Aristotle's Logic (Stanford Encyclopedia of Philosophy) Cite this entry Search the SEP • Advanced Search • Tools • RSS FeedTable of Contents• What's New• Archives• Projected ContentsEditorial Information• About the SEP• Editorial Board• How to Cite the SEP• Special CharactersSupport the SEPContact the SEP ©Metaphysics Research Lab,CSLI,Stanford University  Open access to the SEP is made possible by a world-wide funding initiative. Please Read How You Can Help Keep the Encyclopedia FreeAristotle's LogicFirst published Sat Mar 18, 2000; substantive revision Fri Dec 14, 2007Aristotle's logic, especially his theory of the syllogism, has had anunparalleled influence on the history of Western thought. It did notalways hold this position: in the Hellenistic period, Stoic logic, andin particular the work of Chrysippus, took pride of place. However,in later antiquity, following the work of Aristotelian Commentators,Aristotle's logic became dominant, and Aristotelian logic was what wastransmitted to the Arabic and the Latin medieval traditions, while theworks of Chrysippus have not survived. This unique historical position has not always contributed to theunderstanding of Aristotle's logical works. Kant thought thatAristotle had discovered everything there was to know about logic, andthe historian of logic Prantl drew the corollary that any logicianafter Aristotle who said anything new was confused, stupid, orperverse. During the rise of modern formal logic following Frege andPeirce, adherents of Traditional Logic (seen as the descendant ofAristotelian Logic) and the new mathematical logic tended to see oneanother as rivals, with incompatible notions of logic. More recentscholarship has often applied the very techniques of mathematicallogic to Aristotle's theories, revealing (in the opinion of many) anumber of similarities of approach and interest between Aristotle andmodern logicians.This article is written from the latter perspective. As such, it isabout Aristotle's logic, which is not always the same thing as what hasbeen called "Aristotelian" logic.1. Introduction2. Aristotle's Logical Works: The Organon3. The Subject of Logic: "Syllogisms"4. Premises: The Structures of Assertions5. The Syllogistic6. Demonstrations and Demonstrative Sciences7. Definitions8. Dialectical Argument and the Art of Dialectic9. Dialectic and Rhetoric10. Sophistical Arguments11. Non-Contradiction and Metaphysics12. Time and Necessity: The Sea-Battle13. Glossary of Aristotelian TerminologyBibliographyOther Internet ResourcesRelated Entries [A More Detailed Table of Contents]1. IntroductionAristotle's logical works contain the earliest formal study of logicthat we have. It is therefore all the more remarkable that togetherthey comprise a highly developed logical theory, one that was able tocommand immense respect for many centuries: Kant, who was ten timesmore distant from Aristotle than we are from him, even held thatnothing significant had been added to Aristotle's views in theintervening two millennia. In the last century, Aristotle's reputation as a logician hasundergone two remarkable reversals. The rise of modern formal logicfollowing the work of Frege and Russell brought with it a recognitionof the many serious limitations of Aristotle's logic; today, very fewwould try to maintain that it is adequate as a basis for understandingscience, mathematics, or even everyday reasoning. At the same time,scholars trained in modern formal techniques have come to viewAristotle with new respect, not so much for the correctness of hisresults as for the remarkable similarity in spirit between much of hiswork and modern logic. As Jonathan Lear has put it, "Aristotle shareswith modern logicians a fundamental interest in metatheory": hisprimary goal is not to offer a practical guide to argumentation but tostudy the properties of inferential systems themselves.2. Aristotle's Logical Works: The OrganonThe ancient commentators grouped together several of Aristotle'streatises under the title Organon ("Instrument") and regardedthem as comprising his logical works: CategoriesOn InterpretationPrior AnalyticsPosterior AnalyticsTopicsOn Sophistical RefutationsIn fact, the title Organon reflects a much later controversyabout whether logic is a part of philosophy (as the Stoics maintained)or merely a tool used by philosophy (as the later Peripateticsthought); calling the logical works "The Instrument" is a way of takingsides on this point. Aristotle himself never uses this term, nor doeshe give much indication that these particular treatises form some kindof group, though there are frequent cross-references between theTopics and the Analytics. On the other hand,Aristotle treats the Prior and Posterior Analytics asone work, and On Sophistical Refutations is a final section,or an appendix, to the Topics). To these works should be addedthe Rhetoric, which explicitly declares its reliance on theTopics. 3. The Subject of Logic: "Syllogisms"All Aristotle's logic revolves around one notion: thededuction (sullogismos). A thoroughexplanation of what a deduction is, and what they are composed of, willnecessarily lead us through the whole of his theory. What, then, is adeduction? Aristotle says: A deduction is speech (logos) in which, certainthings having been supposed, something different from those supposedresults of necessity because of their being so. (PriorAnalytics I.2, 24b18-20)Each of the "things supposed" is a premise(protasis) of the argument, and what "results of necessity" isthe conclusion (sumperasma). The core of this definition is the notion of "resulting ofnecessity" (ex anankês sumbainein). This corresponds toa modern notion of logical consequence: X results of necessity from Yand Z if it would be impossible for X to be false when Y and Z aretrue. We could therefore take this to be a general definition of "validargument".3.1 Induction and DeductionDeductions are one of two species of argument recognized by Aristotle.The other species is induction(epagôgê). He has far less to say about this thandeduction, doing little more than characterize it as "argument from theparticular to the universal". However, induction (or something verymuch like it) plays a crucial role in the theory of scientificknowledge in the Posterior Analytics: it is induction, or atany rate a cognitive process that moves from particulars to theirgeneralizations, that is the basis of knowledge of the indemonstrablefirst principles of sciences. 