiiai kvon 
 /loOeTTjtrev edv ns fie6v<ov ajiapTavri. Rhet. a. 25. 
 
APPENDIX C. 197 
 
 proof. Counterproof will obviously be derived from the same 
 repertories as proof. For the repertory j)f proof is the sphere 
 of probabilities, and probabilities support opposite conclusions. 
 Enstasis, or objection, as we said in the Topica, is of four orders : 
 it is the allegation of co-ordinates, or of contraries, or of similars, 
 or of authority. The allegation of co-ordinates is of two kinds. 
 Suppose the enthymematic premiss objected to to be, that no 
 love is evil, we either allege the genus of the subject, and object 
 that all want is evil, or we allege a species of the subject, and 
 object that a Caunian love is evil ®. For an example of the alle- 
 gation of contraries, suppose the enthymematic premiss to be, 
 that a virtuous man is a benefactor to all his friends, we may 
 object that a vicious man does not hurt all his friends ''. For an 
 example of the allegation of similars, suppose the premiss to be, 
 that those who are injured always hate, we object that those 
 who are benefited do not always love*. In the allegation of 
 authority we quote the judgment of the eminent. Suppose the 
 enthymeme to be, that ignorance is an excuse for the violation 
 of law, and therefore intoxication is, we object that if this were 
 true, Pittacus would have been wrong when he increased the 
 penalty for offences produced by intoxication '. 
 
198 NOTES TO 
 
 NOTES TO APPENDIX C. 
 
 1] Enstasis is either the solution of a fallacy by pointing out 
 why the reasoning is inconclusive {biaCpecris), or the disproof of 
 a false premiss (avaCpea-is). It is the latter only that is now 
 examined. Enstasis is neither the mere negation of a propo- 
 sition^ nor the assertion of the contrary or of the contradictory 
 of that proposition, but is the major premiss of a syllogism by 
 which the contrary or contradictory may be proved. 
 
 2] Were it not for this kind of enstasis and the locus of 
 authority, the final appeal in dialectic, on the part both of ques- 
 tioner and answerer, would be solely to induction. But it seems 
 the answerer might not only appeal to induction, but to a prin- 
 ciple more abstract and universal than the proposition in dispute. 
 But for the avros e(j)a of Aristotle, one would have thought that 
 this mode of disproof should be rather called antisyllogism than 
 enstasis. From the modern sense of the word instance (instantia 
 = enstasis) this kind of enstasis, in physical questions at least, 
 seems to have early fallen into desuetude. 
 
 3] In the Topica we have an ethical example of this kind of 
 enstasis. "Ert Srav jxr] jf ^vavriov tu yivu, a-KO-neiv y!r\ fiovov d to 
 evavriov ev roJ avria yevei aWa koI rb ava fxi<Tov. 'Ev u yap to aKpa 
 KoX TO, ava p,i(rov, otov kin Aeu/coS koI p,i\avos. 'Evoraats on rj fiev 
 evbeia Koi viT(p^o\ri iv tw avr^ yivei, ev to koku yap dp-^e), to be 
 ItiTpiov, di/a pAaov 6v tovtwv, ovk ev t(3 kuk^ d\\' iv ru ayada. 
 Topica, 4. 3. ' When the supposed genus of a term has no con- 
 trary, we should observe whether it is the genus not only of the 
 contrary of the term, but also of the intermediate gradations. 
 For (Proposition) contraries and their intermediate gradations 
 belong to the same genus, as we see in colours. Objection : the 
 contraries, excess and defect, belong to the genus evil, while 
 their intermediate gradation, the mean, belongs to the genus 
 good.' [This enstasis is clearly not valid ; for good and evil are 
 accidents, not genera, of the mean and extremes : the common 
 genus is relative quantity.] 
 
APPENDIX C. 199 
 
 4] It is clear that an affirmative proposition may be disproved 
 in the second figure. But Aristotle apparently would call such 
 a disproof not enstasis but antisyllogism* Energetic brevity is 
 a requisite of enstasis : its probative or subversive force must be 
 instantaneously felt without further explanation. The second 
 figure, therefore, being, as is here without much reason assumed, 
 more intricate and cumbrous and requiring more enucleation than 
 the others, is not short, sharp, and decisive enough for enstasis. 
 
 5] Enstatic disproof in the third figure may just as easily be 
 stated in the first : otherwise, regarding the above-given disproof 
 in the first figure as rather antisyllogism than enstasis, we might 
 agree with Whately in calling the third the enstatic figure. 
 
 6] This class has been analysed in the preceding passage. To 
 h9viJ.r]ixa seems, perhaps, rather to point to a conclusion than a 
 premiss : but in this chapter enthymeme is used as the genus 
 of irapdheiyfia or induction, and every dialectical premiss is the 
 result of induction. 
 
 7] Analysing this example as in the preceding passage, we 
 must, as far as I can see, for our minor premiss borrow from the 
 locus of contraries the maxim that the action of the virtuous is 
 opposite and analogous to that of the vicious, and for our major 
 transform the enstasis, that the vicious does not hurt every 
 friend, into the equipollent proposition, that to act oppositely 
 and analogously to the vicious is not to benefit every friend. 
 
 8] For our minor premiss we must borrow from the locus a 
 fortiori, vel minori, vel pari, the maxim that those who are 
 injured act oppositely and analogously to those who are served, 
 and, for our major, transform the enstasis, that those who are 
 served do not always love the benefactor, into the equipollent 
 proposition, that to act analogously and oppositely to those who 
 are served is not always to hate the injurer. Both these exam- 
 ples seem to apply the same maxim. (See, however, Topica, 
 3. 7, quoted below.) They shew that it is unsafe to assume, as 
 is usually done, that the maxims or metaphysical principles of 
 proof always occupy the position of major premisses. 
 
 9] The example is so carelessly given that it is not certain what 
 analysis Aristotle intended. I conjecture the following : The pre- 
 miss objected to is, that ignorance is an excuse : the enstatic syl- 
 logism is. Drunkenness is not an excuse (teste Pittaco), drunken- 
 
200 NOTES TO 
 
 ness is ignorance, therefore some ignorance is not an excuse. 
 This kind of enstasis only differs from the first in the modality 
 of the enstatic premiss. It has no intrinsic probability, derives 
 no evidence from experience, but rests solely on the authority of 
 Pittacus. 
 
 It seems an arbitrary arrangement to call disproof by the loci 
 of contrariety and similarity, not antisyllogism but enstasis; 
 and the illustrations are unfortunately chosen, for, without being 
 told, we should never have suspected that they were taken from 
 different loci. 
 
 Contraries are a locus common to the attack and the solu- 
 tion. SKOTreiv 8e /xr) jxovov eir' aiiTov tov d.pr)\t,ivov, aWa koL km tov 
 evavTiov to evavriov otov Sri to ayadov oix e£ dvdy/cjjs r)hv' ovh'k 
 yap TO KaKOV XvTirjpov ri el tovto KCiKelvo. Kal ei j] biKaiocr6vri em- 
 a-TrJixr), Kal rj abixla Syvoia. Ei be tovto firi, ovb^ 6K€LV0....0vb\v yap 
 a\ko vvv a^Lovfiev ^ to evavrlov tu evavTim clkoKovOuv. Topica, a. 9. 
 'The questioner may quit the subject in dispute and examine 
 its contrary. He may confute the thesis that the good is always 
 pleasant, by the fact that the bad is not always painful, or vice 
 versa, or the thesis that justice is knowledge, by the fact that 
 injustice is not ignorance : the axiom assumed being that con- 
 trary subjects must have contrary predicates.' Similars are also 
 a common locus. "En ek toC opioioos {m6,pxeiv,...el bvo bvalv dpaioas 
 VTt&p\il' €1 yap TO erepov rm erepo) p/q vwapxei, ovbe to Xoiirbv ru 
 Aotir(S' el be imapyeL to ^Tepov t^ erepiD, nal to Xomov t<o XoivS. 
 Topica, 2,. 10. ' Similars are another locus. If there is an equal 
 probability that two subjects have respectively two predicates, 
 if one has its predicate we may infer that the other has, and vice 
 versa.' Aristotle justifies the example he has given of enstasis 
 from similars by what he says in the Topica : Ai p,ev ovv irparai 
 b^o prjdeLcraL [evavTLUiv) (rvpntkoKal ov itoLOVcnv evavTCacriV to yap 
 Tovs (l>(Kovs ev TTOielv T<a Toiis e)(dpovs KaK&s ovk icmv evavTioV d.p- 
 <p6repa yap alpeTO, (cot tov avTov tjOovs. Ovb^ to tovs tplkovs Kaum 
 Tu Toiis e^dpovs eZ, Kal yap TavTa ap,(l>6Tepa (fievKTa koX tov awroii 
 
 ^Oovs To 8^ koma irdvTa TeTTapa iioui evavTi(i(nv. To yap tovs 
 
 0iAovs eS TToieXv tm tovs (^i\ovs Kan&s evavTiov. Topica, a. ']. ' The 
 two first syntheses of contraries are not themselves contraries. 
 Benefiting a friend is not contrary to hurting an enemy, for 
 both are desirable and proceed from the same disposition; nor 
 
APPENDIX C. 201 
 
 is hurting a friend contrary to benefiting an enemy, for both 
 are undesirable and proceed from the same disposition. But the 
 other four combinations, benefiting a friend^ hurting a friend : 
 benefiting an enemy, hurting an enemy : benefiting a friend, 
 benefiting an enemy : hurting a friend, hurting an enemy j are 
 all respectively contraries/ 
 
 The fourfold division of enstasis may be illustrated by a four- 
 fold character of propositions and organa. 'Eo-rt 6e irpo'iacrts Sta- 
 XcKTiK^ fp<ar7)(7ts evbo^os ?j Tracnv r) tois ■TrAetorois fj rots cro(f>OLS, koI 
 TovToii ^ iraaiv ri rois TrXelarois rj tois fiaXtora yvapCixois, fir) itapa- 
 bo^os. QeCrj yap av Tis to boKovv tois o-o(/)Ois, iav p-r] kvavriov tois 
 T&v voKk&v bo^ais 77. EtVt 8e Trpordcreis biaKeKTiKoi Kai to rots iv- 
 60'fots ojioia, Koi TavavTia KOt' avTitfjaariv tois boKOV(nv fvbo^ois flvai. 
 TipoTii.vop.iva, KOI o<7ot Bo'^ot KaTCL TtyvO'S etf' Tas evpr]ij,evas. Topica, 
 1. 10. 'A dialectic proposition is a proposition probable to all 
 or to the majority of mankind ; or an opinion of all or the ma- 
 jority of philosophers or the most eminent of them, not opposed 
 to the opinion of the many ; or a similar proposition respecting 
 similar subjects ; or an opposite proposition respecting opposites ; 
 or any doctrine of the arts/ Tas p^lv'ovv irpoTdcreis fKkeKTeov 
 6(Tax&s biapta-dri....AeL be TrpoTeiveiv koI ras ivavrCas rals <(>aivop.4- 
 vais fvbo^ois Kar avTi^a(nv \pri(np.ov b\ koH to iroieiv avTas iv T(3 
 tKXiyfiv firi jjLOVov tos oiio-as evbo^ovs dXAo Koi ras op-oias TOVTais. 
 Topica, 1. 15. 'The propositions to be collected are, as was said 
 before, the opinions of the many or of philosophers, or the doc- 
 trines of the arts ; and we may use any propositions that bear a 
 certain relation to these, i. e. where opposite antecedents have 
 opposite consequents, or similar antecedents similar consequents/ 
 In fact, propositions respecting a given subject, and, mutatis 
 mutandis, respecting similar or opposite subjects, might be treated 
 as identical. 
 
 Enstasis was the only check on the inartificial induction by 
 simple enumeration practised in dialectic. 'Ear yap eTil navrcov 
 (jiaCvrjTaL biaipeaiv ti poeveynacnv rj em ttoW&v, ^.^lariov /cat KadoKov 
 Tidivai, rt fvorraa-LV ij)epeiv inl tCvos ovx ovtms. 'Eav yap nr)b{Tepov 
 Tutiricv iroifl, &totios (jiavfiTai p-rj TideCs. Topica, a. 3. 'If all or 
 many of the particulars into which a class is divided present an 
 attribute, we may demand either an admission that it is true of 
 the whole class, or an assignment of instances in which it is not 
 
202 NOTES TO APPENDIX C. 
 
 true. If the respondent does neither one thing nor the other, 
 he is unreasonable/ (Antisyllogism was considered hardly suffi- 
 cient) "Ert 8' ev tols yevenv im^XeTrriov, biaipovvra kut etbr} jxi- 
 Xpi T&v hTojxtov. "Av re yap iravrl (^afor;rat vndpxov av re ^.Trfiivi, 
 TToKKa -npoeviyKavTi a^iaiTeov Ka06\ov o/^ioXoyeii', tj (^ipuv evaraa-LV 
 ivl TWOS ovx ovrcos. Topica, 3. 6. ' Subdivision, as far as we can 
 go, is useful; for whether we want an affirmative or negative 
 proposition, we must first adduce particular examples in which 
 it is true, and then challenge the respondent either to admit the 
 general principle or to allege contradictory instances/ 
 
 A disputant who is more accustomed to defence than attack 
 may quicken his wits when he has to attack by imagining him- 
 self on the defensive. "En to Trpo^Xruxa TtpoTacriv kavT^ Tioiovfifvov 
 kvia-Taudai' fj yap eva-rains Icrrai ^TTixelprjixa irpbs Trjv Oecriv. Topica, 
 2. 2. 'The questioner may imagine the thesis to be a premiss 
 against which he has to object as respondent : and his objection 
 to the proposition as a premiss will be a confutation of the pro- 
 position as a thesis.'' 
 
 A common formula for urging an enstasis, especially when it 
 is directed against a major premiss and is a proposition which 
 the opponent is particularly interested not to contradict, is to 
 say that his argument proves too much : that, if good for any- 
 thing, it proves so and so (the contradictory of the enstasis). In 
 this case, instead of being put directly or ostensively, the enstasis 
 assumes the form of a reductio ad impossibile. 
 
203 
 
 APPENDIX D. 
 
 Koival dp)(ai, or, Method-founding principles. 
 
 § I. To understand the nature of the common principles {koi- 
 vdi apxai) is to understand Aristotle^s conception of sciencCj and, 
 indeed, his conception of logic ; for his logic is resumed in the 
 contrast of science and dialectic, and this is the antithesis of 
 common and peculiar principles (Ktat Apxai). We propose in 
 the following essay to collect some of the scattered indications of 
 their nature ; and the necessity of explaining more or less com- 
 pletely each passage as it is quoted must be our excuse if our 
 observations seem to foUow one another without much arrange- 
 ment. 
 
 The most important passage is in the beginning of the 
 Ehetoric : — 
 
 T&v bi ev6viir\ixaTmv [leyCcTTri bLa(popa km i^dKiara XeArj^uta (r^e- 
 bbv &iiavTas ea-rlv rjitep Koi Tsepl Trjv biaKeKTixriv fxedobov t&v avXko- 
 yi.(T]j.S>v. Ta ju^v yap avT&v eari Kara rqv p7)TopiKr\v mairep Koi Kara 
 Trjv biaKeKTiKTiv^ fiedobov t&v avWoyicrii&v, to. bi kut aWas Te)(vas 
 Kal Swdjuets tcls \j.\v avcras ras 6e oiT:(o'KaTiiXr)p,jj.ivai. Ato Koi 
 \av6avov(n tovs aKpoaras, kol jxaWov a-nTajxevoL r) KaTO, TpoTiov fxera- 
 jSaivovcTLV f^ avT&v' ixoKXov be cra(^es eoroi to Xeyonevov bia TT\fi6- 
 vo)v pr]div. Aeyco yap biaXeKTiKOvs re Kal prjTopLKOvs a-vX\oyicrij.ovs 
 eivai trepl Zv tovs tottovs XiyofxsV ovtoi 8' eluXv ol KOivy irepl bLKa(a>v 
 KOI <f)V(TiK&v Kal Tiepl ttoXltik&v Kal Tiepl itoXX&v buu^epoVTtav t<S 
 eiBef olov 6 tov jmiXXov Kal t^ttov tottos" oiibfv yap jxaXXov lorai e/c 
 tovtov ovXXoyl(racT9aL rj evdv[ir]iJi.a eiitfiv irepl biKaCav rj (pvaiK&v f) 
 
 " Kwri is here emphatic. Kara tV Sia\fKTue(iv is equivalent to olKt7a t^i Bio- 
 \(KTMrjs. We must distinguish between appropriate to dialectic and appropriate 
 to a given subject-matter. Those principles are properly dialectical and compose 
 a dialectical proof which are not peculiar to any subject-matter {xoival). Those 
 which arc peculiar to any subject-matter [fSmi tov Tpdy/ii.aTos'] axe extra-dialectical, 
 and constitute a proof scientific or pseudographic. 
 
204 APPENDIX D. 
 
 Tiepl Stovovv kuCtol ravra etbei Siac^e'pei* Ibia be, Sera iK t&v irepl 
 CKaoToy etbos Kal yivos -npoTatre^v kcrriv olov irepl <j)va-LK&v el<Tl 
 TTporaa-eis If &v ovre kvdvp.rip.a otire crvWoyiufWi laTi Ttepl t&v ijfli- 
 K&V KoX Ttepl. TOVTcav aWai e£ &v ovk lorat "nepl t&v ^vcrtK&v' 
 ojoiotius be TovTo e^et eTrl TtdvTtiiv. KaKSiva ixev ov irotTjcret Trepl ovbev 
 yivoi ep.^pova- Ttepl ovbev yap VT!0Keip.ev6v ia-Tf ravTa be, 6cr(a ns 
 hv j3e\TL0Vi eKkeyrjTai tcls TipOTacreis, Krjaei Tiotijcras 6.k\r]v eTiicrTrip,r\v 
 TTJi bidKeKTiK^s KM prjTopiKrji' &v yap evT^xV ^PX^'S', ovk In 8ia- 
 XeKTiKT) ovbk prjToptKTj a\K' eKeCvrj earai rj^ 1^^' ''"^ apxp.^. 'E(tti be 
 TO, wAetcrra t&v evQvp,'r)\J.aTiov Ik roijTaiv t&v elb&v Xey6p.eva t&v KaTh 
 jxepos Kal ibibiv, Ik be t&v koiv&v eXdTTio. KaOcnrep ovv koi ev toIs 
 ToviKoHs, Koi evTavOa biaipereov t&v ev6vp.r]p.&Taiv to, re elbri kcu, tovs 
 TOTtovi If S)V \r]TiTeov. Aeyto b^ etbrj p.ev tos KaQenacrTov yevos ibias 
 Tiporairets, totiovs bi tovs koivovs 6ij,oCa>s TravToiv. liporepov oZv 
 etirw^jLev Trepl r&v elb&v. Rhet. I. 3. 
 
 ' Between rhetorical proofs the most important distinction, 
 a distinction which has been most commonly, not to say uni- 
 versally, overlooked, is one which also exists between dialectical 
 proofs : some are characteristic of rhetoric or dialectic, others 
 properly belong to certain special sciences or arts, whether such 
 sciences and arts are generally recognized or still remain to 
 be invented. If the science has not yet been established, the 
 theorems and proofs are not familiar to the audience to which 
 they are addressed ; and if the prover adheres too closely to 
 the scientific method, he abandons the proper rhetorical or 
 dialectical method. This requires further explanation. Proofs 
 that properly belong to rhetoric and dialectic are applications of 
 a locus communis. Loci communes are principles that apply 
 indiscriminately to ethical, physical, political problems and 
 other heterogeneous spheres, as, for instance, the argument 
 a fortiori or a minori. A dialectical or rhetorical proof of this 
 character applies equally to ethical and physical questions and 
 other subjects different in kind. Intransferable (that is, not 
 properly rhetorical or dialectical) proofs are composed of propo- 
 sitions which relate exclusively to particular departments of 
 nature. For there are propositions respecting physical objects 
 which furnish no rhetorical or dialectical proof on ethical ques- 
 tions, and there are ethical propositions which furnish no proof 
 on physic^:! problems, and so of the other provinces of science. 
 
APPENDIX D. 205 
 
 The common principles give no scientific knowledge of any class 
 of things, for they do not constitute theu essence of any class : 
 whereas the peculiar principles if well selected, though people 
 may not be aware of the fact, go towards constituting a parti- 
 cular science, distinct from rhetoric or dialectic. For if the prover 
 happens to hit upon first principles his proof is not rhetorical or 
 dialectical but scientific. Most rhetorical proofs are composed 
 of specific, that is, particular and intransferable propositions ; 
 only a minority are composed of common principles. A rhetorical 
 treatise, therefore, like a dialectical treatise, must distinguish 
 the specific principles of proof from the loci of proof. Specific 
 principles are principles that exclusively belong to a particular 
 class of problems j loci are methods (premisses) of proof that are 
 equally applicable to all classes.' 
 
 In the last sentence instead of tov9 koivovs we should have 
 expected ras kowch [TrpoTdcreis]. But this passage is one instance 
 of a certain indecision in Aristotle's mind whether to treat the 
 loci as premisses or as methods, as indicative or imperative, as 
 categorical or hypothetical, as constituent principles (in the 
 language of Kant) or as regulative, as objective or subjective, 
 as laws of nature or as rules of procedure. He avoids, there- 
 fore, the unmistakeable term, wporda-ets, and uses the obscurer 
 term, loci. However, even from the present passage, we may 
 certainly infer that the word loci designates premisses. Aristotle 
 does not say. Every proof has two elements ; one is formal or 
 dialectical, the other is material or extra-dialectical : but He 
 says. There are two divisions, two separate classes, of proofs ; 
 one proof is properly dialectical, the other is not properly 
 dialectical. As the specific or sectional character of the pre- 
 misses is the differentia of the one class, the generic or catholic 
 character of the premisses must be the differentia of the contra- 
 distinguished class. We shall see further on [§ 6] that one 
 branch of dialectic may consist entirely of such syllogisms : 
 but considering the subjects handled by the orator, it is clear 
 that in oratorical proofs the maxims [to kolvcl] and specific facts 
 [to. ihia] will be usually combined in the same syllogism. 
 Aristotle would therefore have done better in a rhetorical 
 treatise to found on the distinction of Xbia and Koivd a division 
 not of proofs {ivdvjj.rifj,dT<i)v) but of premisses. 
 
206 APPENDIX D. 
 
 Another proof that locus may denote a premiss we have in the 
 fact that later on in the Rhetoric^ not only the catholic prin- 
 ciples or loci proper but the effirj or specific principles, which are 
 perpetually called premisses, are designated by the term of loci. 
 After giving a collection of specific principles (elbr]) he says : — 
 
 Els jJiSV OVIf TpOTTOS TTJS l/cAoy^S KCU TTp&TOS oStOS 6 TOTIIKOS' TO bk 
 
 (TToix^ia T&v evdvfxrin&Tatv KeycaiMfv. Sroixetov 6^ Aeyw koI tottov 
 evOvfirJuaTos to avro. . . . SxeSoK ix^v ovv fniiv -ntpl kK&(TTa>v t&v 
 elh&v T&v XRV'^H-'"^ """^ avayKaiav exovrai ol tottoi. 'E^iiKiynivai 
 yap ai Trporderets wept 'iKacnov elcriv, war' [exojiiei'] ef Ssv Sei <j)epeiv 
 TO, ev6v}i.rnmTa TOTtav •rnpl ayaOov ri KaKov fi Kakov rj ala-xpov rj 
 btKaCov r] abiKov, koI nepX t&v riO&v koI Tsa6r\ix6,Ta>v koI e^euv axraH- 
 Toos elkrjixfjievoi fjixiv virdp\ov(n TtpoTepov ol tottoi. 'Eti 6' aXXov 
 Tpoirov KaBoKov Trepl anavTonv \<i,j3a)p,ev. Rhet. a. 2,2,. ' One class 
 of materials, and the class that should first be collected, are 
 propositions such as I have given which (as contrasted with to. 
 e^ vTtoyvlov, or the singular facts of each particular case) are in. 
 the nature of loci. We now proceed to the elements of proof, 
 and by elements I mean [another sort of] loci. We are already 
 in possession of loci on the particular subject-matters that are 
 indispensable or useful to the orator : for we have made a collec- 
 tion of propositions and enumerated the loci respecting the 
 expedieat and honorable and right, and respecting characters 
 and passions and dispositions. There still remain another sort 
 of loci of universal application (the loci proper), which we now 
 proceed to enumerate.' When, however, we find that the loci 
 enumerated include etymology, division, definition, induction, it 
 must be confessed that we seem to have rather a list of methods 
 of reasoning than of premisses of syllogism. But the employ- 
 ment of each of these methods has to be justified by certain 
 postulates, expressed or unexpressed ; and if the loci are regarded 
 as propositions, it is these postulates that are the loci. (This 
 subject is resumed § 13.) 
 
 § 2,. We find frequent mention of common principles (rd /cojyd) 
 in the analysis of science under the name of Axioms. 'Aju,e'<rou 
 8' dpx^s crtiWoyKrriKTjy Oiaiv y.\v Xiym rjv p.ri eort Seifat jliij6' dydyxij 
 exeiv Tov nadr]a6fj.€v6v tl' rjv b' avdyKT) e^eLV roi' otiow jxaOrjao- 
 ^evov, a^iaiiia. Analytica Posteriora, i. a. 'Immediate syllo- 
 gistic principles are either theses, that is, are indemonstrable. 
 
APPENDIX D. 207 
 
 but not the necessary conditions of all inference : or axioms, 
 that is, the common conditions of all influence. ■" If science as 
 well as dialectic has both ibiai and koivoX apxo-h how, it may be 
 asked, do they differ, and how can the Koival apxai be the dis- 
 tinguishing badge of dialectic [(cara Trjv StaAexTtK^v, § l] ? The 
 answer is, that the common and peculiar principles exist both 
 in science and in dialectic, but exist in an inverse ratio. In 
 dialectic the common and abstract principles predominate, and 
 the specific concrete facts are reduced to a minimum. In science 
 the specific data predominate, and the common principles are 
 reduced to a minimum, only those being admitted which are 
 requisite to constitute a faculty of inference. Of course when 
 dialectic investigation proceeds without, or with very scanty, 
 specific data, the result can only be a Barmecide feast of abstrac- 
 tions such as we have in the Parmenides. Aristotle himself in 
 his physical inquiries ('Physicam Dialecticse suae mancipavit^), 
 forgetting his own canons, engages in a task which reminds one 
 of that set by Egyptian taskmasters of making bricks without 
 straw. But dialectic may command specific data in various pro- 
 portions, and ranges over a wide field, touching sophistry on 
 the one side and on the other approaching indefinitely near to 
 science. Km, ijmK\ov a-nrotxivoi {t&v ihiuiv) Kara Tpoirov, [iera^al- 
 vovcTiv ef aiiT&v [rfjs prjropLKrjs Koi rfjs biaXeKTiKrjs]. See § I. 
 
 The common principles of science are identified with the com- 
 mon principles of dialectic. 'YiUiKoivavovaL 8e waorat al fTtifniJixai 
 aWrjKais Kara to, koivA {koivo, 8e Xfyoo oTs \p&VTM ms «k to'utcov 
 anobuKvvvTes, aW' ov irepl &v tuKvvovcnv, oiS' o beiKvdova-i) Koi rj 
 biaKiKTLK.fi irdcats, koI ft ns Ka66\ov ■neipZro heiKvvvai to, Koivd, 
 olov on dirav <j)6,vai fj a/wocfidvai, 17 on lira otto tcroov, jj t&v Toiovrav 
 aTTa. Analytica Posteriora, 1. 11. 'The common principles ex- 
 press neither the subject nor the attribute of a theorem, but are 
 the canons of demonstration ; and are the common property of 
 the particular sciences, of dialectic and of (metaphysic or) what- 
 ever science it is which investigates these propositions ; Of two 
 . contradictories one or the other must be true ; Equals from which 
 equals are subtracted have equal remainders; and the like.' 
 We must interpret this to mean that the common principles of 
 science are included among the common principles of dialectic, 
 not that they are coextensive. This is clear from the following 
 
208 APPENDIX D. 
 
 considerations. The axiomSj we saw above, are indispensable 
 to reasoning ; but many of the maxims cannot be indispensable, 
 for science contrives to dispense with them, e. g. the maxims 
 that constitute the unscientific formulas of reasoning by analogy 
 or a fortiori. Secondly, an axiom is a necessary truth, a maxim 
 may be merely a probability. Ovk ia-ri 6' imoOea-is oiib' atrrjiM o 
 avayKrj elvat bt aiiTO Kot boKeiv avdyKrj. An. Post. I. lO. 'An 
 axiom differs from an hypothesis or petition in being necessarily 
 true and necessarily believed.^ We know that dialectic only 
 professes to rest on probabilities (er8o£a), and we find in the 
 Topica that this applies to the common as well as to the specific 
 principles. E. g. *H el Icrn fiev n antfioiv ava jiAaov, k<u t&v 
 elbSiv Kcu T&v yev&v, jOi?j Ofxolas be,. . . ^ubo^ov yap to o/xoicds a/n^oiv. 
 Topica, 4. 3. ' If a term and its contrary are connected by 
 gradations, it is a probable postulate that their genera, when 
 not identical, are connected by similar gradations/ Thirdly, 
 the axioms, as we saw above, are necessarily believed or self- 
 evident; whereas some, at least, of the maxims require the 
 evidence of induction. E. g. Aei yap to, ivavTia ev Ta awu yeVet 
 ftvai, av ij,ribev ivavrCov t<o yivei tj. Oitos 8' evavriov tZ yivu, 
 cTKO-neiv el to ivavTiov iv t<S kvavriw. ^AvdyKt] yap to ivavriov hi 
 r(5 fvavTla elvai, avirep rj ivavTiov tl r<o yivet. f^avepov be tovtcov 
 SKaa-Tov bia ttjs enayayrjs. Topica, 4. 3. ' Contrary terms have 
 the same genus, unless there is a contrary to the genus. If 
 there is a contrary to the genus, it ought to contain the con- 
 trary term. These postulates are evidenced by induction.' 
 Even the laws of conversion require this support. 'Ettei 6' al 
 avTi6i(nis rea-a-apes, cTKOTrelv ^k fjiev t&v avTi(l)d<Teci)v av&'naKiv €/c 
 TTJS aKoKovd^creais xal avaipovvTi /col KaraaKeviiiovTi, Xafi^aveiv 8' ef 
 eTrayu>yrjs' oTov el 6 avdpcuiTOi C'^"" '"o f*^ ^<fov ovk avQpairos. Topica, 
 3. 8. ' There being four kinds of opposites (contradictories, 
 contraries, privatives, relatives) to prove or disprove a sequence 
 of two terms, we should observe whether their contradictories 
 present a converse sequence (i.e. whether the terms admit of 
 conversion by contraposition), and we must establish the law of 
 conversion by induction. For instance, if all man is animal, all 
 not-animal is not-man.' It is not necessary, then, to a dialectic 
 maxim to possess the evidence or necessity of a scientific 
 axiom. 
 
APPENDIX D. 209 
 
 § 3. The peculiar principles of science are definitions and 
 hypotheses, that is, propositions asserting the existence of the 
 things defined, ©ecreaiy 8' ^ fjiev diroTepovovv r&v fioplmv t^s ano- 
 ^6,v<re<os kauPdvova-a, dtov \iy(o to elval Ti rj to ju.^ etvaC ti, vnoOf- 
 (Tts, T) 8' &vev TovTov opio-fio's. Analytica Posteriora, i. a. 'Theses, 
 or peculiar principles, are either hypotheses, that is, afiirmations 
 or negations of existence, or definitions/ Mill denies that defi- 
 nitions are an indispensable basis of science, and maintains that 
 postulates (hypotheses) suffice as germs of scientific evolution. 
 But, aftep pointing out that other logicians had combined the 
 definition with a surreptitious postulate, he himself, when he 
 maintains the self-sufficiency of the postulate, combines the 
 postulate with a surreptitious definition. For without a defini- 
 tion the postulate is merely the proposition, X exists ; and from 
 such a proposition, without any explanation of the nature (defi- 
 nition) of X, it is impossible that any consequences can be de- 
 duced. The specific basis of science is a definition — postulate, that 
 is, is composed of two distinct elements and cannot accurately 
 be called either a definition or a postulate. On this point Ari- 
 stotle has expressed the truth more exactly than either Dugald 
 Stewart or Mill. Tlaaa yap diro8etKriKij kTsi.(Trr)p.r\ ttepl rpla iffrl, 
 oca re elvai TiOerai, TavTa 8' lorl to yivos, o5 t&v Kaff avTa TtaOr}- 
 pArav IotI 0e(i)pr]TiK^, Koi to. Koiva keyopLeva a^idpMTa, If &v Tipc&Tuv 
 airobfUw(ri, kcH Tptrov to, Tt&Qr], &v tC <rrip,aCvei l(caaToj> \ap,fidveL. 
 Evlas /*e'iToi eirnTTTj/itas ovbev KcaXvei Ivia Tovratv irapopav, otov rb 
 yivos p,ri vvoTl9e(78ai thai, &i> fj <t>avepov on lort. . . . Kal to, naOti 
 fii) Xaptpdveiv tI <n\p,alvii, hv jj 8^Xa* &a-iTfp ov8^ to, koivo, ov Xap.- 
 fiavei tC cr]iw,Cv€i, to lira cmb luruv d^c\»z>, on yvdpiiwv, 'AA\' 
 ovhev rJTTov - rf) ye c^j/o-ei Tpia tuvtSl iarTi, wept 8 Te beiKvvcrL koI h 
 iiUvva-i Kal If &v. An. Post. I. lo. 'In all demonstrative science 
 there are three elements: the subject, whose existence is as- 
 sumed and whose essential laws are developed; the axioms, 
 which belong alike to every science ; and the attributes, whose 
 definition is assumed and whose existence in the subject is the 
 law we demonstrate. When any one of these is obvious, it will 
 be neglected : if the existence of the subject is obvious, an hypo- 
 thesis is not needed : if the definition of a predicate is obvious, 
 it may be omitted. The meaning in the axiom of subtracting 
 equals from equals is too plain for definition. But really there 
 
210 APPENDIX D. 
 
 are always, three elements of demonstration, the subject, the 
 attributes^ and the catholic canons of proof.' 
 
 Any classification of the sciences that we choose to adopt will 
 serve as a classification of the specific principles of dialectic 
 {Spyava, elbi]). Aristotle gives one that has had a great currency 
 both in ancient and modern times, though difierent from that 
 which he adopts in his more philosophic writings. He says 
 they may be roughly classed as physical, ethical, and logical 
 (metaphysical). "Eart 8' ws rvira irepiXa^eiv r&v Trpordo-etov koI 
 T&v irpofikrjfji.&Tcav p,€pri rpCa. At fiev yap ■qOiKoi t: porda- f is fl(rlv, 
 al be ^vaiKai, al hi \oyiKaL 'H0i/cai pkv ovv al Toiamai, ohv 
 Ttorepov 8ei rois yoveviri imWov ^ toTs v6p.ois ituQapyjEiv, iav hia- 
 0coi'5(n" KoyiKcii, hk, otov nonpov t&v evavricav fj avrr] lirior^^?; ^ 
 oii" (f)V(nKa,\ be, Ttorepov 6 /cotrftos d'lSios rj oi' Sp-oias be nal to itpo- 
 ^krni,aTa. Ooiat 8' ?KaoTai r&v TTpoeiprjfjJvav, opurpM nev tniK 
 evTteres wnobovvai itepl avroii', rrj be bia rr]s eTTaya>yfjs a-vvrjOeia Ttei- 
 pariov yviopl^eiv eKda-rriv avr&v, Kara ra npoeiprj^xeva napabeiy\iata 
 ima-KOTtovvra. Topica, I. 14. 'Propositions and problems may 
 be roughly thrown into three divisions, ethical, physical, and 
 logical. Of ethical propositions the following is an instance: 
 Should we obey our parents or the laws when their commands 
 are inconsistent ? of logical the following : Are contraries simul- 
 taneously known or not? of physical the following: Is the 
 world eternal or not? And so of problems. To define these 
 classes would not be easy, but we must endeavour to identify 
 them by practice with the help of these examples.' 
 