3.2 Aristotelian Deductions and Modern Valid ArgumentsDespite its wide generality, Aristotle's definition of deduction is nota precise match for a modern definition of validity. Some of thedifferences may have important consequences: Aristotle explicitly says that what results of necessity must bedifferent from what is supposed. This would rule out arguments in whichthe conclusion is identical to one of the premises. Modern notions ofvalidity regard such arguments as valid, though trivially so.The plural "certain things having been supposed" was taken by someancient commentators to rule out arguments with only one premise.The force of the qualification "because of their being so" hassometimes been seen as ruling out arguments in which the conclusion isnot ‘relevant’ to the premises, e.g., arguments in whichthe premises are inconsistent, arguments with conclusions that wouldfollow from any premises whatsoever, or arguments with superfluouspremises.Of these three possible restrictions, the most interesting would be thethird. This could be (and has been) interpreted as committing Aristotleto something like a relevance logic.In fact, there are passages that appear to confirm this. However, thisis too complex a matter to discuss here. However the definition is interpreted, it is clear that Aristotledoes not mean to restrict it only to a subset of the valid arguments.This is why I have translated sullogismos with‘deduction’ rather than its English cognate. In modernusage, ‘syllogism’ means an argument of a very specificform. Moreover, modern usage distinguishes between valid syllogisms(the conclusions of which follow from their premises) and invalidsyllogisms (the conclusions of which do not follow from theirpremises). The second of these is inconsistent with Aristotle's use:since he defines a sullogismos as an argument in which theconclusion results of necessity from the premises, "invalidsullogismos" is a contradiction in terms. The first is also atleast highly misleading, since Aristotle does not appear to think thatthe sullogismoi are simply an interesting subset of the validarguments. Moreover (see below), Aristotle expends great efforts toargue that every valid argument, in a broad sense, can be "reduced" toan argument, or series of arguments, in something like one of the formstraditionally called a syllogism. If we translate sullogismosas "syllogism, ", this becomes the trivial claim "Every syllogism is asyllogism",4. Premises: The Structures of AssertionsSyllogisms are structures of sentences each of which can meaningfullybe called true or false: assertions(apophanseis), in Aristotle's terminology. According toAristotle, every such sentence must have the same structure: it mustcontain a subject (hupokeimenon) and apredicate and must either affirm or deny the predicateof the subject. Thus, every assertion is either theaffirmation kataphasis or thedenial (apophasis) of a single predicate of asingle subject. In On Interpretation, Aristotle argues that a singleassertion must always either affirm or deny a single predicate of asingle subject. Thus, he does not recognize sentential compounds, suchas conjunctions and disjunctions, as single assertions. This appears tobe a deliberate choice on his part: he argues, for instance, that aconjunction is simply a collection of assertions, with no moreintrinsic unity than the sequence of sentences in a lengthy account(e.g. the entire Iliad, to take Aristotle's own example).Since he also treats denials as one of the two basic species ofassertion, he does not view negations as sentential compounds. Histreatment of conditional sentences and disjunctions is more difficultto appraise, but it is at any rate clear that Aristotle made no effortsto develop a sentential logic. Some of the consequences of this for histheory of demonstration are important.4.1 TermsSubjects and predicates of assertions are terms. Aterm (horos) can be either individual, e.g. Socrates,Plato or universal, e.g. human, horse,animal, white. Subjects may be either individual oruniversal, but predicates can only be universals: Socrates ishuman, Plato is not a horse, horses are animals,humans are not horses. The word universal (katholou) appears tobe an Aristotelian coinage. Literally, it means "of a whole"; itsopposite is therefore "of a particular" (kath’hekaston). Universal terms are those which can properly serve aspredicates, while particular terms are those which cannot.This distinction is not simply a matter of grammatical function. Wecan readily enough construct a sentence with "Socrates" as itsgrammatical predicate: "The person sitting down is Socrates".Aristotle, however, does not consider this a genuine predication. Hecalls it instead a merely accidental orincidental (kata sumbebêkos)predication. Such sentences are, for him, dependent for their truthvalues on other genuine predications (in this case, "Socrates issitting down").Consequently, predication for Aristotle is as much a matter ofmetaphysics as a matter of grammar. The reason that the termSocrates is an individual term and not a universal is that theentity which it designates is an individual, not a universal. Whatmakes white and human universal terms is that theydesignate universals.Further discussion of these issues can be found in the entry on Aristotle's metaphysics.4.2 Affirmations, Denials, and ContradictionsAristotle takes some pains in On Interpretation to argue thatto every affirmation there corresponds exactly one denial such thatthat denial denies exactly what that affirmation affirms. The pairconsisting of an affirmation and its corresponding denial is acontradiction (antiphasis). In general,Aristotle holds, exactly one member of any contradiction is true andone false: they cannot both be true, and they cannot both be false.However, he appears to make an exception for propositions about futureevents, though interpreters have debated extensively what thisexception might be (see further discussionbelow). The principle that contradictories cannot both be true hasfundamental importance in Aristotle's metaphysics (see further discussion below). 