 § 4. In the Topica the word opyava denotes the particular 
 premisses (eXbrj). Aristotle elsewhere, or whoever named his 
 logical treatises opyavov, uses the word in a different significa- 
 tion. In the Topica it signifies the materials (i/Xtj) which are 
 furnished to the artist, and the loci or maxims, as contradis- 
 tinguished from the materials, represent the tools with which he 
 works. But when the name of organon is given to the whole 
 of logic, it denotes the latter, i.e. the loci or purely logical 
 principles, which constitute an organ or faculty of cognition, 
 co-ordinate with the natural organs of perception [Kpir^pia), the 
 eye, the ear, the hand, or with artificial organs of appreciation, 
 the thermometer, chronometer, barometer. 
 
 When the problem is ethical or physical, there is a difference 
 
APPENDIX D. 211 
 
 in kind between the organa and loci, and they present the con- 
 trast of special and catholic principles. But when the problem 
 belongs to the third divisionj that is, when it is logical, the dis- 
 tinction disappears, the organa and loci coincide, and logical 
 conceptions are the materials as well as the tools of the dialec- 
 tician. Accordingly in another classification of problems Ari- 
 stotle describes the third division (to. Xoyticci) as instrumental 
 and subordinate theorems, that is, in terms which are equally 
 appropriate to the loci. Ylpo^Kruxa 8' £(ttI biaXsKTiKov ds(&pritia to 
 (niVTfivov rj irpbs aipe(Tiv koi ^vyriv, ?j irpos aXrjd^iav kcu yv&criv, rj 
 avTO ff ms avvepyov Trpos ti trepov t&v toiovtcov. . . . "Evia fjiev yap 
 T&v TtpofiktiixaTtov xp'qcri^wv eiievai Tipbs to kXicrOai r\ (jjvye'iv, olov 
 •noTipov fi rjbovj] aiperbv rj ov, evia 8e irpos to eibivaL fiovov, olov 
 voTepov 6 Koa-jjios Mbios fj oij, ivia h\ avTO, p.ev Kaff avTCL irpos ovbi- 
 Tfpov TovTinv, (Tvvepyb, bi iari Trpos nva t&v roioijTcov. TioKKa yap 
 avra iiip icafl' avTa ov ^ovkop.fQa yvapCCetv, eripcov S' IveKa, S-ncoi 
 biM ToiTmv &XKo ti yvo)p((T(i>p,ev. Top. I. II. 'A dialectic problem 
 is either a practical (ethical) or speculatiYC (physical) theorem, 
 or is subservient to the decision of a practical or speculative 
 question (logical). That is to say, the solution of some pro- 
 blems is useful for our guidance in action, as whether pleasure 
 is to be pursued ; that of others has no end beyond knowledge, 
 as whether the world is eternal : another class are in themselves 
 neither useful nor interesting but are ancillary to ulterior 
 inquiries.' 
 
 § 5. From our present point of view we may see that Whately's 
 distinction of logical and extra-logical fallacies will not bear 
 examination. He considers that some forms of fallacy, for in- 
 stance, the fallacy of equivocation, are essentially extra-logical. 
 Adopting the theory that logic is conversant not with things 
 or ideas but with words, he says that, whenever to detect a fal- 
 lacy it is necessary to understand the meaning of a word, the 
 fallacy is extra-logical. The logician may happen to know the 
 meaning of the word, but, if he does, he does so not as a logi- 
 cian, but as a moralist or mathematician, or in some other 
 capacity. This is untenable. It is clear that the logician must 
 know the meaning of some terms. He must at least know the 
 meaning of all the terms of his own science. Unless a parrot 
 can be a logician, no one can be a logician to whom the terms 
 
 P 2 
 
212 APPENDIX D. 
 
 universal, particular, antecedent, consequent, necessary, contin- 
 gent, are mere words without meaning'. This list may be ex- 
 tended almost indefinitely. If we reflect on what is discussed 
 in logical treatises, we see that the logician requires all the 
 conceptions as well as the vocabulary of — what till we find a 
 better name we will call — ontology {to, \oyiKd). When, there- 
 fore, the problem belongs to the sphere of ontology, the logician, 
 by his logical knowledge, will be able to detect any fallacy that 
 depends on the meaning of the terms, and such fallacies will 
 be purely logical. The dialectician, however, has a still wider 
 range than the pure logician. He has to deal with all ethical or 
 physical conceptions that fall within common cognition (IfSofo, 
 boKovvra tols iroWoTs). Ethical or physical premisses, though 
 special or particular propositions in one sense, that is, in respect 
 of the subjects to which they apply, are common or universal 
 opinions in another sense, that is, in respect of the minds by 
 which they are entertained. Fallacies from the application of 
 principles that lie beyond the range of ordinary information are 
 extra-dialectical (■^evboypaiprJiJ.aTa) . Whether ethical problems 
 can furnish a pseudographema may be doubted. Even the physic 
 of Aristotle's day, composed, as Bacon says with some truth, of 
 vulgar notions loosely abstracted, could hardly farnish argu- 
 ments beyond the competence of the dialectician. Accordingly 
 the only examples of pseudographema that Aristotle gives, are, 
 agreeably to the etymology of the name, geometrical. 
 
 § 6. Without stopping to discuss the relation of logic in its 
 modern sense to the logic {to, koyiKo) of the Topica, assuming, 
 moreover, that the latter (of whose nature Aristotle has scarcely 
 given us any means of judging beyond the passages already 
 quoted) is the science to which the maxims properly belong, we 
 may regard it as more or less completely identical with ontology 
 or metaphysic. We have already seen (An. Post. i. ii, quoted 
 in § 2), that the common principles are found alike in the par- 
 ticular sciences, in dialectic and in a certain universal science. 
 The name of this science is not given, but we are elsewhere told 
 it is metaphysic or philosophia prima. 'Eirel bi 6 jiia9?jjoionicos 
 XP^roi Tois KoivoHs IbCais, koI ras Toirav apyai h> etij ^ewp^o-ai t^s 
 wpj^Tijs <^t\o(ro(^ios. Metaphysica, 11. 4. 'As the mathematician 
 only makes a limited application of the common principles, their 
 
APPENDIX D. 213 
 
 adequate investigation belongs to metaphysic/ A paradox here 
 arises. The common principles are the me%as by which the phi- 
 losopher makes himself intelligible to the unphilosophic, they 
 are the intellectual capital, the common sense, of the ignorant, 
 npos 8^ Tas ivreij^ets xPW'^l^os V Ttpayiiarela, Siori ras t&v ■noKK&v 
 KaTXipuBiuinevoi. bo^as ovk e/c t&v &X.\oTp[mv a\)C €k t&v olKelmv 8oy- 
 I/Athv o^uXT^a-onev Ttpos avro-is, p-eTajii^dCovres Sn hv firi koK&s (jtaC- 
 vmvTM Xiyeiv fnuv. Topica, 1.2. • Dialectic is useful to the phi- 
 losopher in his intercourse with the world, because, giving him 
 possession of the creed of the uneducated, it enables him to 
 reason with them on their own principles and to influence their 
 opinions when he thinks them mistaken.' To say that the igno- 
 rant talk metaphysic without knowing it, and that metaphysical 
 reasoning is the reasoning of the uneducated, seems paradoxical, 
 and sounds like the sarcasm of a positivist. But though it is 
 asserted that the principles of the ordinary public are in sub- 
 stance metaphysical, it is not maintained that they apprehend or 
 state them with any precision. Tmha yap (r& koivo) ovhiv rjrrov 
 Itratriv avToC (01 ih&Tai) k&v boK&crt X(av Ifa) Xiyeiv. Sophistici 
 Elenchi, II. 'The uneducated possess the common principles 
 as well as the educated, though their expression of them may 
 be very inaccurate.'' Besides, the truth is, that all reasoning, 
 scientific and unscientific, involves metaphysical principles ; and 
 unscientific reasoning is only called pre-eminently metaphysical, 
 because it is composed in a larger proportion of those abstract 
 principles which, either because they are innate or because they 
 are the easiest and earliest generalizations, are of general accepta- 
 tion, than of the specific facts which can only be learnt by a 
 specially directed observation. 'En bl itpbs ^vfof s ovb' el ttjv aKpt- 
 jSeordrTji; I)^oi/uei' Iwiottj/xiji/ pqbiov am sKeCvris Treiaai XeyovTas' 8i8a- 
 (TKoXlas ydp fffnv 6 Kara ttjv ^■niiTT'qp.r]v \6yos, tovto be oMvarov 
 aW av&yKi] bia t&v koiv&v itoieicrOai, rai iriorets Koi tovs \6yovs, 
 &(n:ep koI ev tois roTTi/cois kKiyofiev irepl Trjs itpbs tovs itoXkovs 
 ivTiiu^eods. Rhet. i. i. 'To some minds the most exact science 
 would not enable us to convey persuasion. A teacher and a 
 learner are implied in the proper scientific proof, and this rela- 
 tion may be out of the question. Then the catholic methods 
 are the only means of persuasion or conviction, as I said in the 
 Topica about the intercourse of the philosopher with the world.' 
 
214 APPENDIX D. 
 
 Plutarch, or the author of Placita Philosophorum, says that the 
 Stoics (who very likely took the doctrine from Aristotle) held 
 that the axioms, or principles that constitute the logical faculty, 
 are fully developed by seven years of age. T&v 6' ivvoimv al fih 
 <j)v<TLKal ylvovrai Kara tovs elpr)ii,ivov<i rponovs Koi aviT!iTe)(vriTii>s, at 
 8' ^8)7 81' rjixerepas bibatTKakCas koX i-niixekeCas' avrai, fx^v oBv ^vvoiai 
 KaXovvTai fiopov, SKt'ivaL b^ Kal wpoXTji/^ets. 'O 8^ Xoyos K&ff bv irpoir- 
 ayopevopLfda koyiKol ex t&v •npokqy^remv avfiTiXripoviTdai Xiytrai Kara 
 Trjv 7!p(!>Tr)v efibop.6.ba. 4. 1 1 . ' Ideas are either natural, that is, 
 acquired in the way we have mentioned (sensation and expe- 
 rience had been mentioned), and inartificial, or are artificial and 
 the result of culture. The latter are specially called ideas, the 
 former are specifically called anticipations (axioms). The rea- 
 son, in virtue of which all men are called rational, is formed by 
 the development of the anticipations in the first seven years of 
 life.' In illustration of the statement that logical principles 
 are metaphysical theorems, we might refer to the ontologieal 
 inquiries on which the rudiments of logic are based in the 
 Sophistes of Plato, to the position of the axioms in the Meta- 
 physic of Aristotle, or to the metaphysical discussions in Mill's 
 System of Logic, on the uniformity of nature, on the law of 
 causation, on chance, &c. &c., which lay the foundation for his 
 exposition of inductive method. 
 
 § 7. After reviewing these general statements on the nature 
 of the loci, if we proceed to examine the list of them given in 
 the Topica and Rhetoric, our first impression is one of surprise. 
 The loci given are not easy to reduce to any common principle, 
 and their common principle, so far as it is perceptible, is not 
 what we might have expected. From Aristotle's apparent iden- 
 tification of the maxims and axioms, we might have expected 
 to find the maxims to be applications or specifications or corol- 
 laries of the axioms. For some reason or other, perhaps to 
 reserve something for his immediate disciples, Aristotle has care- 
 fully avoided giving the loci in the form of propositions, so that 
 it would be rash to assert that the propositions which he con- 
 ceived to be grouped under the loci bear no relation to the 
 axioms : but we may safely say that no such relation is 
 obvious. 
 
 Many of the loci, most of those given in the Rhetoric, may 
 
APPENDIX D. 215 
 
 easily be grouped under the category of correlatives. When 
 unable to demonstrate the attributes of any term taken by itself, 
 that isj when we have not materials for scientific reasoning {KaO' 
 avTO, Kar ovaCav), we still may reason dialectically {kut S,\\o, 
 Kara avii^e^rjuos) , by leaving the term and examining another 
 term to which it stands in some definite relation, and then, 
 mutatis mutandis, transferring the attribute of the second term 
 to the first. The mutation to be efiected, or the conditions of 
 the transfer, may be supposed to be expressed in an axiom or 
 topical maxim. Such correlatives are : Contraries, Similars, 
 (giving rise to the methods of induction, analogy, argumen- 
 tum a pari) ; Terms similar in quality and dissimilar in quantity 
 (giving rise to the argument a fortiori and a minori) : Parts 
 (giving rise to the methods of partition and division) : Elements, 
 (giving rise to definition) : Antecedent, Consequent, Name (giving 
 rise to the argument from etymology), &e. &e. But the vast 
 majority of loci in the Topica are of a different nature, and are 
 held together by a different bond of union. 
 
 The nature of the arguments to be employed in a discussion, 
 and of the rules for their invention, must be determined by the 
 nature of the problem discussed or the thesis controverted. Every 
 proposition that is supported or subverted must assert or deny 
 a relation of subject and predicate, and this relation must be one 
 of four, that is, if ^4 is the predicate and S the subject, the pro- 
 position must assert or deny that A is an accident, or a genus, 
 or a property, or the definition of £. Of course the definitions 
 of accident, genus, property, definition, must decide respectively 
 what is the nature of the proof required in support of any such 
 conclusion. Aristotle accordingly breaks these four definitions 
 mto as many fragments as possible, presents them under as 
 many different aspects as he can imagine, and calls these frag- 
 ments and aspects of the definitions by the name of loci. But 
 the theories of accident, genus, property, are all resumed in the 
 theory of definition : for definition must be a truth or matter 
 of fact {aXriOh elveiv) like accident, and a law like genus and 
 property, besides presenting its own peculiar characteristics. All 
 the loci, therefore, that arise from these four definitions may be 
 grouped under one head, the definition of definition. Up&Tov 
 ovv d«opr]Tiov fK Tiv<av fi juc'dodos. Et 8^ Xa^oinfv irpbs i:6<ra koI 
 
216 APPENDIX D. 
 
 TToia Kal Ik tCvuiv oi \6yoi, koI ■n&s rovratv tvirop'^a'oixfv, ^o(/biev hv 
 Ikuvus to TipoKeCiievov. 'Eort 8' UptBii^ l(Ta mi to. avra If &v re o\ 
 Xoyoi KciX Ttfpl &v oi avkkoyiffiwC. TCvovrai /ikv yap oi Xdyoi l/c t&v 
 wpordo-euv, iiepl S>v h'k ol avWoyurfwi, to, TrpojSXTj/xardt eori, Tiouxa 
 h\ -npoTtuns Kal -nav TipoPKrjfm rl yfvos 17 ibiov rj (rvju/SejSrjKds StjXo?. 
 Topica, I. 4. 'Let us first enquire of what branches the method' 
 is composed, and when we have classified conclusions and pre- 
 missesj and shewn how to obtain the latter, we shall have accom- 
 plished our task. The classes of premisses and conclusions, that 
 is, of propositions and problems, are identical ; for every propo- 
 sition and problem expresses either a genus, a property, or an 
 accident/ Property is then subdivided into property and defi- 
 nition. M^ XavQaviTut 8' rums 8n to. irpbs to Xbtov koI to yivos koH 
 
 Th (n;jw./3e^r;K(5s irdura Kot irpos tovs opuriMrus app.6afi Xiyecrdcu 
 
 ilore Kara tov ip/npovdev amohoOivTa Koyov S/iravr &v ewj TpoTtov 
 Tiva opiKa TO, KarripiOfiriniva. Topica, 1,6. ' The rules for pro- 
 perty, genus, and accident all apply to definition: so that all 
 the rules may be regarded as rules of definition.' Upos (xev oSv 
 TO avfi^e^riKOi bia t&v toioiutwv koI oSrmy kTuxeiprfriov. Mera 8^ 
 ToSro TsepX t&v npos to yivos Kal to ibiov liturKemiov. 'Eirn tik 
 TavTa aroiysia t&v wpos tovs opovs' 'nepl aiiT&v 8^ ToiTiav oKvy&KK 
 al o-KEi/cets yivovrai rots bidkeyofiivois. Topica, 4. I. 'After these 
 rules for disproving accident, the rules for examining pretended 
 genus and property must be expounded. These will be elements 
 of the method of testing definition. Genus and property are 
 seldom themselves the final object of dialectic discussion.' T^s 
 8^ TTfpl rois opovs TTpayixaTeCas ft^ipr] TtivTi kaTiv. *H yap on oAtos 
 ovK iXrjO\s eLTteiv, Kaff' o5 Tovvop.a, Koi tov \6yov (Sei yap tov toS 
 avOpdirov opKrpJbv Kara navros avBpditov akridev&Tdai) ^ on ^iiros 
 yevovs ovk eOrjKev eis to yevos rj ovk els to oiKeiov yivos Idrj/ce (8ei 
 yap tov opiCofievov (Is to yevos OivTa ray hia^opas itpoaaTtTeiv pA- 
 Atora yap t&v ev tS opurp^ to yivos hoKel ttjv tov 6piCop,ivov ovcrlav 
 (rriixaCveiv) , rj otl ovk tbtxis 6 Aoyos {bet yap Tbv opuifiov Ihiov eivoi), 
 ri el Ti&VTa to. elprip.iva Treiroiijiccis ju^ &pi<TTai, p.'qb' etprjKe t6 tI r\v 
 etvai T& opi^oixevco. AoLitov 8^ irapa to. elpfr\p.iva, el &puiTai pkv p,Ji 
 KoASff 8' &pi.aTat. Topica, 6. i. 'The method of examining defi- 
 nition has five branches. We either shew, as in the case of 
 accident, that the predicate is not true; or that the genus, at 
 least the proximate genus, the dominant part of the essence, is 
 
/ 
 
 APPENDIX D. 217 
 
 not given; or, as in the case of property, that the subject is not 
 siffieiently distinguished ; or, that the essejice is not expressed ; 
 or, that the expression is inelegant/ 
 
 § 8. We have seen that all the loci of solution by distinction 
 (iia(p((ris) , that is, all the means of exposing the inconclusive- 
 ness of a disproof, may be reduced to the definition of confuta- 
 tion. [*H 6^ otJrws biaiperiov tows ^aivo^iivovs cuAXoyitr/iioiis Koi 
 ikiyxovs, ^ ir&vTas civaKreov els rriv tov eXiyXP'" "■yvoiav. "Ean yap 
 S/jtavras avakvffai tows kexdlvras Tpanovs els tov tov eKiyKov bio- 
 puriiov. Sophistici Elenchi, 6.] We now see that the loci of con- 
 futation, and, therefore, also the loci of solution by antisyllo- 
 gism and objection {avalpea-is) , are all reducible to another defi- 
 nition, the definition of definition. The former definition is the 
 basis of what Cicero calls the log^c of judgment, the latter of 
 what he calls the logic of invention. See his Topica, eh. a. 
 
 Though the definition of proof or disproof properly furnishes 
 the loci of solution, yet the questioner as well as the respondent 
 may sometimes appeal to this definition. This, however, is only 
 when the respondent has raised the question, whether the proof 
 is conclusive. "'En <2<7irep ovb' ev troXXoyio-juu XanJSdveTai, rl lori to 
 srvXKeKoyiaBai, ae\ yap SKt] ^ iiipos fi Ttporacns e^ &v 6 (TvWoyicriios, 
 oikws ovbe to tC ^v etvat bei eveivat kv ru avKKoyicrfj^ dAAa ytopls 
 TovTO T&v Keiptfvtov elvai.' koI Trpbs Thv dju^tcr/SjjTowro el avXXeXo- 
 yioTM ^ firi TOVTO, arravTCLV, 8n, tovto yap ^v (TvWoyKTfxos' Kai irpos 
 TOV on oil TO tC Jiv etvai avKXeXoyiarai, on vaC, roiJro yap Ixetro 
 Tjfuv to tL r(v elvai. "ilo'Te avdyKt] koI i.vev tov tC avWoyurixos ^ tov 
 tC ^v elvai (rvX\e\oy[<T6ai ti. An. Post. a. 6. ' As in proving we 
 do not define proof, for the terms of the syllogism are always 
 related as whole and part, so in demonstrating a definition (de- 
 fining) we ought not to assume among our terms a definition of 
 definition ; but as, if our proof is disallowed, we maintain it by 
 defining proof; so if our proof of definition is disallowed, we may 
 reply by defining definition. As we draw a conclusion inde- 
 pendently of the definition of proof, so we ought to prove a 
 definition (define) independently of the definition of definition.' 
 
 [To digress from our present subject, we may observe that the 
 objection here raised by Aristotle to a mode of proving definition 
 hardly seems to express his final view. Indeed it admits of an 
 obvious answer. All dialectical proof is based, as we have just 
 
218 APPENDIX D. 
 
 seen, on the definition of definition; a particular proof there- 
 fore, i. e. the proof of definition, may well rest on the same basis. 
 For a further answer to this objection see § 13.] 
 
 That the questioner sometimes appeals to the definition of 
 proof appears from another passage. To bl jn?j hbe^firdaj, aim 
 (pdpai KoX airocfidvai ovbeixCa Xafi^dvei, diro'Setf w, dXX' rj eav berj Seifai 
 Kol TO avjj/nipaaixa oiVcos. AeCxwraL be \a^ovai to -np&Tov Kara 
 Tov fxia-Qv oTi aXrjdis, airo^dvai 5' ovk dkrides. To be ijJtrov [icaTh. 
 Tov TTp^TOV AXijfles] ovbev buKJ)epei flvai xal /j-rj etvai Ka^flv, acraij- 
 Toos Koi TO TpiTov [(CttTa TOV {licTov] . El yap eb66r), Koff o? cLvdpwnov 
 aKr\&ks ehielv, el kcu [xafl' oij firi-avOpairov &\ridis, AAA' el /jlovov 
 [icafl' oB] &,v6p(ttirov, fuov elvai yJq-^'mov be p.-ff lorat oKrfih eVneiv, 
 JkaWiav, el km jxri-KaWlav, Sfias C^ov /jLTj-^aov 8' ov. An. Post. 1. 1 1. 
 ' That of two contradictory predicates one must be false, is never 
 expressed in demonstration, except when we wish to maintain the 
 cogency of a proof. We maintain it successfully if we can shew 
 that we have a major truly affirmed of a middle and not truly 
 denied [and this middle similarly related to a minor] . If we have 
 this, it is indifierent whether the middle can be truly denied of 
 the major or the minor of the middle. For if all man is animal, 
 and not not-animal [and Callias is man and not not-man], it 
 follows that Callias is animal and not not-animal, even though 
 not-Callias be also man, and not-man be also animal.' The 
 passage is not very lucid, and a disputant would have very little 
 chance of victory unless he could shew with rather more force 
 and clearness than Aristotle in the text, that his reasoning was 
 an apphcation of the axiom, and therefore satisfied the condi- 
 tions of proof. The passage, however, is interesting, as, com- 
 pared with the one last quoted, it raises a strong presumption 
 that in Aristotle's mind the axiom is identical with the defini- 
 tion of proof. If so, the antithesis between axiom and definition 
 (two of the three classes into which he divides scientific prin- 
 ciples) has a point where it vanishes, the axiom being transform- 
 able into the definition of syllogism. 
 
 § 9. It seems that at one time Aristotle thought that the loci 
 of invention (confutation) as well as the loci of solution might 
 be obtained from the definition of proof. This seems to have 
 been his theory when he wrote the Prior Analytic. After ex- 
 plaining the nature of syllogism and subdividing it into its 
 
APPENDIX D. 219 
 
 moods and figuresj he tells us, in effect, that these may serve as 
 so many sign-posts to guide us in our se§rch for arguments. 
 nSs fifv oZv yiviTai ttSs (7uAAoyttrjoios koX hia noaaiv opatv Kot wpo- 
 Tia-euv kol tt&s ex"""''**' '"'P^s aXX.rj\as, en 8^ ttolov itpofiKrijj.a iv 
 eKOffTU cr)(riiJ,aTi kcA iioiov iv iiKeCoat ital itoiov kv kX&TTOtri beUvvTai, 
 hrjKov Ik t&v v.pr\fiAi'a>v. Urns 6' evTroprja-oiiev avrol Ttpbs to TtOepifvov 
 del (rv\Koyi(TiJ,&v, kcu, 6ta TToCas obov \r]\}f6iji,e6a ras irtpl iKaa-TOV 
 apxAs, pvv rjbr) KiKTeov. Ov yap [iovov terms Sei ttjv yivediv Oecopeiv 
 T&v avkXoyi,(Tfj,&v, aXKa koI ttjv bvvaixiv ^x^iv tov ■noulv. Anal. 
 Priora, i. 37. ' The nature of syllogism and the number and 
 relations of its terms and premisses, and the figures in which 
 any conclusion may be proved, have been explained. It re- 
 mains to point out the sources from which we may obtain them 
 and the method of discovering premisses for each conclusion : 
 for we want not only to know the way in which proofs are pro- 
 ducedj but to acquire a power of producing them.' He after- 
 wards recapitulates in similar terms. 'Er woVots p.iv olv <T)(rip.a<ri 
 Kai hia Ttoimv Koi itoaiav TTpoTaaeatv kol wore km, ttSs yCverai cri/X\o- 
 yLa-p,6s, iTL 6' ets iroia ^iXfmiov avaa-KevaCovTL koI KaTacrKiv&^ovTi, 
 Ital ttSs Set fTj^eti' irepl tov TipoKeipiAvov xa^' oTtoiavovv pAOobov, ^ti 
 be bia iroiai obov Xi\\^6p,e6a ras Ttepi Ixacrroi' ap\as, ijbr] SteXrjAjJ- 
 dafiev. An. Priora, 2. i. * The number of the figures, the num- 
 ber and nature of the premisses, and the conditions of proof, the 
 cardinal points in affirmative and negative proof, the universal 
 methods of investigation, and the paths which we must follow 
 in our search for evidence, have now been sufficiently explained.' 
 The preliminary accumulation or registration of facts and ma- 
 terials is spoken of in the same terms as in the Topica. ['EkAo/a- 
 Paveiv, eKXrjTiTeov, eKKeyew, fKKeKreov, eicXoyTj, biayeypaij,p,eva, bia- 
 ypaiprj.^ The precepts indicating the ground to be reconnoitred, 
 or the points to which our attention must be directed, are not 
 caUed aroixeta or rdirot, as in the Topica, but eTTi^Kiyj/eis, eiri- 
 crKe\j/eLs, or VKe'^eis. E. g. (pavepbv be xal oti ai &k\ai a-K4\j/eis t&v 
 Kara ras exAoyas a-xpeioi irpbs to TroieXv cruK\oyiap,6v. An. Prior. I . 
 a8. ' To ascertain other relations among the facts we have 
 registered will be of no service in our reasonings.' AijXov bk koi 
 on oTtoM TavTo, \r]itTeov ra^ KaTO. rrfv eTrCa-Kexj/iv, Kal ov)^ OTTOia Irepa 
 y] evavTia. Ylp&rov p,ev on roC p,e<rov xA-piv fj €7ri/3Aev/fts, to bi p,ecTov 
 
220 APPENDIX D. 
 
 ovX ^repov AWa toiitov 8ei Aa/Seiv. Ibid. ' In scanning our ma- 
 terials we must try to find propositions with, a common factor, 
 because we want middle terms, which these only can give/ 
 'SiVjx^aivei hj) Tois oiirtoy eTncTKOitovcrt irpoaeTn^KiTieiv oWtji* 68bv 
 TTJi &vayKaCas. Ibid. 'To look for other relations would be to 
 make an unnecessary search in paths where we cannot find what 
 we seek.' The rules, introduced with such pretensions, only 
 amount to this : After accumulating our materials we must look 
 through them to find the terms of our proposed conclusion so 
 related, respectively, to any third term as they are in any of the 
 moods of any of the figures in which such a conclusion could be 
 proved. When we have found this, we have found our proof. In 
 this system it is evident that the moods of syllogism correspond 
 in function to the loci of the Topica. A brief trial of the system 
 would probably suffice to demonstrate its impotence, and the 
 loci, probably, were a second and more successful attempt to 
 found a method of invention. This order of succession of the 
 systems is confirmed by the fact that roiros, the technical term 
 of the supposed second system, does not occur in the first; while 
 iTil^keyj/is, the technical term of the first, perpetually recurs in 
 the second. If our supposition is correct, the following passage 
 of the Analjrtic, which pretends to refer to the Topica as abeady 
 composed, must be regarded as a subsequent interpolation. Kaflo- 
 kov fjbkv ovv tv Set TpoTtov Tos trporda-eLs iKkeyeiv, elpr/rot axebov 
 bi' BLKpifieCas 8^ btekijkMat/.ei' iv rfj irpayfxare^^t rrj irepl r^r 8ta- 
 keKTiKrjv, An. Prior, i . 30. ' We have given a summary account 
 of the method of collecting materials. A more detailed account 
 is to be found in my treatise on Dialectic' It is to be observed 
 that this passage only identifies the method of collection (eicXoy^) 
 in the two systems : it does not identify the iTiL^ki^eis with the 
 To'iroi. They cannot be identified ; for the one are deduced from 
 the nature of the predicables, the others from the nature of syl- 
 logism. If the term iKkiynv is here misapplied and refers not 
 to the organa but to the loci, it is pretty certain that the sen- 
 tence was not written by Aristotle. 
 
 We have supposed that Aristotle himself recognized the in- 
 efiicacy of his first system. If successful, it would have been a 
 triumph of simplification, for it would have founded the whole 
 of dialectic on a single definition, the definition of proof. 
 
APPENDIX D. 221 
 
 § 10. From many expressions of Aristotle it might appear 
 that he would make the differentia betweei^ dialectic and science 
 to consist in the fact that science is based on definitions and 
 dialectic is not. ^ kvTitrrpl^ei 8e imWov to. ev rois ixaBrjixacriv Srt 
 oibiv avjx&i^KOi Xajx^dvovaiv, aWa koI roira hi,a<^ipov<n t&v ev 
 Tois bia\6yoK, dA\' 6pur\xcrus. An. Post. I. la. 'The converse 
 of a scientific proposition is often true because no accidental 
 conjunctions are admitted as premisses in science^ which herein 
 differs from dialectic, but only definitions.^ *H d fji.lv ovrats vito- 
 \ij\/f€Tai TO fx^ hb€x6fj,eva S.\Kais exetv &crTiep ix'^iv [ibs ix.a>v ?] 
 TOWS optcrfiois 8i' Siv al aTrobfC^eis, ov 8ofa(ret dA\' iiriarrrjcreTai' el 
 8' dX?j5rj jxiv etvai, ov nivToi Tavrd ye ovtols vnApxeiv kut' ovalav 
 KoJ Kara to eibos, Sofdo-ei Kot ovk eTTior^crerai dKr]d&s. An. Post. 
 I. 33. ' When the belief of a necessary law is founded on defi- 
 nitions which serve as the basis of demonstration, the belief is 
 not opinionative (dialectic) but scientific : whereas a belief in 
 the same proposition, without the knowledge that it is deducible 
 from the definition or essence of the terms, is not science but 
 opinion.' 'Eksivos 6' evXoycos efijret ro rC ecni, a-vWoyi^ecrdai yap 
 ^■qTei, apxTj 8e t&v (rvWoyiafi&v to tC eanv. AiaXeKTiKT} yap to-xiis 
 ojjffo) tot' ?jvj cSore bijva<Tdai Kal )(a)pls tov ri ivTi Tavavrla e-nuTKo- 
 •niiv KM T&v evavrCaiv el ij avTri e'UKrrriy.T]. Avo ydp iariv & tis &v 
 aiioholri ^untpArei biKaCa>s, ror/s r' eTraKTiKoiis \6yovs Kal to opl^ea-dai 
 Ka66\ov Tavra ydp eariv dju^o) irepl dpxrjv eniarrip.yii. Met. 12. 4. 
 ' It was natural that Socrates should seek for definitions, for he 
 wanted proof, and definitions are the foundation of proof. Men 
 were not then aware of the resources of dialectic, which enable 
 us to dispense with definitions in discussing the Socratic pro- 
 blems ; and two procedures may be fairly assigned to Socrates, 
 induction and definition ; both of which aim at laying the 
 foundation of deductive science.'' From what has preceded, it 
 appears that these statements must be accepted with some re- 
 serve. Dialectic as well as science is based on definitions, 
 though on definitions of objects of a different order. The defini- 
 tions on which science rests are definitions of a peciiliar subject- 
 matter and its attributes (tSta), those on which dialectic rests 
 are definitions of fact, law, cause, experience, definition, proof, 
 that is of certain catholic relations permeating every sphere (Koivd). 
 Equipped with definitiqns of these shadowy abstractions, dialectic 
 
222 APPENDIX D, 
 
 in entering the controversial lists with the sole purpose of con- 
 structing opinion can dispense with the more solid and concrete 
 special information which scientific method requires for the 
 evolution of genuine knowledge. 
 
 Unsubstantialj however^ as are these ahstractions, they occupv 
 in this art the position of final causes, so that, from this point 
 of view, the maxims may be regarded rather as imperative and 
 hypothetical than as indicative or categorical. This character 
 is suggested by the formula Aei, which so often occurs in the 
 Topica. (See end of § 7-) Another term, to, TraprjyyfXfieva, pre- 
 cepts of art, suggests the same conclusion. T&v be irpos ramov 
 KaTaa-Kivaa-TlK&v Toitav o^Sets \p-q<niMS ■npbs opov. Ov yap diro'xpij 
 Seifai TaiiTov to virb tov \6yov koX rovvoixa irpos to KaTaa-Keyda-ai 
 Sti opKTfjios, aWa koI to. aWa itavTa det Ix^'" ™ irapriyyeXfiiva tov 
 6pi(Tfx6v. Topica, 7. 2. 'The topics for proving the identity of 
 the subject and predicate do not sufiice to prove definition; for 
 if the predicate is a definition of the subject it must satisfy all 
 the other prescribed conditions.^ As in the arts or productive 
 sciences, so in dialectic, we define the end we wish to accom- 
 plish (which here is the establishment of theorems of a certain 
 character), and the maxims are dbroUaries or conclusions from 
 those definitions, dictating the means to be employed if such 
 objects are to be realized. Dialectic then, like science, is based 
 on definitions, and, like practical science, on definitions of its 
 final cause. 
 
 Kant treats the logical maxims as rather hypothetical and 
 imperative than indicative and categorical, when, to explain, or 
 explain away, the autonomy or legislative power of the specula- 
 tive reason, he bids us regard her dicta not as a priori revela- 
 tions of the laws of the external universe, but as precepts issued 
 by reason for her own behoof, that is, in order to provide herself 
 exercise for her own functions. Being a syllogistic faculty she 
 bids us look at the world in such a way as will enable her to 
 syllogize. For instance, she issues the precept of generalization, 
 and specification, i. e. she commands us wherever we have 
 species or plurality to find their genus or reduce them to unity, 
 and wherever we have generic unity to subdivide it into specific 
 multiplicity, not because she knows a priori that nature is uni- 
 form or that things are arranged in classes and a hierarchy of 
 
APPENDIX D. 
 
 law above l&w, but because, unless we contrive by some arrange- 
 ment of the logical lenses to discern such a hierarchy of classes 
 and laws, reason can have no scope for her inductive and deduc- 
 tive functions. The laws of the speculative reason (reflexions- 
 gesetze), then, he makes, in effect, hypothetical rather than 
 categorical. As far as I recollect, he avoids applying the term 
 hypothetical to the laws of the understanding (verstandes- 
 gesetze) ; but as he perpetually refers them to the possibility of 
 experience as their end and final cause, they may be, as a matter 
 of fact, categorical, but, so far as his system explains them, 
 they are only hypothetical, for such must be the character of 
 conclusions deduced from the conception of an end. 
 
 § II. One application of dialectic is said to be the investiga- 
 tion of the first principles of science. 'Ert 8e xp'qa-iiMs rj irpay- 
 liania irpos to. Trp&ra t&v irepl excioTiji' ewio-T^jurjy &px&v. 'E(C jxev 
 yap T&v oheCaiv t&v KaTa rfiv ■npoTedei(rav iTTia-Trnjjriv ap\&v " 
 ahwarov etireti» n Trepl avr&v, euetS^ irp&Tai, al ap)(al cnrdvTaiv 
 iiaC, bia bi t&v vepl ^Koora evboltav^ avayKrf vepl avT&v bi,e\6eiv. 
 TovTO 8 tbLov fi /xaAttrro oiKeiov Trjs biakeKTiKrjs eorfo" e^eraoriK^ 
 yap ovaa irpos Ta.<t airacr&v t&v fiedobav apxas obbv ^x^'- Topica, 
 I. 2. ' Further, dialectic is useful for fixing the primary prin- 
 ciples of the particular sciences. There are no theorems com- 
 mensurate or coextensive with the principles of a (deductive) 
 science that can furnish us premisses for the investigation, for 
 the principles themselves are the primordial theorems ; and 
 therefore there are only the common principles to which we can 
 appeal ; and their application is the proper function of dialectic, 
 or belongs to it more properly than to any other method. For 
 its power of criticism maikes it a method for determining the 
 principles of all other methods.' We will not stop to ask how 
 dialectic, the method of opinion, can be competent to investigate 
 the principles of science (a question which Aristotle never suflS- 
 
 " To avoid ambiguity Aristotle should have written, iie tUv otKeiwv tois 
 
 ^ TSi» hS6(av is a term of vague meaning. If we are to accept the statement, 
 we must interpret it to mean, ix rav koiv&v apx^v Kot ruv ipaivo^ivuv [t^s ifinct- 
 pias]. Before dialectic method can become scientific both elements must be 
 purified : the common principles must not be mere probabilities, and the specific 
 data must not be mere rumours of the great public but exact observations, and, 
 above all, quantitatively determinate. 
 