4.3 All, Some, and NoneOne major difference between Aristotle's understanding of predicationand modern (i.e., post-Fregean) logic is that Aristotle treatsindividual predications and general predications as similar in logicalform: he gives the same analysis to "Socrates is an animal" and "Humansare animals". However, he notes that when the subject is a universal,predication takes on two forms: it can be eitheruniversal or particular. Theseexpressions are parallel to those with which Aristotle distinguishesuniversal and particular terms, and Aristotle is aware of that,explicitly distinguishing between a term being a universal and a termbeing universally predicated of another. Whatever is affirmed or denied of a universal subject may beaffirmed or denied of it it universally(katholou or "of all", kata pantos), inpart (kata meros, en merei), orindefinitely (adihoristos).AffirmationsDenialsUniversalP affirmed of all of SEvery S is P, All S is (are) PP denied of all of SNo S is PParticularP affirmed of some of SSome S is (are) PP denied of some of SSome S is not P, Not every S is PIndefiniteP affirmed of SS is PP denied of SS is not P4.3.1 The "Square of Opposition"In On Interpretation, Aristotle spells out the relationshipsof contradiction for sentences with universal subjects as follows: AffirmationDenialUniversalEvery A is BNo A is BUniversalSome A is BNot every A is BSimple as it appears, this table raises important difficulties ofinterpretation (for a thorough discussion, see the entry on the square of opposition). In the Prior Analytics, Aristotle adopts a somewhatartificial way of expressing predications: instead of saying "X ispredicated of Y" he says "X belongs (huparchei) to Y". Thisshould really be regarded as a technical expression. The verbhuparchein usually means either "begin" or "exist, bepresent", and Aristotle's usage appears to be a development of thislatter use.4.3.2 Some Convenient AbbreviationsFor clarity and brevity, I will use the following semi-traditionalabbreviations for Aristotelian categorical sentences (note that thepredicate term comes first and the subject termsecond): AbbreviationSentenceAaba belongs to all b (Every b is a)Eaba belongs to no b (No b is a)Iaba belongs to some b (Some b is a)Oaba does not belong to all b (Some b is not a)5. The SyllogisticAristotle's most famous achievement as logician is his theory ofinference, traditionally called the syllogistic(though not by Aristotle). That theory is in fact the theory ofinferences of a very specific sort: inferences with two premises, eachof which is a categorical sentence, having exactly one term in common,and having as conclusion a categorical sentence the terms of which arejust those two terms not shared by the premises. Aristotle calls theterm shared by the premises the middle term(meson) and each of the other two terms in the premises anextreme (akron). The middle term must beeither subject or predicate of each premise, and this can occur inthree ways: the middle term can be the subject of one premise and thepredicate of the other, the predicate of both premises, or the subjectof both premises. Aristotle refers to these term arrangements asfigures (schêmata): 5.1 The FiguresFirst FigureSecond FigureThird FigurePredicateSubjectPredicateSubjectPredicateSubjectPremiseababacPremisebcacbcConclusionacbcabAristotle calls the term which is the predicate of the conclusion themajor term and the term which is the subject of theconclusion the minor term. The premise containing themajor term is the major premise, and the premisecontaining the minor term is the minor premise. Aristotle's procedure is then a systematic investigation of thepossible combinations of premises in each of the three figures. Foreach combination, he seeks either to demonstrate that some conclusionnecessarily follows or to demonstrate that no conclusion follows. Theresults he states are exactly correct.5.2 Methods of Proof: Conversion and ReductionAristotle shows each valid form to be valid by showing how to constructa deduction of its conclusion from its premises. These deductions, inturn, can take one of two forms: direct orprobative (deiktikos) deductions anddeductions through the impossible (dia toadunaton). A direct deduction is a series of steps leading from the premises tothe conclusion, each of which is either a conversionof a previous step or an inference from two previous steps relying on afirst-figure deduction. Conversion, in turn, is inferring from aproposition another which has the subject and predicate interchanged.Specifically, Aristotle argues that three such conversions aresound:Eab → EbaIab → IbaAab → IbaHe undertakes to justify these in An. Pr. I.2. From amodern standpoint, the third is sometimes regarded with suspicion.Using it we can get Some monsters are chimeras from theapparently true All chimeras are monsters; but the former isoften construed as implying in turn There is something which is amonster and a chimera, and thus that there are monsters and thereare chimeras. In fact, this simply points up something aboutAristotle's system: Aristotle in effect supposes that allterms in syllogisms are non-empty. (For further discussion of thispoint, see the entry on the square of opposition).As an example of the procedure, we may take Aristotle's proof ofCamestres. He says:If M belongs to every N but to no X, then neither will Nbelong to any X. For if M belongs to no X, then neither does X belongto any M; but M belonged to every N; therefore, X will belong to no N(for the first figure has come about). And since the privativeconverts, neither will N belong to any X. (An. Pr. I.5,27a9-12)From this text, we can extract an exact formal proof, asfollows:StepJustificationAristotle's Text1. MaNIf M belongs to every N2. MeXbut to no X,To prove: NeXthen neither will N belong to any X.3. MeX(2, premise)For if M belongs to no X,4. XeM(3, conversion of e)then neither does X belong to any M;5. MaN(1, premise)but M belonged to every N;6. XeN(4, 5, Celarent)therefore, X will belong to no N (for the first figure has comeabout).7. NeX(6, conversion of e)And since the privative converts, neither will N belong to anyX.5.3 Methods of Disproof: Counterexamples and TermsAristotle proves invalidity by constructing counterexamples. This isvery much in the spirit of modern logical theory: all that it takes toshow that a certain form is invalid is a singleinstance of that form with true premises and a falseconclusion. However, Aristotle states his results not by saying thatcertain premise-conclusion combinations are invalid but by saying thatcertain premise pairs do not "syllogize": that is, that, given the pairin question, examples can be constructed in which premises of that formare true and a conclusion of any of the four possible forms is false. When possible, he does this by a clever and economical method: hegives two triplets of terms, one of which makes the premises true and auniversal affirmative "conclusion" true, and the other of which makesthe premises true and a universal negative "conclusion" true. The firstis a counterexample for an argument with either an E or an Oconclusion, and the second is a counterexample for an argument witheither an A or an I conclusion.5.4 The Deductions in the Figures ("Moods")In Prior Analytics I.4-6, Aristotle shows that the premisecombinations given in the following table yield deductions and that allother premise combinations fail to yield a deduction. In theterminology traditional since the middle ages, each of thesecombinations is known as a mood (from Latinmodus, "way", which in turn is a translation of Greektropos). Aristotle, however, does not use this expression andinstead refers to "the arguments in the figures". In this table, " " separatespremises from conclusion; it may be read "therefore". The second columnlists the medieval mnemonic name associated with the inference (theseare still widely used, and each is actually a mnemonic for Aristotle'sproof of the mood in question). The third column briefly summarizesAristotle's procedure for demonstrating the deduction.Table of the Deductions in the FiguresFormMnemonicProofAab, Abc AacBarbaraPerfectEab, Abc EacCelarentPerfectAab, Ibc IacDariiPerfect; also by impossibility, from CamestresEab, Ibc OacFerioPerfect; also by impossibility, from CesareSECOND FIGUREEab, Aac EbcCesare(Eab, Aac)→(Eba, Aac)CelEbcAab, Eac EbcCamestres(Aab, Eac)→(Aab, Eca)=(Eca, Aab)CelEcb→EbcEab, Iac ObcFestino(Eab, Iac)→(Eba, Iac)FerObcAab, Oac ObcBaroco(Aab, Oac +Abc)Bar(Aac, Oac)ImpObcTHIRD FIGUREAac, Abc IabDarapti(Aac, Abc)→(Aac, Icb)DarIabEac, Abc OabFelapton(Eac, Abc)→(Eac, Icb)FerOabIac, Abc IabDisamis(Iac, Abc)→(Ica, Abc)=(Abc, Ica)DarIba→IabAac, Ibc IabDatisi(Aac, Ibc)→(Aac, Icb)DarIabOac, Abc OabBocardo(Oac, +Aab, Abc)Bar(Aac, Oac)ImpOabEac, Ibc OabFerison(Eac, Ibc)→(Eac, Icb)FerOab5.5 Metatheoretical ResultsHaving established which deductions in the figures are possible,Aristotle draws a number of metatheoretical conclusions, including: No deduction has two negative premisesNo deduction has two particular premisesA deduction with an affirmative conclusion must have twoaffirmative premisesA deduction with a negative conclusion must have one negativepremise.A deduction with a universal conclusion must have two universalpremisesHe also proves the following metatheorem: All deductions can be reduced to the two universaldeductions in the first figure.His proof of this is elegant. First, he shows that the two particulardeductions of the first figure can be reduced, by proof throughimpossibility, to the universal deductions in the second figure: (Darii) (Aab, Ibc, +Eac)Camestres(Ebc, Ibc)ImpIac(Ferio) (Eab, Ibc, +Aac)Cesare(Ebc, Ibc)ImpOacHe then observes that since he has already shown how to reduce all theparticular deductions in the other figures except Baroco and Bocardo toDarii and Ferio, these deductions can thus be reducedto Barbara and Celarent. This proof is strikinglysimilar both in structure and in subject to modern proofs of theredundancy of axioms in a system. Many more metatheoretical results, some of them quite sophisticated,are proved in Prior Analytics I.45 and in PriorAnalytics II. As noted below, some of Aristotle's metatheoreticalresults are appealed to in the epistemological arguments of thePosterior Analytics.5.6 Syllogisms with ModalitiesAristotle follows his treatment of "arguments in the figures" with amuch longer, and much more problematic, discussion of what happens tothese figured arguments when we add the qualifications "necessarily"and "possibly" to their premises in various ways. In contrast to thesyllogistic itself (or, as commentators like to call it, theassertoric syllogistic), this modal syllogisticappears to be much less satisfactory and is certainly far moredifficult to interpret. Here, I only outline Aristotle's treatment ofthis subject and note some of the principal points of interpretivecontroversy. 5.6.1 The Definitions of the ModalitiesModern modal logic treats necessity and possibility as interdefinable:"necessarily P" is equivalent to "not possibly not P", and "possibly P"to "not necessarily not P". Aristotle gives these same equivalences inOn Interpretation. However, in Prior Analytics, hemakes a distinction between two notions of possibility. On the first,which he takes as his preferred notion, "possibly P" is equivalent to"not necessarily P and not necessarily not P". He then acknowledges analternative definition of possibility according to the modernequivalence, but this plays only a secondary role in his system. 5.6.2 Aristotle's General ApproachAristotle builds his treatment of modal syllogisms on his account ofnon-modal (assertoric) syllogisms: he works his waythrough the syllogisms he has already proved and considers theconsequences of adding a modal qualification to one or both premises.Most often, then, the questions he explores have the form: "Here is anassertoric syllogism; if I add these modal qualifications to thepremises, then what modally qualified form of the conclusion (if any)follows?". A premise can have one of three modalities: it can benecessary, possible, or assertoric. Aristotle works through thecombinations of these in order: Two necessary premisesOne necessary and one assertoric premiseTwo possible premisesOne assertoric and one possible premiseOne necessary and one possible premiseThough he generally considers only premise combinations which syllogizein their assertoric forms, he does sometimes extend this; similarly, hesometimes considers conclusions in addition to those which would followfrom purely assertoric premises. Since this is his procedure, it is convenient to describe modalsyllogisms in terms of the corresponding non-modal syllogism plus atriplet of letters indicating the modalities of premises andconclusion: N = "necessary", P = "possible", A = "assertoric". Thus,"Barbara NAN" would mean "The form Barbara with necessarymajor premise, assertoric minor premise, and necessary conclusion". Iuse the letters "N" and "P" as prefixes for premises as well; a premisewith no prefix is assertoric. Thus, Barbara NAN would be NAab,Abc NAac.5.6.3 Modal ConversionsAs in the case of assertoric syllogisms, Aristotle makes use ofconversion rules to prove validity. The conversion rules for necessarypremises are exactly analogous to those for assertoric premises: NEab→NEbaNIab→NIbaNAab→NIbaPossible premises behave differently, however. Since he defines"possible" as "neither necessary nor impossible", it turns out thatx is possibly F entails, and is entailed by, x is possiblynot F. Aristotle