224 APPENDIX D. 
 
 ciently laid to heart), but assuming that dialectic includes all 
 that is opposed to deductive science (oSoy airb t&v &pxoiv), and 
 that some severer branch of it, with a positive (/carao-/cevatrTtK7j), 
 not merely a negative (avaa-nevacmK'^) function, may be identi- 
 fied with inductive method (66os iiri rets dpx<is), we will proceed 
 to consider what is the character of the principles which it has 
 to establish. 
 
 If the principles of science are definitions, it is evident that 
 we cannot accept Mill's account of definition. After maintain- 
 ing that propositions refer not to words or ideas, but to facts, he, 
 somewhat inconsistently, makes an exception against the most 
 carefully considered propositions, definitions. This cannot be 
 admitted if we regard definitions as the result of inductive and 
 basis of deductive science. If induction and science deal not 
 with words but with facts, definition, the crown of induction 
 and foundation of deduction, must also relate not to words but 
 to facts. 
 
 Aristotle makes two orders of definition — verbal, which are all 
 that Mill recognizes, relating to words, and real, relating to 
 facts. The latter order is subdivided according as the term 
 defined is that somewhat ideal object, something absolutely 
 irresolvable and elementary, or something derivative and resolv- 
 able into antecedent terms. The latter class is again subdivided : 
 it is either merely the precise statement or circumscription of a 
 phenomenon, and corresponds to the conclusion of a syllogism 
 in which the phenomenon is demonstrated; or it is a causal 
 proposition giving the invariable and adequate antecedent of a 
 phenomenon^ and represents the premisses or the whole of the 
 syllogism in which the existence of the phenomenon is demon- 
 strated. Opiaiibs 6' eTteibrj kiyerai etvai XJyoy tov tL kari, ^avepbv 
 8ti 6 fi.iv US earai \6yos tov tI <rrip.aivfi jh ovojia ^ X.6yos erepos 
 6vonaT(i8ris, ohv to tC (rr^fmCvei, tC icntv fj rplyuvov. "Oirep Ix^ves 
 Sri eoTt, fjjToCjuev 8i^ n e<mv. . . . EFs (tlkv bri Spos i(rrlv opov. o 
 €lprip.ivo$, aWos 8' kcrTlv opos \6yos 6 brjk&v 6ia tC itrnv. 'flore 6 
 fjLiv irporepos crtjjiiairet pikv, beCKVvai 6' oi, 6 8' itTTepos (pavepbv on 
 i<TTai oXov imobei^is tov tl eori, tj} Oiaei bia(f)4pa>v ttjs AiroSetJfws. 
 Aiatf>4p€i yhp eheiv bia t[ ^povr^ koI tC ian ^povTrj. 'Epei yhp 
 ovTia /x^v biSTL imotrfiivvvTai Tb "nvp Iv rots vetpeffC rl 8' iarX fipovTrj j 
 \l/6(f)0s imoff^fvuvnivov itvpbs iv v^<I)€<ti. "Slarf 6 avTbs \6yoi &\Kov 
 
APPENDIX D. 225 
 
 Tpoitov \4yfTai, KM uibl jxiv diroSeifis (rvvexv^i ^S' S' opianos. 'Ert 
 ((Ttlv opos ^povrffi y\r6<^os fV ve^itn' tovto H iari Trjs tov tC kaiiv 
 .InroieC^eiiis (ivp,Tsepa(Tfj,a. 'O h\ t&v aixea-cov opiapLos Ofms earrl tov 
 tI i<mv di'auoSeiKros. E(rTiv &pa optcr/nos els p-ev Xoyos tov ti e<rTiv 
 ava-nobfLKTOS, ets hi (Tv\\oyicTpi.bs tov tC iari, vrcia-ei bia^epav Trjs 
 airohei^eooi, Tplros 6e t^s tov tI eortv oTroSeifeftis (rvprnipaafxa. An. 
 Post. 2. 10. "EoTtj' d 6pi(Tp,bs fi &.pxv aTtobeC^eais, ri diroSetfis O^o'sl 
 8ia(/)^pou(ra, ^ <Tvp.T:ipa(Tp,& n dT7o8eife<os. Ibid. I. 8. 'Definitidn 
 is an exposition of essence, and one kind exhibits the significa- 
 tion of a name, or of a circumlocution, such as, triangular cha- 
 racter, equivalent to a name. When we know that an object 
 exists corresponding to the name, we may investigate its cause. 
 ..... Besides nominal definition there is real definition ; a state- 
 ment exhibiting the cause producing a phenomenon. The 
 former kind indicated without proof : the latter is a demonstra- 
 tion of essence without a demonstrative form. When it is asked. 
 Why does it thunder ? the answer may be. Because fire is ex- 
 tinguished in a cloud. When it is asked. What is thunder ? the 
 answer may be. The extinction of fire in a cloud. Thus one aad 
 the same statement, disguised in form, becomes either a defini- 
 tion or a proximate demonstration. Another definition is the 
 conclusion of an essential demonstration : as when we define 
 thunder, a certain noise in the clouds. Another kind is the 
 indemonstrable thesis or position of the immediate. Real defi- 
 nition, then, has three species : it is an indemonstrable state- 
 ment of the essence, or a deduction of the essence without the 
 deductive form, or a conclusion of a deduction of the essence.' 
 'Definition is either the premiss of demonstration, or the con- 
 clusion, or the whole demonstration dislocated.'' 
 
 It is evident that the two last kinds present the contrast 
 which obtains between colligation and induction. Colligation 
 of facts is a term invented by Whewell to designate the explica- 
 tion of a conception or the precise circumscription of a pheno- 
 menon, which he regards as the final result of induction. Mill 
 retains the term colligation but makes it merely a preliminary 
 of induction, to which he attaches a new signification, making 
 it connote the whole process of discovery of first principles (oSos 
 ^fi ras ipx"^*)- According to him the end of induction is the 
 discovery of causal propositions, i. e. ptopositions which define 
 
226 APPENDIX D. 
 
 the unconditional and inseparable antecedent of that consequent 
 which was provisionally defined in colligation. If we use the 
 term 'induction' to connote not the whole process but its result, 
 it is clear that colligation is equivalent to Aristotle's definition 
 which expresses the conclusion, and induction to his definition 
 which expresses the premisses, of demonstration. 
 
 In the syllogism to which Aristotle refers, the major term 
 represents the phenomenon or consequent, the minor term the 
 cause or antecedent, and the middle term the causal definition of 
 the major, indicating its relation of dependence on the ante- 
 cedent or minor. The major premiss then is the definition of 
 the attribute. "Eort 8^ to h4(tov koyos tov irpdrov &Kpov, 6io 
 naaai al imarrjixai bi opurfiov yCyvovrai. An. Post. a. 17. 'The 
 middle (in the ultimate syllogism) must be the definition of the 
 major, which shews that the basis of science must be definition.' 
 We may suppose that the definition of the primary subject or 
 ultimate irreducible cause will appear as the minor premiss of a 
 prior syllogism, but here Aristotle's logic is incomplete, leaving 
 many questions unanswered, and it may be doubted whether the 
 framework of the elementary syllogism is not too narrow to 
 exhibit the mechanism of causation. 
 
 It is clear that the definition of an attribute may be a causal 
 proposition, but it is not equally clear respecting primary 
 subjects or elementary substances. Aristotle for the sake of 
 symmetry calls these also causal, saying they are self-caused. 
 'EoTiv, 0)9 e^aixfVf tovtov to elbevat tC Icrn koI to eibevai, to alTkov 
 
 TOV tC icTTl. AoyOS 8^ TOijTOV OTt loTt Tl TO oCtIOV, Kol TOVTO Tj TO 
 
 avTo rj &\\o. An. Post. a. 8. ' To know the essence, as we said, 
 is the same as to know the cause of the existence, for every 
 thing has a cause, whether distinct from itself or identical.' 
 
 He elsewhere says that only substances are properly definable, 
 and that attributes are definable only in a secondary and inferior 
 degree, ^avepov oSv oti 6 ^rpt^rwy Kal cmX&s opia-fwi xal to ti ^v 
 elvai, T&v ova-i&v kaTlv ov plr^v &.W0L km t&v SXkatv o/uoiius k<rr\ 
 ■nXriv ov iipc&Tios. Met. 7. 4. ' The primary and proper objects 
 of definition are substances : attributes are only definable in a 
 secondary degree.' But it is clearly a straining of language to 
 call definitions of the uncaused or self-caused, causal proposi- 
 tions ; and if the essential function of definition is the expression 
 
APPENDIX D. 227 
 
 of causation, we must reverse Aristotle's dictum and say that 
 attributes or effects alone are properly 4efiiiable, substances, at 
 least elementary substances, only in a secondary degree. 
 
 We have now before us the character of the propositions 
 which dialectic must establish if she is to lay the foundation of 
 deductive science ; and her loci of invention must be governed 
 by this character, just as the loci for investigating accident, 
 property, and genus were governed by the character of accident, 
 property, and genus. It follows that the loci of definition in 
 the Topica, none of which refer to the nature of causation, are 
 useless for evolving scientific principles. For loci of invention, 
 founded on the nature of causation, we must turn our eyes 
 elsewhere. 
 
 § I a. We must look for them in the modern method of induc- 
 tion : and as a comparison of its ultimate principles with the 
 ultimate principles of dialectic will illustrate the conception of 
 dialectic method, let us examine the former as stated in Mill's 
 System of Logic, in his lusooinous exposition of the methods of 
 agreement and difference. 
 
 Method of agreement. "The mode of discovering and 
 proving laws of nature which we first examine proceeds upon 
 the following axiom : whatever circumstance can be excluded 
 without prejudice to the phenomenon, or can be absent notwith- 
 standing its presence, is not connected with it in the way of 
 causation." [This axiom is evidently a definition, or corollary 
 from the definition, of cause or effect.] " The casual circum- 
 stances being thus eliminated, if only one remains, that one is 
 the cause which we are in search of; if more than one, they 
 either are, or contain among them, the cause : and so, mutatis 
 mutandis, of the effect. As this method proceeds by comparing 
 different instances to ascertain in what they ag^ee, I have termed 
 it the method of agreement; and we may adopt as its regu- 
 lating principle the following canon :— If two or more instances 
 of the phenomenon under investigation have only one circum- 
 stance in common, the circumstance in which alone all the in- 
 stances agree is the cause (or effect) of the given phenomenon." 
 For instance, let the problem be, to find the effect of a given 
 cause : and let causes be represented by the capitals, A,B, C, &c., 
 and effects by the italics, a, b, c, &c. " Suppose that A is tried 
 
228 APPENDIX D. 
 
 along with B and G, and that the effect is abe; and suppose 
 that A is next tried with D and E, and that the eflPect is ade. 
 Then we may reason thus : b and c are not effects of A, for they 
 were not produced by it in the second experiment ; nor are d 
 and e, for they were not produced in the first. Whatever is 
 really the effect of A must have been produced in both in- 
 stances" [definition, or corollary from the definition, of cause 
 or effect]. " Now this condition is fulfilled by no circumstance 
 except a. The phenomenon a cannot have been the effect of B 
 or G, since it was produced where they were not j nor of I) or E, 
 •since it was produced where they were not. Therefore it is the 
 effect of ^." [Why? In obedience to the celebrated principle 
 of the sufficient reason, that every event must have a cause. 
 This principle gives a categorical character to the otherwise 
 hypothetical conclusion of the method of agreement. Mill 
 derives it, under the name of the law of universal causation, 
 from induction by simple enumeration, and speaks of it in terms 
 similar to those in which Aristotle speaks of the axiom, as the 
 most certain of our beliefs, and one capable of serving as a cri- 
 terion by which all other beliefs may be tested. "On jiier ovv rj 
 ToiatJrij iran-av ^e^aioTArr] apxrj, bfj\ov. . . . Aib 7r<£vTes ot airobeiK- 
 vvvres els TavTXjv avayovaiv ia-\dTj]v bo^av. ^■uaei yap ap\ri koI 
 T&v &\\a>v a^twfiaraji; ayrri -nAvrav. Met. 3. 3. ' This is of all 
 principles the most certain, and the one to which all demonstra- 
 tion appeals in the last resort ; for it is the natural basis of all 
 other axioms".^ From the preceding analysis it appears that 
 a single step of the method of agreement is an application of a 
 definition and postulate by an agglutination of at least six ele- 
 mentary syllogisms.] 
 
 Next let the problem be, to find the cause of a given effect. 
 '' We may observe a in two different combinations, abc and ade; 
 and if we know or can discover that the antecedent circum- 
 stances in these cases respectively were A B G and ADE, we 
 may conclude by a reasoning similar to that in the preceding 
 
 6 " A general proposition inductively obtained is only then proved to be truie, 
 when the instances on which it rests are such that if they have been correctly 
 observed, the falsity of the generalization would be inconsistent with the constancy 
 of causation ; with the universality of the fact that the phenomena of nature take 
 place according to invariable laws of succession." Mill on Positivism. 
 
APPENDIX D. 
 
 example that A is the antecedent connected with the consequent 
 a by a law of causation. B and C, we n^^y say, cannot be causes 
 of a, since in its second occurrence they were not present ; nor 
 are D and E, for they were not present on its first occurrence/' 
 
 Method of difierence. "In the method of agreement we 
 endeavoured to obtain instances which agreed in the given cir- 
 cumstance but differed in every other : in the present method we 
 require, on the contrary, two instances resembling one another 
 in every other respect, but differing in the presence or absence 
 of the phenomenon we wish to study. ... If the effect o{ A B G 
 ia abc, and the effect of B C, he, it is evident that the effect of 
 A is a. So again, if we begin at the other end, and desire to 
 investigate the cause of an effect a, we must select an instance, 
 as ahc, in which the effect occurs, and in which the antecedents 
 were ABC, and we must look out'"' [kiti^XeitTiov] " for another 
 instanee in which the remaining circumstances be occur without 
 a. If the antecedents in ^hat instance are B G, we know that 
 the cause of a must he A. . . . The axioms which are taken for 
 granted in this method are evidently the following : WhatevefS 
 antecedent cannot be excluded without preventing the pheno- 
 menon, is a cause or a condition of that phenomenon ; whatever 
 consequent can be excluded with no other difference in the ante- 
 cedents than the absence of a particular one, is the effect of that/ 
 one." [Definition, or corollaries from the definition, of cause or 
 effect.] " Instead of comparing different instances of a pheno- 
 menon to discover in what they agree, this method compares 
 an instance of its occurrence with an instance of its non-occur- 
 rence to discover in what they differ. The canon which is the 
 ^■egulating principle of the method of difference may be expressed 
 as foUows: — If an instance in which the phenomenon under 
 investigation occurs, and an instance in which it does not occur, 
 have every circumstance save one in common, that one occurrmg 
 only in the former ; the circumstance in which alone the two 
 instances differ is the effect or cause, or a necessary part of the 
 .effect or cause, of the phenomenon. . . .The method of agreement 
 stands on the ground that whatever can be eliminated" (can be 
 absent consistently with the existence of the phenomenon) "is 
 not connected with the phenomenon by any law. The method 
 of difference has for its foundation, that whatever cannot be 
 
230 APPENDIX D. 
 
 eliminatedj is connected with the phenomenon by a law." [Defi- 
 nitions, or corollaries from the definitionj of causation.] 
 
 The preceding exposition suggests several observations. The\ 
 foundation and keystone of inductive method, it appears, is ther 
 definition of causation. The foundation of dialectic method isj 
 the definition of definition. If a definition is a causal proposi- 
 tion, as Aristotle asserts in the Analytica, these two foundations 
 ought to coincide. But when Aristotle enumerated the loci of 
 definition in the Topica, he does not seem to have attained to 
 the view which he explains in the Analytica, that the scientific 
 definition of a phenomenon is the declaration of its cause. The 
 principal branch of his Logic is founded on the definition of 
 science, which is declared to be the knowledge of causes. 'EirC- 
 (rraa-Oai olofXiOa ^KacrTov orav Trjv t ahCav oltiixiOa yivdxTKfiv hi i}v 
 TO -npayiiA kcrriv, on eKeivov airCa IcttI, koX fifi h'bexeaOai tovt 
 ttXA-ffls Ixetv. An. Post. i. a. 'Science is the knowledge of 
 necessary facts and their causes.' But instead of deducing from 
 this conception the method of inductive science, a problem that 
 asked the aid of the philosopher, he merely developes from it 
 theorems respecting the nature of deductive science, a province 
 which might have been safely left to the fostering care of the 
 mathematicians. Hegel was full of the notion that certain 
 metaphysical ideas were capable of being developed into regula- 
 tive principles and furnishing methods of reasoning; but he 
 never advanced beyond the haziest generalities, in which none 
 but the cloudiest intellect could find satisfaction. It is to Mill 
 that the honour belongs of solving the problem that had so long 
 hovered before the eyes of philosophers, and shewing how the 
 idea of cause can be developed into various methods of rigorous 
 scientific inference. 
 
 Definition, which perhaps at some periods in the history of 
 logic was unduly exalted as a scientific process, undergoes in 
 Mill's System of Logic, along with syllogism, a deal of vili- 
 nihili-parvi-pauli-pili-nauci-fiocci-fication, and is degraded from 
 all her dignities. But for the ultimate foundation and evi- 
 dence, and the sole foundation and evidence, of inductive me- 
 thod as expounded in this system, we are forced, as we have 
 seen, to have recourse, reversing the bill of attainder passed 
 against them, to definition and syllogism. Induction in its 
 
APPENDIX D. 231 
 
 strictest sense seems to be merely the idealization or universal- 
 ization of a singular fact, the transformation of the proposition, 
 this ^^C is followed hy abe, into the proposition, all ABC is 
 followed by abc. The faculty of making this transformation 
 can, doubtless, not be identified with, or made dependent on, the 
 syllogistic faculty. But if, as in Mill's writings, the word in- 
 duction is used to signify the whole process of discovering first 
 principles (68os eTri rhs &px^i)) then it appears, as we noticed 
 when quoting his exposition, that every single step of induction 
 is a crowd, at least an ample cluster, of syllogisms. Instead, 
 then, of declaring with Mill, that all deduction is induction, it 
 appears more accurate to assert that all induction is deduction. 
 
 The two elements, one general the other special, which Ari- 
 stotle found in dialectic and demonstration, are also to be dis- 
 tinguished in inductive science. Inductive method, as we saw 
 (§ lo) was the case with dialectic, assumes one definition and 
 proves another. The definition assumed, that of causation, 
 throws equal light on all inquiries, i. e. is a catholic principle 
 (koivt] apxifj) : the definition proved is a causal proposition, or law 
 of causation in a special department of nature, and is a truth 
 confined to a particular science {ibCa apxij). 
 
 Here we may resume a former topic. Aristotle objected (see 
 § 8, quoting Anal. Post. a. 6) to a proposed proof of definition, in 
 which one premiss should express the conditions of definition, and 
 the other assert their fulfilment, that every proof ought to have 
 some apparent cogency prior to any express exhibition of logical 
 rules and apparatus. If we consider the mode of reasoning in 
 the methods of agreement and difference, we shall perceive that 
 Aristotle's objection is by no means fatal, and that his requisition 
 can be easily satisfied. The man who, assuming the validity of 
 the methods of agreement and difference, shews the invariable 
 and unconditional antecedent, let us say, for example, of dew, 
 has demonstrated its definition without expressly invoking any 
 logical or metaphysical canons. If an unconvinced critic de- 
 mands further satisfaction, he may justify the process by appeal- 
 ing in the way Mill indicates to the axioms and canons of in- 
 duction. 
 
 Another point that has been discussed will receive light from 
 the same consideration. We observed (§ i) that the dialectic 
 
232 APPENDIX D. 
 
 maxims may either be regarded as constitutive or as regulative, 
 i, e. either as premisses or as methods. The same is true of the 
 inductive canons. Possibly no inductive operator ever reasoned 
 as Mill reasons to shew the cogency of his methods. The in- 
 vestigator of nature employs the methods without troubling 
 himself about the metaphysical or ontologieal principles on 
 which they are based. But if he would demonstrate the validity 
 of the methods^ these metaphysical or ontologieal principles must 
 be expressed and furnish the premisses of proof. 
 
 § 1^. This seems the proper place for a few words concern- 
 ing the celebrated question, whether definition is susceptible of 
 proof? In the Topica Aristotle had asserted it is. 
 
 Avaipiiv ij.\v oSv opov ovtcos km bia tovtoiv ael Tteipareov. 'Eav 
 6^ KaTaa-KtvdCeiv ^ouXcifieda, itp&Tov p.\v elbevai, bei on ovbels fj 
 oAtyoi T&v biaXeyofi&iav opov (rvWoyi^ovrai, aWa irAvTes is cipXV^ 
 70 TOLovTov kap.^6.vov(TLV olov olVc Ttspl yebip.eTpiav xal apidnoiis kclL 
 Tas oKkas ras rotavTas fxaOi^aeis. Ei9' on 6t' UKpi^eias piiu &\Kris 
 fcrrl TipayixanCas AirobovvM kw, tl itmv opos koI ii&s opi^eaOai bti. 
 NCj; 6 , B,(Tov iKavov vpos riji) ■napovirav xpeiav, too-ovtov p-ovov Ae/c- 
 t4ov, on 8iii'aroi' yeveadai 6piap,ov kol tov tl ^v elvai (TvWoyiapAv. 
 Et yap io'Tiv opos Aoyos 6 to tC ^v ilvai tu Tipayp.aTi bri\&v, itot 8el 
 TO, fv 7(0 8p<p KaTTiyopovneva kv r&J tI ecrn tov ■wpayp.aTOi p-ova Karrj- 
 yopiiadai (KaTTfyopeiTai bi ev tu tI eo-Tt to, yivrj xal al biacpopaC) 
 <t>avtpov, &)s et ns Aci/Soi Tavra povov ev r&i t( eort roi; ■npiyp.aTOS 
 KaTriyop€ia-6aL, otl 6 TavTa ^)(a>v \6yos opos ii avdyicqs &v elrf ov 
 yap kvbi)(iTai hepov eivai opov toiJ irpdypaTos, itreibri ovbfv iTfpov 
 ev ru n' eort toS T,p6,yp,aTos KaTriyopilTai. "On p,ev ovv ky)(Uipv, crv\- 
 Xoyicrpov opov yeviaOai, ^avepov. Topica, 7. 2. 
 
 ' The disproof of a definition employs the foregoing topics. 
 As to the proof, we must observe, in the first place, that defi- 
 nitions are rarely or never proved by the questioner in dialectic 
 discussion, but are assumed as a basis of proof, as in geometry, 
 arithmetic, and similar sciences. In the second place, the exact 
 rules for the form and process of definition belong to another 
 method, and we have now merely to say what may suffice for 
 the present occasion. We say, then, that essence and definition 
 are susceptible of proof. For if definition is a proposition de- 
 claring the essence of a thing, and is composed of all the predi- 
 cates that say what it is, that is, of all its genera and differentise, 
 
APPENDIX D. 233 
 
 it follows that if certain predicates fulfil these conditions in re-- 
 gard to a given ternij the proposition in which they are resumed 
 is the definition of that term, and there can be no other defi- 
 nition, for there are no other generic predicates. It is clear, 
 then, that we may prove a definition/ This seems to be plausi- 
 ble enough, and may be made more so if a little differently 
 worded. If we assume a priori that a certain relation of terms 
 is the relation of effect and cause, or of phenomenon and defi- 
 nition, and find a posteriori by appropriate evidence that this 
 Nation exists between two given terms, we may conclude that 
 these terms are related as effect and cause, or as phenomenon 
 and definition. In the Analytic, however, Aristotle asserts 
 that such a proof, which he calls hypothetical, is vitiated by a 
 petitio principii. 'AA\' Spa lori koI airobd^ai to tC icm kut ovcriav, 
 ef VTroBicreats be, kafiovra to ijl^v tI rjv ewai sk t&v iv ra tC eariv 
 Ibmv, Tabl be iv tu t[ eo-ri jiova, kcu, Ibiov to vav. Tovto yap iaTC 
 TO ilvai. iKiivto. H TtaKiv fiKrj^e to tl rjv ftvai KWrkv tovt(o ; avayKt) 
 yap bia tov /xeVov Setfat. An. Post. a. 6. ' Is definition sus- 
 ceptible of a hypothetical proof, if we assume as our major that 
 the i-eeiprocating or convertible combination of essential predi- 
 cates is the definition ; and as our minor, that certain predicates 
 are essential, and, when combined, reciprocate with the subject ; 
 and then conclude that these predicates compose its definition ? 
 No : here, as in the former case, the minor premiss is a petitio 
 principii.' Accordingly his definitive doctrine appears to be 
 that definitions are indemonstrable. *H to. irpma opicrixol iaovTai 
 avaitobeiKToi. An. Post. 2. 3. ' The first principles are indemon- 
 strable definitions.' Without controverting his assertion, that 
 the proof of a definition is not demonstrative, we maintain that 
 the reason he alleges is untenable. It is clear that if the prior 
 definition assumed as a premiss in order to prove a definition is 
 a definition of the same term, as in one of the modes of proving 
 definition which Aristotle examines, there is a petitio principii, 
 and, if the possession of the prior definition means anything 
 beyond the power of rightly applying a name, or of recognizing 
 an object when presented to sensation, such a proof hardly de- 
 serves the name which Aristotle concedes it, of dialectical {Koyi- 
 Kos] proof. Ovros fxiv ovv 6 Tpoiros 5tl ovk liv dr] anobeiiis, eipriTai 
 tipoTepov, aW" iaTt KoyiKos (TvKKoyi.ffp.bs tov tC ia-Tiv. An. Post. a. 8. 
 
234 APPENDIX D. 
 
 But in the hypothetical proof, or, what is a similar process, the 
 establishment of causal propositions by the methods of induction, 
 the definition assumed (that of essence or cause) is a general or 
 metaphysical definition (koivov), the definition to be established 
 is a specific or scientific definition (tbiov). The things defined 
 are quite disparate, the premisses are distinct from the conclu- 
 sion, and therefore there is no petitio principii. How then did 
 Aristotle come to imagine that there was this vice in the proof? 
 The cause of the hallucination seems to have been his own tauto- 
 logical way of defining definition or essence. His account, in 
 efiect, amounts to this : Definition {t6 tC ^r eivai) is composed 
 of — ^the elements of definition (ra ev tu tC eort), or, essence is 
 composed of — the elements of essence. From so tautological and 
 unmeaning a premiss it would have been strange if any conclu- 
 sion could be drawn without a petitio principii. That he was 
 doubtful of the conclusiveness of his own reasoning we may 
 infer from his adding another objection, which we have already 
 discussed, § 8. 
 
 The true avenue to a possibility of error in the proof of 
 essence or causation lies, as Mill has indicated, in the fallibiliiy 
 of observation. " But if we cannot artificially produce the phe- 
 nomenon A, the conclusion that it is the cause of a remains 
 subject to very considerable doubt This arises from the diffi- 
 culty of assuring ourselves that A is the only immediate ante- 
 cedent common to both the instances. If we could be certain 
 of having ascertained aU the invariable antecedents, we might 
 be sure that the unconditional invariable antecedent or cause 
 must be found somewhere among them.'' This applies to the 
 method of agreement, and the method of difference may be 
 vitiated by similar non-observation. 
 
 Another method whereby it had been proposed to prove defi- 
 nition entirely a priori, namely, the method of division, is justly 
 charged by Aristotle with involving a series of petitiones prin- 
 cipii. "On 6' ^ 8i^ T&v yev&v biaCpecris yuKpov rt fwpiov ecru rrjs 
 elpriiJiivris p.ed6bov, pqbiov Ibeiv. "Ecm yhp fj biaCptcris oTov &(T0evris 
 av\koyuTiM6s' h fiev yap bei bei^ai aheiTai, avXXoyC^eTai 6' aeC ti r&v 
 ava>0ev. IIp&Tov 6' amb tovto i\e\rj6ei tovs xP"'!^^*"^'"^ "ir^ iidvTas, 
 Koi TteiOeiv iTrexfCpovv m ovtos bvvarov Trepl ova-Cas aitobei^iv yCve- 
 uQai Koi. Tov t( i<rTiv. An. Prior. 1.31. ' Specification or subdivi- 
 
APPENDIX D. 235 
 
 sion is a small item in the method of invention. Subdivision is 
 a sort of feeble proof wherein the exclusion wanted is always 
 assumed^ and proof is only adduced of some antecedent propo- 
 sition. This vice was not detected by those who first practised 
 the method, and they would persuade us it was possible hereby 
 to demonstrate definitions and primary laws/ To shew his 
 meaning he supposes that the problem is to define man. We 
 begin by an assumption that man is an animal, and after di- 
 viding animal into mortal and immortal, we prove conclusively 
 that man is either mortal or immortal. This however is not 
 the conclusion we want, and we make a second assumption that 
 man is mortal. Zuoi; Ovryrop hi [iXvai tov 6.v6p(aitov\ ovk avayKoiiov 
 dA\' ahilrai. ToOro 6' riv h I8et avWoyuTavOai. Ibid. Then sub- 
 dividing mortal animal into footed and not-footed, we can prove 
 that man is either footed or not-footed : we want, however, 
 something more positive than this, and are obliged as a third 
 assumption to postulate that he is footed. 'Ttiotiovv 8' o^k avdyKt] 
 [eivai TOV &v6p<ai!0v] aWa Xan^dvei, ToSro 6' ?)f & e8ei -rrdXiv hei^at. 
 Ibid. And so on. It is evident that the defect of this method 
 consists in its pretension to be entirely a priori or independent 
 of experience, and the defect is removed as soon as we admit 
 that experience or a posteriori truths are an essential element in 
 the establishment of definition. This is given by Aristotle as 
 the key of the enigma in the preceding chapter. Ato ras apxas 
 ras irepl eKaarov ep/neipias k(TTl itapahovvai. An. Prior. I. 30. 'The 
 specific principles of proof must be derived from experience.'' A 
 petitio is a premiss that is assumed without any evidence. "Orav 
 TO pit) 6t' avTov yvaxTTov 81' avrov rts eTTixeipfj beiKvvvai, tot aheiTai 
 TO k^ apyri^. An. Prior, a. 16. But as soon as sensation or ex- 
 perience is recognized as an authentic criterion of truth, what 
 was before an afrjj/xa becomes an al<j6r]p.a, that is, a premiss 
 evidenced by the most unexceptionable authority. Speaking of 
 the method of division, Aristotle observes that its most im- 
 portant premisses are the arbitrary concessions of the disputant. 
 Ou8auo() yap avayKt) ylverai to irpaypu eKeivo etvai Tiavbl ovtcov ' 
 
 oi yap 8ei to (Tvpntepaapa, epuyrav, ovhi T(f bovvai ftvai, a\K' 
 
 hvaym (If dvayKr\sf) etvai sKeivav ovTa>v, k&v jutj <^5 " amoKpivo- 
 aevos. An. Post. 3. 5. ' The conclusion of the process is deficient 
 in necessity : now a conclusion should not be a matter of ques- 
 
236" APPENDIX D. 
 
 tion or concession, but the inevitable consequence of the pre-? 
 misses, unaffected by concession or denial.' In the inductive 
 method the decisive premisses are gained by interrogation, not 
 of a disputant but, of nature : and a criterion, somewhat hastily 
 rejected as unscientific, plays an essential part in the process. 
 Tis 6vv d\Aos TpoTtos [jov Tr\v oviriav rj to tI kcTTi huKVvvaC] Koasos; 
 ov yap bri Sei'fet ye rfj alaO'qa-ei rj tu baKTvXa. An. Post. 3. 7. 
 ' What other method remains ? The definer, surely, does not 
 point out the essence with his finger as an object of sensation ?' 
 
 If, then, the coUigative or phenomenal definition cannot be 
 proved, we still maintain, looking at the modern methods of in- 
 duction, that the more important, the inductive or causal defini- 
 tion, is capable of proof. The assumption, however, of so catho- 
 lic a principle {kowti apxq) as the definition of causation, to say 
 nothing of the admitted possibilities of error in observation, re- 
 moves the proof from the sphere of deductive science or demon- 
 stration (dTToSeifis), which rests exclusively on axioms and tbtai 
 apxaC, to that of dialectic, or, to speak more accurately, philo- 
 sophic, method. So much for the limit of the power of the 
 catholic or methodic principles working on the special data of 
 experiment and observation. 
 
 § 14. The reader may desire to have some specimens of the 
 dialectic maxims, about which so much has been said. As we 
 have stated, Aristotle avoids formulating them in the Topica; 
 but the schoolmen coined them in abundance after his indica- 
 tions. The following are taken from Sanderson's Compendium. 
 They are divested of all reference to the predicables, and to each 
 maxim are appended certain limitations or exceptions, which he 
 calls fallentise. In dialectic the falsity of the maxim, that is, its 
 employment without due limitations and qualifications, though 
 it led to a false conclusion, was not considered to make the argu- 
 ment sophistic; but we have stated our opinion (see notes to 
 ch. viii), that in pirastic at least such false premisses constitute 
 the proof a sophism. 
 
 Loci a causa et efiectu : — 
 
 Posita causa, ponitur efiectus, et sublata tollitur. 
 
 Fallit in causa impedita : ut gravia non semper descendunt, 
 quia possunt ab aliquo impediente prohiberi. 
 
 Posito effectu, ponitur causa, et sublato tollitur. 
 
APPENDIX D. 237 
 
 Fallit in effectu permanente post causam ; ut manet sedifieium 
 mortuo sedificatore: in effectu prodnpibili a diversis causisj ut 
 potest esse mors non epoto veneno : in effectu causse quae ali- 
 quando fuit ; ut corruere potest sedifieium superstite sedificatore. 
 
 Here we have the materials for the methods of agreement 
 and difference, but the architect was wanting. 
 
 Loci a subjecto et accidente : — 
 
 Posito subjectOj ponitur accidens 
 
 Sublato accidente, toUitur subjectum. 
 
 Posito antecedente, concomitante, consequente, ponitur conse- 
 quens, concomitans, anteeedens : ut, si est eclipsis, est plenilu- 
 nium. 
 
 Fallit si non est mutua necessitas ; ut quamvis, si est eclipsis, est 
 plenilunium, non tamen si est plenilunium, continuo erit eclipsis. 
 
 Loci ex oppositis et comparatis : — 
 
 Posito altero relatorum ponitur reliquum, et sublato toUitur. 
 
 Posito uno eontrariorum, tollitur alteram. 
 
 Fallit in remissis qualitatibus ; quia remissio qualitatis fit 
 semper per admistionem contrarii. 
 
 Sublato uno eontrariorum, ponitur alteram. 
 
 Fallit in contrariis mediatis-; ut mel nee album nee nigrum 
 est, sed flavum. 
 
 Contrariorum eontraria est ratio ; ut si frigus congregat hete- 
 rogenea, calor secernit. 
 
 Fallit in ratione subjecti; ut quia sanitas convenit animatis, 
 non propterea morbus inanimatis: et in eausis quarum actio 
 determinatur a dispositione materise; non enim emollit lutum 
 frigus, quia indurat calor. 
 
 Posito altero contradictoriorum, tollitur reliquum, et sublato 
 ponitur. 
 
 Similibus et proportionatis similia conveniunt et proportion- 
 aliaj dissimilibus et improportionatis dissimilia et non propor- 
 tionalia. 
 
 Fallit nisi intelligatur reduplicative, de similibus qua similia ; 
 omne enim simile est etiam dissimile : unde non sequitur corvum 
 rationalem esse, quia ^Ethiops est rationaUs. 
 
 Maximae comparatse rationis sunt istse : — 
 
 Eorum quse seque sunt aut non sunt talia, si unum est tale, 
 et reliquum, si non est, nee reliquum. 
 