generalizes this to the case of categoricalsentences as follows: PAab→PEabPEab→PAabPIab→POabPOab→PIabIn addition, Aristotle uses the intermodal principle N→A: that is,a necessary premise entails the corresponding assertoric one. However,because of his definition of possibility, the principle A→P doesnot generally hold: if it did, then N→P would hold, but on hisdefinition "necessarily P" and "possibly P" are actually inconsistent("possibly P" entails "possibly not P"). This leads to a further complication. The denial of "possibly P" forAristotle is "either necessarily P or necessarily not P". The denial of"necessarily P" is still more difficult to express in terms of acombination of modalities: "either possibly P (and thus possibly not P)or necessarily not P" This is important because of Aristotle's proofprocedures, which include proof through impossibility. If we give aproof through impossibility in which we assume a necessary premise,then the conclusion we ultimately establish is simply the denial ofthat necessary premise, not a "possible" conclusion in Aristotle'ssense. Such propositions do occur in his system, but only in exactlythis way, i.e., as conclusions established by proof throughimpossiblity from necessary assumptions. Somewhat confusingly,Aristotle calls such propositions "possible" but immediately adds " notin the sense defined": in this sense, "possibly Oab" is simply thedenial of "necessarily Aab". Such propositions appear only as premises,never as conclusions.5.6.4 Syllogisms with Necessary PremisesAristotle holds that an assertoric syllogism remains valid if"necessarily" is added to its premises and its conclusion: the modalpattern NNN is always valid. He does not treat this as a trivialconsequence but instead offers proofs; in all but two cases, these areparallel to those offered for the assertoric case. The exceptions areBaroco and Bocardo, which he proved in the assertoriccase through impossibility: attempting to use that method here wouldrequire him to take the denial of a necessary O proposition ashypothesis, raising the complication noted above, and he must resort toa different form of proof instead. 5.6.5 NA/AN Combinations: The Problem of the "Two Barbaras" and Other DifficultiesSince a necessary premise entails an assertoric premise, every AN or NAcombination of premises will entail the corresponding AA pair, and thusthe corresponding A conclusion. Thus, ANA and NAA syllogisms are alwaysvalid. However, Aristotle holds that some, but not all, ANN and NANcombinations are valid. Specifically, he accepts Barbara NANbut rejects Barbara ANN. Almost from Aristotle's own time,interpreters have found his reasons for this distinction obscure, orunpersuasive, or both. Theophrastus, for instance, adopted the simplerrule that the modality of the conclusion of a syllogism was always the"weakest" modality found in either premise, where N is stronger than Aand A is stronger than P (and where P probably has to be defined as"not necessarily not"). Other difficulties follow from the problem ofthe "Two Barbaras", as it is often called, and it has often beenmaintained that the modal syllogistic is inconsistent. This subject quickly becomes too complex for summarizing in thisbrief article. For further discussion, see Becker, McCall, Patterson,van Rijen, Striker, Nortmann, Thom, and Thomason.6. Demonstrations and Demonstrative SciencesA demonstration (apodeixis) is "a deductionthat produces knowledge". Aristotle's Posterior Analyticscontains his account of demonstrations and their role in knowledge.From a modern perspective, we might think that this subject movesoutside of logic to epistemology. From Aristotle's perspective,however, the connection of the theory of sullogismoi with thetheory of knowledge is especially close. 6.1 Aristotelian SciencesThe subject of the Posterior Analytics isepistêmê. This is one of several Greek words thatcan reasonably be translated "knowledge", but Aristotle is concernedonly with knowledge of a certain type (as will be explained below).There is a long tradition of translating epistêmêin this technical sense as science, and I shall followthat tradition here. However, readers should not be misled by the useof that word. In particular, Aristotle's theory of science cannot beconsidered a counterpart to modern philosophy of science, at least notwithout substantial qualifications. We have scientific knowledge, according to Aristotle, when weknow:the cause why the thing is, that it is the cause of this,and that this cannot be otherwise. (Posterior AnalyticsI.2)This implies two strong conditions on what can be the object ofscientific knowledge: Only what is necessarily the case can be known scientificallyScientific knowledge is knowledge of causesHe then proceeds to consider what science so defined will consist in,beginning with the observation that at any rate one form of scienceconsists in the possession of a demonstration(apodeixis), which he defines as a "scientific deduction": by "scientific" (epistêmonikon), I mean thatin virtue of possessing it, we have knowledge.The remainder of Posterior Analytics I is largely concernedwith two tasks: spelling out the nature of demonstration anddemonstrative science and answering an important challenge to its verypossibility. Aristotle first tells us that a demonstration is adeduction in which the premises are: trueprimary (prota)immediate (amesa, "without amiddle")better known or more familiar(gnôrimôtera) than the conclusionprior to the conclusioncauses (aitia) of the conclusionThe interpretation of all these conditions except the first has beenthe subject of much controversy. Aristotle clearly thinks that scienceis knowledge of causes and that in a demonstration, knowledge of thepremises is what brings about knowledge of the conclusion. The fourthcondition shows that the knower of a demonstration must be in somebetter epistemic condition towards them, and so modern interpretersoften suppose that Aristotle has defined a kind of epistemicjustification here. However, as noted above, Aristotle is defining aspecial variety of knowledge. Comparisons with discussions ofjustification in modern epistemology may therefore be misleading. The same can be said of the terms "primary", "immediate" and "betterknown". Modern interpreters sometimes take "immediate" to mean"self-evident"; Aristotle does say that an immediate proposition is one"to which no other is prior", but (as I suggest in the next section)the notion of priority involved is likely a notion of logical prioritythat