238 APPENDIX D. 
 
 Si quod magis videtur esse tale, non est, etiam quod minus 
 videtur esse, non eritj ut, non placuit omnibus Homerus, qui 
 placebit Msevius ? 
 
 Si quod minus videtur esse, est tale, etiam id quod magis ; 
 ut, fur si est suspendio dignus, certe dignior sacrilegus. 
 
 Loci a conjugatis (otJotoixo) : — 
 
 Quorum unum convenit alteri, eorum conjugatum unius con- 
 venit conjugate alterius et negative similiter ; ut, si albedo est 
 color, et album erit coloratum. 
 
 Fallit arguendo a eoncretis ad abstracta; ut, non propterea 
 albedo est dulcedo, quia album est dulce : et arguendo ab ab- 
 stractis ad conereta; ut, quia nulla albedo est dulcedo, non 
 propterea nullum album erit dulce. 
 
 Loci a toto et parte : — 
 
 Posito toto, ponuntur partes. 
 
 Fallit in toto mutilatoj ut potest esse homo, quantumvis 
 amputato digito vel manu. 
 
 Sublato toto, partes tolluntur. 
 
 Positis partibus, ponitur totum. 
 
 Loci a divisione : — 
 
 Membrorum condividentium uno aut altero sublato, ponitur 
 reliquum, et posito toUitur. 
 &c., &c., &c. 
 
 The criticism suggested by these numerous but inefficacious 
 maxims is contained in a homely Greek proverb : — 
 
 IloW olb' A\(^TTjjf, dW' i\ivos kv iifyd. ' Many tricks knows 
 reynard ; one good one suffices the hedgehog.'' 
 
APPENDIX E. 
 
 LIMITS TO THE COMPETENCE OP PIRASTIC. 
 
 It would not be surprising, if, after the performances of 
 Socrates with the elenchus, some of the Soeratici viri overesti- 
 mated the power and value of pirastic. The professed function 
 of pirastic is to examine a man's pretensions to a given science, 
 although neither the examiner nor the auditory are themselves 
 in possession of it j and in the infancy of all the sciences, and 
 the absence of faculties or universities to pronounce on anybody's 
 attainments, there was doubtless abundant scope for its exer- 
 cise. In the Charmides, where pirastic as producing self-know- 
 ledge is discussed under the name of sobriety, [i. e. a-ca(ppoa-6vri as 
 opposed, not to aicokacrCa but, to )(avv6Tris or oA.afoi'eta, an am- 
 biguity which we need not pause to discuss,] it is shewn that 
 pirastic alone is not competent to the discharge of this function. 
 To test a man's possession of a given science the examiner ought 
 to possess not only the theory of science in general, i. e. logic, 
 but also a knowledge of the theorems and methods peculiar to 
 the particular science in question. "On /xev 8^ eTrurrrjiirjv rtva 
 Ij^et, yvdcrfTai 6 caxfiputv top larpov kiti^eip&v h\ 8^ -neipav X.aj3etv 
 iJTK kariv, aXKo tl a-Ke^erai 3iv tiv&v ; . . . Ovkovv iv tovtoh &vay- 
 Koiov a-KOTteiv rbv ^ov\6p.evov larpiKriv a-KOTSiiir, kv ots ttot ea-riv. 
 Oil yap briTTOv iv ye rois efo) ev oh ovk ^<ttiv. — Ov brJTa. — 'Ev rots 
 vyiHVois apa Koi voaahiaiv iTna-Kdyjferai tov iarpov, fi larpiKos kvTiv, 
 6 6p6Q>s OKOTSO'CjJ.evos, — ■"EotKev. — ''H oSv aveu laTpLKrjs b-6vaiT av ns 
 Toirotv TioTipois kicaKoXovdr](TaL ; — Ov brjra. — 0^8^ ye &\kos ovbeCs, 
 ws loiKe, Ttkriv iarpos, ovre 6?j 6 <T(&^p(ov iarpos yap hv drj irpbs ttJ 
 am<i)po(r6vn. — ■'Eort Tavra. — Ilafros apa fioKKov, el fj am^poa-ivq 
 iitiaTniiris i'ni-<rrqfirf \mvov ecrrl koX aveTti(rTr)fjLocrivr]i, ovre larpov 
 
240 APPENDIX E. 
 
 biaKpivai ota re Icrrai k-nKTT&fxevov to. rrji Tixvr\i r) ^7) eirtoro/xej'oj.'j 
 •npoa-noiovixevov 8e r\ oi6fi,evov, mire 6.Xkov oiihiva t&v ewiora/xevwv 
 Koi OTiovv, ttAtjv ye top airoC optorexyov, waitep oi S.W01 brjiiiovpyoi. 
 — ^aCverai, ec^Tj. — -'Ap' oZif, rjv 6' eyd, tovt exei ro ayaBov fjv vvv 
 evpia-KOixev crm^poo-vvriv oZirav, to iTn(TTr}iJ,r)V iTrCcrraa-dai, koI avein- 
 arr)p,oa'6v7\v , 6ti 6 twuttjv Ix'^''> ^" ^^ "^^0 lJiO.vd6.vri, pa6v re fiadrj- 
 trerai, koI ivapyia-repa TrdvTa avra ^aveirai, are irpos exdoTu <S hv 
 jxavdavrj irpotTKaOop&vTi ttiv eTrtor^/oiTjj' ; (cal robs aWovs brj kAWlov 
 Iferdirei Ttepl &v hv Koi avTos fidOri, ol 8^ &vev tovtov f^erACovrei 
 aadevfiTTepov koi ^avKoTepov tovto hp&novcri. Charmides, 40-43. 
 ' That tlie pretended physician possesses some science, sobriety 
 (pirastic) may discover ; but before it can pronounce what science, 
 that is, in what province, it must examine him, not in extraneous 
 topics, but in his own province, that is, in questions of health 
 and disease. But no one understands these except the physician, 
 and if the sober-making man (dialectician) understands them, 
 he must possess medical science as well as sobriety (dialectic). 
 Sobriety (pirastic) then, or the science of science and nescience, 
 cannot distinguish between the genuine physician and the pre- 
 tended or self-fancied physician, nor between any genuine and 
 false professor of science, except in her own sphere (logic), and 
 must leave other artists to the judgment of their peers. The 
 only use, then, of the science of science, is that it enables us to 
 learn more easily and appreciate more completely any other 
 science, as it enables us in each province to see science in addi- 
 tion to truth : and it will enable us to sift more thoroughly the 
 pretensions of others to any other science that we ourselves may 
 happen to have acquired.' 
 
 Aristotle asserts the same, though with some exceptions in 
 practical matters. As a general rule, he says, to be competent 
 to judge whether a man possesses a given science, we ourselves 
 must have at least -naibeia, a sort of demi-science, an acquaint- 
 ance with the leading principles and peculiar methods of the 
 science in question. The physician can only receive his diploma 
 and the geometer his certificate of proficiency from a board of 
 physicians or geometers. But the title of physician may be 
 given to those who have had an education (iratSei'a) in medical 
 science as well as to the professional physician. "Exet 8' ^ T({fis 
 avrq T^s TToXifefas anoplav, irp^Trjv p,iv &n So'feiei; iiv tov airdv 
 
APPENDIX E. 241 
 
 ctvat TO Kplvat rCs opd&s lArpevKev o^Trep koX to larpeiia-ai Koi iroifjaai 
 vyia rov Kap.vovTa t^s v6(tov tjJs trapovgris' crSros 6' iarlv larpos. 
 'Ofiouos bi TOVTo Koi T!ipl Tas aWas ip-TieipCas km rexi^ay. "D.(nt€p 
 o^v larpbv Set bihovai ras evO'ivas fv larpois o^tco koX tovs aAAovs iv 
 Tois op-oCois. 'larpos 8 o re brjixiovpybs ko.1 6 &p)^LT<fKTovnc6i koi 
 rpCros 6 iTeTicubevfj,€VOs "nepX T7]V rixvrjv' el<n ydp Tivfs toiovtol Kai 
 wepl Trdcras i>s flTrfw ras r^xvas* aTjobCboiJifv 8^ to xpCvftv ovbiv tjttov 
 TDK ■neiraibevp.fvot.s rj tois flb6(Tiv. "ETretra Koi Ttepl ri^v aXpecrw 
 Tov avTov h.v bo^eiiv l)(eiv Tpoirov. Kal yap to e\4a-dai opO&s t&v 
 ■€lhorr<av ^pyov eoru', olov ye<i>fi.iTp7)V re t&v y€a)p,eTpiK&v Kal KvjSepvi^- 
 Ttiv T&v KV^fpvrjTiK&v. El yap KOi mpl fvicov epytav Kal rexv^v 
 fieriypvai Kal t&v ibia>T&v Tivis, oKX' oiJrt t&v etboTav ye pJaXkov. 
 
 . "Qo'Te (cara fiiv tovtov tov Kcyov ovk &v eijj to TrKijOos iroirjTiov 
 Kvpiov oiTf T&v apxaipea-L&v ovre t&v evQvv&v. 'AW' Xfrws ov 
 TT-dvTa TavTa kiyer^u Ka\&s bia re tov TidKai, \6yov. . . . koI on iiepl 
 iviav otire fiovov 6 TToirjaas otjt api(TT &v KpCveiev, ocrmv r&pya 
 yiyvdta-KOWi KoX ot p,r\ fxovTfs ttjv t^x*"?"! "^o" oiKiav ov fwvov eort 
 yv&vai TOV irotijcrairos aWa Kal fie\Tiov 6 )(piip,evos avTfi nptvei, 
 XpfJTat 8' 6 oiKov6p,os, Kal TtribdMov Kv^epv^T-qs rekTovos, xal Qoivr)v 
 6 baiTvpMv ak\' ovx b jxAyeipos. Pol. 3. ii. 'The hypothesis that 
 the people are qualified to elect and oontrol the magistrates 
 presents a difficulty, because to judge whether the medical func- 
 tions have been rightly performed a man ought to be able to 
 perform them himself, that is, ought to be a physician j and so 
 in the other arts and sciences. As, then, a physician ought 
 to be judged by physicians, so ought other functionaries to be 
 judged by their peers. Now the title of physician may be given 
 either to the person who practises, or to the person who com- 
 bines practice Vidth theory, or to the person who does not prac- 
 tise but has had an education in medical science. Some hold 
 this position in every province, and are thought as competent 
 to judge as the scientific. The same may be said in respect of 
 the electoral power. Qualification to select requires knowledge, 
 and a geometer can only be rightly selected by geometers, a 
 pilot by those who know the pilot's art. If there are any func- 
 tions and operations of which the uneducated are competent to 
 
 judge yet they cannot be more competent than the educated. 
 According to this reasoning the people should not have the 
 power of election or control ; but perhaps it is open to objection. 
 
242 APPENDIX E. 
 
 both on other grounds and because there are certain operations 
 of which the artist is not the sole nor the best judge, nor go 
 good as a person who knows nothing about the art j as a house 
 is better appreciated by the householder than by the architect, 
 a rudder by the steersman than by the shipwright, a banquet 
 by the banqueter than by the cook.'' llepl ■navav Oewpiav Koi 
 fxidobov ojuouuf raiTfivoTepav re Kol TLixunTepav bvo (paivovTai rpSitoi 
 Trjs ?^ea)s ftvai, &v TrjV iJ,iv iiii<TTriiJ,r]v tov TTp6,yp,aT0i Ka\&s lx«i 
 TrpouayopevfLv Tr]v 8' dtov iraibeCav rivd. YliTtaibeviMVov yap ean 
 KUTo, rpoTTov TO bvvacrdai Kplvuv e^oroxws ri KoKm rj y.r) koX&s Awo- 
 biboiULv 6 \eya>v. Tolovtov yap brj Tiva xal rbv SAcos ire'naibevp.ivov 
 OLop,ed ftvai, Kal TTeTtaibeiia-dai to bvvaaOai TTOifiv to flpripivov. 
 TSkrjv TovTov iji,\v lapl irdvTcov as eiweiv two, KpiTiKov vop.l^op,€V, iva 
 TOV apiOiwv ovra, tov hi Tiepi twos ^weus d^copLO-p^vris' elri yap 
 &v TLs ^Tepos TOV avTov rpoTTov biaKeLiJ,fvos t^ €lpr\p,iv<a ■nepl li; 
 p,opCov. "Q,a-T€ StjAok on Kal t^s TTfpl (f)Vi7e<>)s ia-TopCas bei Tivas 
 vnap\(iv opovs toiovtovs, Trpos o^s avac^ipav amobi^erai tov TpSirov 
 T&v beiKwixiviov \(iip\s tov Tt&s Ix*' TaK7)des, etre oiItcos e?T€ dAXms. 
 De Partibus Animalium, i . i . ' Every theory and method, how- 
 ever humble or exalted its function, has two degrees in which 
 it may be mastered, one of which may be called science, the 
 other education. Education makes a man a competent judge 
 of the performances of the professional artist. Such a compe- 
 tence belongs to universal education, and indeed constitutes its 
 criterion. But while some are thus competent to criticize in 
 every province, others have a corresponding power in a limited 
 province. Physiology then, like other sciences, must have 
 certain canons by which, as by a standard of reference, a critic 
 will judge a writer's method of demonstration, irrespectively of 
 the truth of his doctrines.' 
 
 Prom this passage it is clear that, according to Aristotle, there 
 are as many branches of education as of science ; and that if he 
 speaks of logic as education it is not as universal education but 
 only as one of many branches, though perhaps one of the most 
 important. *Ocra 6' eyxeipoCcrt t&v XfyovTwv Tivis irepl rrjs oXt)- 
 6e[as hv TpoTTOV bei dTrobi^ea-Oai, 8i' &iraibev(T(av t&v Siva\vriK&v 
 TovTO bp&tnv. Aei yap wept tovtoiv rJKfiv •npoeTtiarap.ivovs aXKa fwj 
 iiKoiovTas Crireiv. Met. 3. 3. ' Discussions in the exposition of 
 a physical system, respecting the method of demonstration to be 
 
APPENDIX E. 
 
 required, betray a want of education in logic ; for such questions 
 should be previously determined, and not investigated in a phy- 
 sical treatise.' * 
 
 The grand problem for the educated critic is the appropriate 
 method of the particular science and the degree of accuracy 
 {&.KpCfieLa) to be demanded in the demonstrations. Ae'yotro 6' hv 
 iKavm el Kara tjjv v7T0Keifj.fvr]V vKr]V bia(Ta<pri6eCri, To yap aKpi^^s 
 ovx 6]Mi(c>>s fv at!a(n Tots Ao'yois ktii^rfnjTeov, &tnrep 0118^ iv rois 
 hr]fuovpyovfJi,ei>ois. . . . Tbv cwtov 6e rpdnov koI aitobexea-Oai xpi^v 
 fKaffTov T&v Xeyofi^vaV ireiraiifvixevov yap kariv i-m. to<70vtov 
 TUKpiPfs iTn(riTeiv Kaff kKacrrov yivos eij) oaov ij rod TtpdyfxaTos 
 <j>v(ns emSexerai. TlapaT:k-qa'iov yap (paCverai p.adr]fjt,aTi,KOV re Ttida- 
 voKoyovvTos a/nohi^scrOai Kot prjTopiKov a/nobei^eis aTraiTeiV. Exa- 
 tTTOs 8e Kpivei Ka\&s h yivdxTKH, Kal TO'VTav ityTiv ayaBbs Kptrjyy. 
 Ka6' ^KauTov apa 6 TTeiTai^evixivos, airX&s bi 6 Ttepl irav ireTraibev- 
 ptfvos. Ethica Nic. i. 3. 'The exposition is adequate if it is as 
 precise as the subject admits. For the same amount of exacti- 
 tude is not to be required in all sciences any more than in all 
 arts. . . . General statements, then, must be admitted in ethical 
 science, for the educated critic varies in his demand of precision 
 in the different provinces of science, and no more asks for 
 demonstration from the orator than he accepts probabilities from 
 the mathematician. Competence to judge requires knowledge 
 of the subject-matter, and belongs in each province to the 
 educated ; ,universal competence, therefore, requires universal 
 education.' 
 
 We have seen that sophistic proof as differing from paralogism 
 depends on the employment of an inappropriate method or inad- 
 missible evidence -. the pretender to science proves a theorem by 
 an unscientific method (ch. 6, note 5), or the questioner con- 
 futes the answerer accidentally, i. e. on topics not essentially 
 connected with the department he professes to have mastered 
 (ch. 18, note i). The one case is simulated pirastic, the other 
 simulated science (ch. xi). In neither can the sophism be 
 detected by the ignorant judges (dicpoarat) of a pirastic con- 
 troversy; for, as we have said "before, we must not limit the 
 simulation of pirastic to the employment of thirteen principles 
 covering the defects of the thirteen paralogisms. It is clear 
 that the admission of legitimate and exclusion of illegitimate 
 
 R a 
 
244 APPENDIX E. 
 
 evidence in proof of a scientific theorem or disproof of a man's 
 pretensions to science is a function beyond the capacity of an 
 ignorant jury and which requires an educated judge. 'Artaibev- 
 tria ydp eort irepl ^kojttov ■npayfxa to imj hvvacrOai. Kpiveiv tovs t 
 olKelovs \6yovs tov irpiyixaTos (cat roiis aWorplovs. Ethica Eud. 
 I. 7. 'Those who are uneducated in a given department of 
 science are unable to discriminate between the theorems and 
 methods peculiar to it and those ^hich are alien/ This explains 
 the recommendation to the genuine geometer (ch. 6, note 5) 
 to decline the pirastic tribunal. A large branch, then, of 
 sophisms, accidental or inappropriate confutations, and accidental 
 or inappropriate demonstrations, are merely indicated, not ex- 
 amined, in the present treatise. 
 
245 
 
 APPENDIX F. 
 
 THE QUADBATURE OP THE CIRCLE BY HIPPOCRATES, 
 ANTIPHO, AND BBYSO. 
 
 As the quadrature of the circle by Hippocrates and the quad- 
 rature by lunules are the only examples which Aristotle gives 
 of a pseudographema, it is desirable to examine them with some 
 attention. The quadrature of the circle by means of lunules, 
 i. e. spaces limited by the intersecting arcs of two circles, is as 
 follows. We first invent a method of squaring a lunule : — 
 
 On the diameter AB describe the semicircle AGB; in this 
 inscribe the isosceles triangle A GB ; and on the sides A 0, GB 
 describe the semicircles ADG, GEE. 
 
 Because the angle A GB is inscribed in a semicircle, it is a 
 right angle (Euclid, 3. 31), and the square of the hypotenuse 
 AB is equal to the sum of the squares of the sides AO, OB 
 (Euclid, 1.47). But circles, or semicircles, are to one another 
 as the squares of their diameters (Euclid, la. 2,), therefore the 
 semicircle AGB is equal to the sum of the semicircles ABC, 
 GEB. Take away from these equals the segments AFG, CGB 
 %hich are common to each, and the remaining triangle AGB is 
 
246 APPENDIX F. 
 
 equal to the sum of the lunules ABO FA, CEBGC, or the tri- 
 angle ACE is equal to the lunule ABC FA. We therefore have 
 found a rectilinear area equal to a given lunule. 
 
 According to Alexander Aphrodisiensisj Hippocrates applied 
 this to the quadrature of the circle in the following manner : — 
 
 On the diameter AB describe the semicircle ACBJB ; in this 
 inscribe three lines, AC, CB, BB, each equal to the radius AK 
 (this is the same thing as inscribing a hexagon in the circle; 
 Euclid, 4. 15). On these describe the semicircles AFC, CGB, 
 BHB; and describe a fourth semicircle ^ equal to one of these. 
 
 Then because circles or semicircles are as the squares of their 
 diameters (Euclid, 1%. 3), the semicircle ACBB is equal to the 
 sum of the semicircles E, AFC, CGB, BHB. Take away the 
 segments which are common to these equals, and the remaining 
 rectilinear area ACBB is equal to the sum of the semicircle F 
 and the three lunules. But we discovered a method of deter- 
 mining a rectilinear area equal to a lunule; take away, then, 
 from the rectilinear area ACBB spaces equal to the three lunules, 
 and the remaining rectilinear area will be equal to the semi- 
 circle E. q. E. F. 
 
 Wliat is the fallacy in this construction ? This : it is true 
 that we found a method of squaring a particular kind of lunule, 
 that is, one whose upper arc was a semicircle and whose lower 
 arc was the fourth of a circle; but we found no method of 
 squaring such a lunule as we now have, i. e. one whose upper 
 arc is a semicircle and whose lower arc is the sixth of a circle. 
 This is clearly the quadrature by lunules, and therefore (see 
 ch. xi) was not the method of Hippocrates. His method is 
 described by Simplicius on Phys. Ausc. i. a, on the authority 
 
APPENDIX F. 247 
 
 of Eudemus, disciple of Aristotle, a witness whose evidence on 
 the question must be taken as decisive. « 
 
 According to Eudemus, Hippocrates not only squared a lunule 
 whose outer arc was a semicircle, hut also lunules whose outer 
 arc was greater or less than a semicircle. He then proceeded to 
 ■square the circle in the following manner : — 
 
 Let AC, BC he the radii of two concentric circles, and let 
 AC^ equal 6 £C^. In the inner circle inscribe a hexagon 
 {Euclid, 4. 15). Producing the radii CD &c. to the outer circle, 
 and joining AG, GE, &c., we inscribe a hexagon in the outer 
 circle. Join AM, and on. AE describe a segment A HE similar 
 to the segment A G (Euclid, 3. 33) . The inner circle plus the 
 lunule AG E H sh&W. equal the triangle AGE plus the hexagon 
 in the inner circle. 
 
 Because AEF, being an angle inscribed in a semicircle, is a 
 right angle (Euclid, 3. 31), therefore AE'^ equals AF'^ minus 
 FE^ (Euclid, I. 47). But AF'^ equals ^AC^ ; and FE, being 
 the side of an inscribed hexagon, equals the radius AC (Euclid, 
 4. 15): therefore AE^ equals ^AC^. But the radius ^C equals 
 the side of the hexagon AG ov GE, and A C^ by construction 
 equals 6BC^ or 6BD'^. Therefore AE^ equals AG^ plus GE^ 
 plus 6BD^. But similar segments are as the squares of their 
 chords [Hippocrates deduced this from the theorem that circles 
 are as the squares of their diameters (Euclid, la. a)]: therefore 
 the segment AHE equals the segment AG plus the segment 
 
248 APPENDIX F. 
 
 GE plus the six segments of tbe inner circle. To these equals 
 add the area inclosed by the arc AHE and the straight lines 
 AG, GB; therefore the triangle AGE equals the lunule AG EH 
 plus the six segments. To these equals add the hexagon in the 
 inner circle; therefore the triangle plus the hexagon equals the 
 lunule plus the inner circle. 
 
 To complete the quadrature of the circle Hippocrates must 
 have added: But we have shewn how to square any lunule: 
 deduct, then, from the triangle and hexagon an area equal to 
 the lunule, and the remaining rectilinear space is equal to the 
 circle. Next construct a square equal to this rectilinear space 
 (Euclid, 3. 14), and we have found a square equal to a circle. 
 
 q. E. F. 
 
 It is obvious that the fallacy of this is the same as that of the 
 previous method. Hippocrates was the first who wrote a treatise 
 of elementary geometry. Montucla (Histoire des Mathema- 
 tiques) suggests what is very probable, that the construction 
 was offered as a specimen of fallacious reasoning, and that Hip- 
 pocrates as a geometer only intended to assert that we should 
 solve the problem of squaring the circle as soon as we could 
 square all the lunules as satisfactorily as he had squared certain 
 definite lunules. This seems to have been Aristotle^s view ; at 
 least be gives the proof by lunules, which has the same defect 
 as the proof of Hippocrates, as an instance of abduction or 
 reduction {aitayatyri), i. e. a ratiocination which, though incom- 
 plete, advances one step towards the solution of a problem. 'ATra- 
 yatyri 8' iarlv orav roJ n^v \xi(T(si to rrpmrov brj\ov fj vTrdp)(op, ra 6 
 i<T)^dT(o TO fxiaov abrjKov fiiv, ofwCas 6^ ttkttov ^ fmkkov tov avimi- 
 p&aiiaTOs' Irt h,v dkCya jj to, jne'o-a rov icr)(A.TOv koX tov jxecrov navTons 
 
 yap kyyuTepov elvai avpiPawfi Trjs eTrurrrip.'qs Olov el to A ei?) 
 
 TiTpayiovlCeadai, to 6' e^' <b E evOvypaniiov, to h' l(^ a Z kukXos' fl 
 TOV EZ pLovov dr] ixecrov ro p,fTa p/qvCa-Kaiv taov ylve(T6ai ev8vyp6,p,p,i^ 
 TOP KijKKov, eyyvs &v etr) tov eibivai. An. Pr. 2. 35. ' Abduction 
 is a proof whose major premiss is certain and whose minor pre- 
 miss, though doubtful, is as certain or more certain than the 
 conclusion, or whose minor premiss requires but few steps for 
 its proof J for such a reasoning brings us one step nearer to 
 knowledge. For instance, let P (major) be a square, M (middle) 
 a rectilinear space, S (minor) a circle. If for the establishment 
 
APPENDIX P. 249 
 
 of the minor premiss SM (the equation of the circle to a recti- 
 Hnear area) only one step is necessaryf> the elimination of the 
 lunules that enter into an equation we have discovered, this 
 preliminary equation is an advance towards solving the problem 
 SP, i. e. finding the equation of the circle to a square/ 
 
 An expression of Aristotle's that apparently refers to this 
 subject (Tm yap ^ to. ^^iiievKXia irepiypacpeiv imtj as bei, rj ypajxixds 
 Tivas ayeiv p/q &s &v aydeirjiTav, tov irapaKoyurpov itoLflTaL [o yjrevSo- 
 ypa<f!&v]. Topics, i. i. 'The pseudogxaphema depends on semi- 
 circles being improperly described or lines improperly drawn') 
 seems to indicate that Hippocrates or some one else introduced 
 some further trick in the manipulation of the ruler or com-, 
 
 Eudemus introduces his account of the quadrature of lunules 
 (not the quadrature of the circle by lunules) in the following 
 terms. Kal ol t&v iJ,rivC(TKaiv 6^ mpayiavKTpoi, bo^avres flvai t&v 
 ovK eirmoXaCav hi.aypap.p.i.T(av hia Tr\v okeforjjTa t^v Tiphs tov kvkKov, 
 v(j) 'iTtiroKpAxovs eyp6,<pir\a6,v re wpoiJTWs (cat koto rpotrov iSofaz; otto- 
 boOfjvai, btoTrep iTiiitkiov a^^p,edd re koi bi.e\Ocop,€v. ' The quadra- 
 ture of the lunules, which is regarded as no superficial demon- 
 stration because it is based on the essential properties of the 
 circle, was invented by Hippocrates, and is generally admitted 
 to be scientific, and deserves a fuUer notice in a history of 
 geometry/ Here iTtnro\aCa>v seems a reminiscence of Aristotle's 
 definition of sophistic principles : OvOev yap t&v Keyop,eva>v evbo- 
 foij; firiiroKauJV l^^i itavrek&s TrjV ^avracrCav, Kada/nep Trepl ras t&v 
 epianK&v \6y(ov &pxas <Tvp,pipriKev ex^etv (ch. viii, note i): though 
 Eudemus uses it to distinguish sophistic premisses, not, as Ari- 
 stotle, from dialectic, but from scientific. OlKetoTrjTa reminds of 
 the okeiai apxaC which are characteristic of science. 
 
 Antipho inscribed a square in a circle, and in the four seg- 
 ments inscribed four isosceles triangles, in the eight smaller 
 segments eight smaller isosceles triangles, and so on, ad infini- 
 tum. He then probably proposed some method of summing 
 the series of triangles, and said that the sum of the series of 
 triangles plus the inscribed square was the rectilinear area 
 required. 
 
 Montucla observes that if he could have determined the law 
 ty which the triangles diminish in area, he might have summed 
 
250 APPENDIX P. 
 
 the series and solved the problem. He therefore says that there 
 is nothing sophistical or ungeometrical about the procedure of 
 Antipho. It was by a similar method that Archimedes after- 
 wards succeeded in squaring the parabola. He first inscribed a 
 triangle in the parabola; then another in each of the segments, 
 and so on, and proved that the area of the fi.rst triangle, the two 
 second triangles, the four third triangles, &c., formed the pro- 
 gression I, ^, -jJg-, &c., and that the sum of this series was i^. 
 Thus the parabola which is the sum of these triangles is -^ of the 
 inscribed triangle or f of the circumscribed parallelogram. 
 
 Probably if Aristotle had recognized the method of exhaus- 
 tion, or limits, or infinitesimals, as a scientific procedure, he 
 would have pronounced Antipho's reasoning not sophistic but 
 pseudographic, or have conceded to it the name which he gave 
 to that of Hippocrates, Reduction. As it is, he clearly con- 
 sidered it as sophistical and unworthy the attention of the geo- 
 meter. His remarks are worth giving at length. To ijiv ovv d 
 If Kal aKlvy]Tov to 6v a-KOTreXv ov irepl (fivcrfds kcm, cmoTTeiv. "ila-iiep 
 yap Koi t£ yimfxerpri ovk hi Koyos eari Trpos rov aviKovra ras apxAs, 
 a\X. TjTOL krepas ^TtoT^ftijs 17 TratrSv Koivfis, oUtus ovbe t<S irepl ^v- 
 
 (Tea>s Oixoiov brj to aKOireiv «t ovtoos Iv koI irpos aX\r]v deaiv 
 
 oTtoiavovv bia\eye<r6aL t&v \6yov iveKa \eyop.ivmv, olov rriv 'Hpa- 
 K\eiTeiov^..,,r] kviiv koyov ipicTTiKov. "Oirep a^upoTepoi jxep expv- 
 criv 01 Xoyoi koi 6 MeAto-o-ou Kal 6 YlapfXivlhov, koL yap y^euh-r] kap,- 
 ^dvovat Kal a(rv\\6yLcrT0i ettn, pi,aXKov be 6 MeXC(T<rov (fiopTtKhs Kal 
 OVK exwv aTTOpiav, &W' kvbs aroTrov bo'OevTos raWa <Tvp.fiaivw Tmiro 
 be ovbev \aXeTr6v. 'Hfjuv be iiroKetcr^o) to, (jyvtrei ^ Ttdvra ^ evia 
 Kivovp.eva eXvai. ArjKov be eK ttjs eTraycayrfs, &p,a bi ovbe Xvuv 
 &TiavTa Trpoo-jjKei AA\' ?) ocra eK t&v apy&v tis einbeiKvvs ■^evbeTai, 
 Sera be jxri, oti. OXov tov TeTpaya>vi(Tp.ov tov p,ev bia t&v Tp.r]iJ,dTa>v 
 yewixeTpLKOv biaXva-ai, tov bi ' Avtkjj&vtos ov yemp.eTpiKov. Ov pr)v 
 &KK e-neibri Tiepl (ftvcrecas pi^v ov, (ftvo'iKas be airopCas avpL^aCvei kiyeiv 
 avTois, ta-ios ^x^l Ka\&s IttJ piKpoii biaXexOfjvai Tiepl avT&v, eyet yap 
 <lii\oa-o(j)Cav rj a-Ki\j/is. Phys. Ausc. I. 3. 'The question whether 
 existence is one and unchangeable is not a physical problem; 
 for as the geometer does not reason with one who denies his 
 principles, but leaves him to be dealt with by some separate 
 science or by some power that is a common element of all the 
 sciences, no more does the physical inquirer. The examination 
 
APPENDIX P. 251 
 
 of such a doctrine must resemble the confutation of a paradoxical 
 thesis like the tenet of Heraclitus, or th* solution of a sophistic 
 proof. Such indeed are the reasonings both of Melissus and of 
 Parmenides, for the premisses are false and the conclusions are 
 illegitimate, though that of Melissus is the grosser and less sug- 
 gestive of the two. For he starts from an inadmissible premiss 
 and then obtains paradoxical conclusions; which is easy. We, 
 then, postulate as a first principle, that the natural world, in 
 whole or in part, is a scene of change. For this we may appeal 
 to the evidence of observation; and we are not bound to en- 
 counter, even by way of solution, any doctrine except such as 
 admits the principles of the science : just as the geometer is 
 bound to examine the quadrature of the circle by segments, but 
 is not bound to notice the reasoning of Antipho. However, as 
 the thesis, though unphysical as regards its truth, is physical 
 as regards the subject, let us examine it briefly. Por the exami- 
 nation is philosophic and not merely dialectic' Quadrature by 
 segments is an apt description of the method explained by 
 Eudemus, and doubtless refers to the method of Hippocrates. 
 The contradiction of geometrical principles, which in Aristotle's 
 judgment made Antipho's method ungeometrical, was either the 
 assumption (now admitted) that the sides of a many-sided poly- 
 gon coincide with the circumference of a circle, which contra- 
 dicts the theorem that a straight line only touches a circle in a 
 single point (Euclid, 3. J 6), or (as this is rather the contradiction 
 of a conclusion than of a principle) the assumption that, starting 
 from the inscribed square, it is possible, by subdivision of the 
 segments, to reach the circumference, an assumption which 
 contradicts the principle of the infinite divisibility of space. 
 
 Bryso appears to have inscribed one square in a circle and cir- 
 cumscribed another, and to have said that as the circumscribed 
 square was greater than the circle, and the inscribed square less, 
 a third square that should be the mean between the two others 
 would be equal to the circle ; assuming that whenever two things 
 are greater and less respectively than the same other things, 
 they must be equal to one another. 
 
 It is plain that Bryso does not reason like a geometer; 
 Antipho's reasoning approaches nearer to a pseudographema. 
 Bryso's pemisses bear no relation to the principles of geometry ; 
 
APPENDIX F. 
 
 Antipho^s contradict them, but still lie without the geometrical 
 sphere : for, whatever may be the case with natural philosophy, 
 geometry, being in Aristotle^s view a purely deductive science, 
 takes no cognizance of any reasoning which calls her first prin- 
 ciples in question. 
 
 With respect to the method of lunules and the method of 
 Hippocrates, a difficulty suggests itself. The principle or method 
 of these fallacies is evidently the omission of a limitation. Be- 
 cause we can square a particular kind of lunule, it is assumed 
 that we can square every kind of lunule ; that is, the arguments 
 fall under the fallacy a dicto secundum quid ad dictum sim- 
 pliciter. How then can it be said that the principle of these 
 fallacies is not transferable to any other province ? 
 
 It is true that lunules cannot be applied to the solution of 
 ethical or physiological problems, but the suppression or sub- 
 stitution of limitations is practicable in every kind of discussion. 
 If these fallacies are pseudographemas because the rest of their 
 reasoning is geometrical, whereas Bryso's and Antipho's are 
 entirely ungeometrical, it would seem that there is no intrinsic 
 difference between a pseudographema and a sophism, only a dif- 
 ference in the accompaniments. But Aristotle speaks of them 
 as different in kind. He apparently considers the fallacy of the 
 pseudographemas to consist in the false geometrical proposition, 
 that every lunule must belong to one of the classes whose 
 quadrature has been given. 
 
Works by the same Author. 
 
 THE PHILEBUS OF PLATO, with a revised Text 
 
 and English Notes. 
 
 Oxford : at the University Press. 
 
 PHILEBUS, a Dialogue of Plato; translated into 
 
 English. 
 
 London : Longmans, Green, and Co. 
 
 THE LOGIC OF SCIENCE, a translation of the 
 
 Later Analytics of Aristotle, with an Introduction and Notes. 
 London : W. Heath, New Oxford Street. 
 
LECTURES ON THE HISTORY OF ANCIENT 
 PHILOSOPHY. 
 
 By the Kev. W. ARCHEK BUTLER, M.A., late Professor of Moral 
 Philosophy in the University of Dublin. Edited by the Rev. Wm. 
 Hepwokth Thompson, Master of Trinity College, Cambridge. 
 2 vols. 8vo. cloth, price 25s. 
 
 THE REPUBLIC OF PLATO. 
 
 Translated into English, with Analysis and Notes, by J. LI. DA VIES, 
 M. A., and D. J. VAUGHAN, M. A., with Vignette Portraits of 
 Plato and Socrates, engraved by Jeens from an Antique Gem. 
 Printed on toned paper and bound in extra cloth, i8mo. price 4s. 6d. 
 (The Golden Treasury Series.) Also 8vo. cloth, price los. 6d. 
 
 THE ILIAD OF HOMER. 
 
 Translated into English accentuated Hexameters, by SIR JOHN 
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