it is hard to detach from Aristotle's own logical theories."Better known" has sometimes been interpreted simply as "previouslyknown to the knower of the demonstration" (i.e., already known inadvance of the demonstration). However, Aristotle explicitlydistinguishes between what is "better known for us" with what is"better known in itself" or "in nature" and says that he means thelatter in his definition. In fact, he says that the process ofacquiring scientific knowledge is a process of changing whatis better known "for us", until we arrive at that condition in whichwhat is better known in itself is also better known for us.6.2 The Regress ProblemIn Posterior Analytics I.2, Aristotle considers two challengesto the possibility of science. One party (dubbed the "agnostics" byJonathan Barnes) began with the following two premises: Whatever is scientifically known must be demonstrated.The premises of a demonstration must be scientifically known.They then argued that demonstration is impossible with the followingdilemma: If the premises of a demonstration are scientifically known, thenthey must be demonstrated.The premises from which each premise are demonstrated must bescientifically known.Either this process continues forever, creating an infinite regressof premises, or it comes to a stop at some point.If it continues forever, then there are no first premises fromwhich the subsequent ones are demonstrated, and so nothing isdemonstrated.On the other hand, if it comes to a stop at some point, then thepremises at which it comes to a stop are undemonstrated and thereforenot scientifically known; consequently, neither are any of the othersdeduced from them.Therefore, nothing can be demonstrated.A second group accepted the agnostics' view that scientific knowledgecomes only from demonstration but rejected their conclusion byrejecting the dilemma. Instead, they maintained: Demonstration "in a circle" is possible, so that it is possible forall premises also to be conclusions and therefore demonstrated.Aristotle does not give us much information about how circulardemonstration was supposed to work, but the most plausibleinterpretation would be supposing that at least for some set offundamental principles, each principle could be deduced from theothers. (Some modern interpreters have compared this position to acoherence theory of knowledge.) However their position worked, thecircular demonstrators claimed to have a third alternative avoiding theagnostics' dilemma, since circular demonstration gives us a regressthat is both unending (in the sense that we never reach premises atwhich it comes to a stop) and finite (because it works its way roundthe finite circle of premises). 6.3 Aristotle's Solution: "It Eventually Comes to a Stop"Aristotle rejects circular demonstration as an incoherent notion on thegrounds that the premises of any demonstration must be prior (in anappropriate sense) to the conclusion, whereas a circular demonstrationwould make the same premises both prior and posterior to one another(and indeed every premise prior and posterior to itself). He agreeswith the agnostics' analysis of the regress problem: the only plausibleoptions are that it continues indefinitely or that it "comes to a stop"at some point. However, he thinks both the agnostics and the circulardemosntrators are wrong in maintaining that scientific knowledge isonly possible by demonstration from premises scientifically known:instead, he claims, there is another form of knowledge possible for thefirst premises, and this provides the starting points fordemonstrations. To solve this problem, Aristotle needs to do something quitespecific. It will not be enough for him to establish that we can haveknowledge of some propositions without demonstrating them:unless it is in turn possible to deduce all the other propositions of ascience from them, we shall not have solved the regress problem.Moreover (and obviously), it is no solution to this problem forAristotle simply to assert that we have knowledge withoutdemonstration of some appropriate starting points. He does indeed saythat it is his position that we have such knowledge (An. Post.I.2,), but he owes us an account of why that should be so.6.4 Knowledge of First Principles: NousAristotle's account of knowledge of the indemonstrable first premisesof sciences is found in Posterior Analytics II.19, longregarded as a difficult text to interpret. Briefly, what he says thereis that it is another cognitive state, nous (translatedvariously as "insight", "intuition", "intelligence"), which knows them.There is wide disagreement among commentators about the interpretationof his account of how this state is reached; I will offer one possibleinterpretation. First, Aristotle identifies his problem as explaininghow the principles can "become familiar to us", using the same term"familiar" (gnôrimos) that he used in presenting theregress problem. What he is presenting, then, is not a method ofdiscovery but a process of becoming wise. Second, he says that in orderfor knowledge of immediate premises to be possible, we must have a kindof knowledge of them without having learned it, but this knowledge mustnot be as "precise" as the knowledge that a possessor of science musthave. The kind of knowledge in question turns out to be a capacity orpower (dunamis) which Aristotle compares to the capacityfor sense-perception: since our senses are innate, i.e., developnaturally, it is in a way correct to say that we know what e.g. all thecolors look like before we have seen them: we have the capacity to seethem by nature, and when we first see a color we exercise this capacitywithout having to learn how to do so first. Likewise, Aristotle holds,our minds have by nature the capacity to recognize the starting pointsof the sciences. In the case of sensation, the capacity for perception in the senseorgan is actualized by the operation on it of the perceptible object.Similarly, Aristotle holds that coming to know first premises is amatter of a potentiality in the mind being actualized by experience ofits proper objects: "The soul is of such a nature as to be capable ofundergoing this". So, although we cannot come to know the firstpremises without the necessary experience, just as we cannot see colorswithout the presence of colored objects, our minds are already soconstituted as to be able to recognize the right objects, just as oureyes are already so constituted as to be able to perceive the colorsthat exist.It is considerably less clear what these objects are and how it isthat experience actualizes the relevant potentialities in the soul.Aristotle describes a series of stages of cognition. First is what iscommon to all animals: perception of what is present. Next is memory,which he regards as a retention of a sensation: only some animals havethis capacity. Even fewer have the next capacity, the capacity to forma single experience (empeiria) from many repetitions of thesame memory. Finally, many experiences repeated give rise to knowledgeof a single universal (katholou). This last capacity ispresent only in humans.See Section 7 of the entry on Aristotle's psychology for more on his views about mind.7. DefinitionsThe definition (horos, horismos) wasan important matter for Plato and for the Early Academy. Concern withanswering the question "What is so-and-so?" are at the center of themajority of Plato's dialogues, some of which (most elaborately theSophist) propound methods for finding definitions. Externalsources (sometimes the satirical remarks of comedians) also reflectthis Academic concern with definitions. Aristotle himself traces thequest for definitions back to Socrates. 7.1 Definitions and EssencesFor Aristotle, a definition is "an account which signifies what it isto be for something" (logos ho to ti ên einaisêmainei). The phrase "what it is to be" and its variantsare crucial: giving a definition is saying, of some existent thing,what it is, not simply specifying the meaning of a word (Aristotle doesrecognize definitions of the latter sort, but he has little interest inthem). The notion of "what it is to be" for a thing is so pervasive inAristotle that it becomes formulaic: what a definition expresses is"the what-it-is-to-be" (to ti ên einai). Romantranslators, vexed by this odd Greek phrase, devised a word for it,essentia, from which our "essence" descends. So, anAristotelian definition is an account of the essence of something.7.2 Species, Genus, and DifferentiaSince a definition defines an essence, only what has an essence can bedefined. What has an essence, then? That is one of the centralquestions of Aristotle's metaphysics; once again, we must leave thedetails to another article. In general, however, it is not individualsbut rather species (eidos: the word is one ofthose Plato uses for "Form") that have essences. A species is definedby giving its genus (genos) and itsdifferentia (diaphora): the genus is the kindunder which the species falls, and the differentia tells whatcharacterizes the species within that genus. As an example,human might be defined as animal (the genus)having the capacity to reason (the differentia). Essential Predication and the PredicablesUnderlying Aristotle's concept of a definition is the concept ofessential predication (katêgoreisthai entôi ti esti, predication in the what it is). In any trueaffirmative predication, the predicate either does or does not "saywhat the subject is", i.e., the predicate either is or is not anacceptable answer to the question "What is it?" asked of the subject.Bucephalus is a horse, and a horse is an animal; so, "Bucephalus is ahorse" and "Bucephalus is an animal" are essential predications.However, "Bucephalus is brown", though true, does not state whatBucephalus is but only says something about him. Since a thing's definition says what it is, definitions areessentially predicated. However, not everything essentially predicatedis a definition. Since Bucephalus is a horse, and horses are a kind ofmammal, and mammals are a kind of animal, "horse" "mammal" and "animal"are all essential predicates of Bucephalus. Moreover, since what ahorse is is a kind of mammal, "mammal" is an essential predicate ofhorse. When predicate X is an essential predicate of Y but also ofother things, then X is a genus (genos) ofY.A definition of X must not only be essentially predicated of it butmust also be predicated only of it: to use a term from Aristotle'sTopics, a definition and what it defines must"counterpredicate" (antikatêgoreisthai) with oneanother. X counterpredicates with Y if X applies to what Y applies toand conversely. Though X's definition must counterpredicate with X, noteverything that counterpredicates with X is its definition. "Capable oflaughing", for example, counterpredicates with "human" but fails to beits definition. Such a predicate (non-essential but counterpredicating)is a peculiar property or proprium(idion).Finally, if X is predicated of Y but is neither essential norcounterpredicates, then X is an accident(sumbebêkos) of Y.Aristotle sometimes treats genus, peculiar property, definition, andaccident as including all possible predications (e.g. TopicsI). Later commentators listed these four and the differentia as thefive predicables, and as such they were of greatimportance to late ancient and to medieval philosophy (e.g.,Porphyry).7.3 The CategoriesThe notion of essential predication is connected to what aretraditionally called the categories(katêgoriai). In a word, Aristotle is famous for havingheld a "doctrine of categories". Just what that doctrine was, andindeed just what a category is, are considerably more vexing questions.They also quickly take us outside his logic and into his metaphysics.Here, I will try to give a very general overview, beginning with thesomewhat simpler question "What categories are there?" We can answer this question by listing the categories. Here are twopassages containing such lists:We should distinguish the kinds of predication (tagenê tôn katêgoriôn) in which the fourpredications mentioned are found. These are ten in number: what-it-is,quantity, quality, relative, where, when, being-in-a-position, having,doing, undergoing. An accident, a genus, a peculiar property and adefinition will always be in one of these categories. (TopicsI.9, 103b20-25) Of things said without any combination, each signifies eithersubstance or quantity or quality or a relative or where or when orbeing-in-a-position or having or doing or undergoing. To give a roughidea, examples of substance are man, horse; of quantity: four-foot,five-foot; of quality: white, literate; of a relative: double, half,larger; of where: in the Lyceum, in the market-place; of when:yesterday, last year; of being-in-a-position: is-lying, is-sitting; ofhaving: has-shoes-on, has-armor-on; of doing: cutting, burning; ofundergoing: being-cut, being-burned. (Categories 4, 1b25-2a4,tr. Ackrill, slightly modified)These two passages give ten-item lists, identical except for theirfirst members. What are they lists of? Here are three waysthey might be interpreted: The word "category" (katêgoria) means "predication".Aristotle holds that predications and predicates can be grouped intoseveral largest "kinds of predication" (genê tônkatêgoriôn). He refers to this classificationfrequently, often calling the "kinds of predication" simply "thepredications", and this (by way of Latin) leads to our word"category".First, the categories may be kinds of predicate:predicates (or, more precisely, predicate expressions) can be dividedinto ten separate classes, with each expression belonging to just oneclass. This comports well with the root meaning of the wordkatêgoria ("predication"). On this interpretation, thecategories arise out of considering the most general types of questionthat can be asked about something: "What is it?"; "Howmuch is it?"; "What sort is it?"; "Where isit?"; "What is it doing?" Answers appropriate to oneof these questions are nonsensical in response to another ("When isit?" "A horse"). Thus, the categories may rule out certain kinds ofquestion as ill-formed or confused. This plays an important role inAristotle's metaphysics.Second, the categories may be seen as classifications ofpredications, that is, kinds of relation that may hold betweenthe predicate and the subject of a predication. To say of Socrates thathe is human is to say what he is, whereas to say that he isliterate is not to say what he is but rather to give a quality that hehas. For Aristotle, the relation of predicate to subject inthese two sentences is quite different (in this respect he differs bothfrom Plato and from modern logicians). The categories may beinterpreted as ten different ways in which a predicate may be relatedto its subject. This last division has importance for Aristotle's logicas well as his metaphysics.Third, the categories may be seen as kinds of entity, ashighest genera or kinds of thing that are. A given thing can beclassified under a series of progressively wider genera: Socrates is ahuman, a mammal, an animal, a living being. The categories are thehighest such genera. Each falls under no other genus, and each iscompletely separate from the others. This distinction is of criticalimportance to Aristotle's metaphysics.Which of these interpretations fits best with the two passages above?The answer appears to be different in the two cases. This is mostevident if we take note of point in which they differ: theCategories lists substance (ousia)in first place, while the Topics listwhat-it-is (ti esti). A substance, forAristotle, is a type of entity, suggesting that the Categorieslist is a list of types of entity. On the other hand, the expression "what-it-is" suggests moststrongly a type of predication. Indeed, the Topics confirmsthis by telling us that we can "say what it is" of an entityfalling under any of the categories:an expression signifying what-it-is will sometimes signifya substance, sometimes a quantity, sometimes a quality, and sometimesone of the other categories.As Aristotle explains, if I say that Socrates is a man, then I havesaid what Socrates is and signified a substance; if I say that white isa color, then I have said what white is and signified a quality; if Isay that some length is a foot long, then I have said what it is andsignified a quantity; and so on for the other categories. What-it-is,then, here designates a kind of predication, not a kind of entity. This might lead us to conclude that the categories in theTopics are only to be interpreted as kinds of predicate orpredication, those in the Categories as kinds of being. Evenso, we would still want to ask what the relationship is between thesetwo nearly-identical lists of terms, given these distinctinterpretations. However, the situation is much more complicated.First, there are dozens of other passages in which the categoriesappear. Nowhere else do we find a list of ten, but we do find shorterlists containing eight, or six, or five, or four of them (withsubstance/what-it-is, quality, quantity, and relative the most common).Aristotle describes what these lists are lists of in different ways:they tell us "how being is divided", or "how many ways being is said",or "the figures of predication" (ta schêmata têskatêgorias). The designation of the first category also varies:we find not only "substance" and "what it is" but also the expressions"this" or "the this" (tode ti, to tode, toti). These latter expressions are closely associated with, but notsynonymous with, substance. He even combines the latter with"what-it-is" (Metaphysics Z 1, 1028a10: "… one sensesignifies what it is and the this, one signifies quality…").Moreover, substances are for Aristotle fundamental for predicationas well as metaphysically fundamental. He tells us that everything thatexists exists because substances exist: if there were no substances,there would not be anything else. He also conceives of predication asreflecting a metaphysical relationship (or perhaps more than one,depending on the type of predication). The sentence "Socrates is pale"gets its truth from a state of affairs consisting of a substance(Socrates) and a quality (whiteness) which is in that substance. Atthis point we have gone far outside the realm of Aristotle's logic intohis metaphysics, the fundamental question of which, according toAristotle, is "What is a substance?". (For further discussion of thistopic, see the entry on Aristotle's metaphysics, and in particular, Section 2 on the categories.)See Frede 1981, Ebert 1985 for additional discussion of Aristotle'slists of categories.For convenience of reference, I include a table of the categories,along with Aristotle's examples and the traditional names often usedfor them. For reasons explained above, I have treated the first item inthe list quite differently, since an example of a substance and anexample of a what-it-is are necessarily (as one might put it) indifferent categories.Traditional nameLiterallyGreekExamples(Substance)substance"this"what-it-isousia tode ti ti estiman, horse Socrates"Socrates is a man"QuantityHow muchposonfour-foot, five-footQualityWhat sortpoionwhite, literateRelationrelated to whatpros tidouble, half, greaterLocationWherepouin the Lyceum, in the marketplaceTimewhenpoteyesterday, last yearPositionbeing situatedkeisthailies, sitsHabithaving, possessionecheinis shod, is armedActiondoingpoieincuts, burnsPassionundergoingpascheinis cut, is burned7.4 The Method of DivisionIn the Sophist, Plato introduces a procedure of "Division" asa method for discovering definitions. To find a definition of X, firstlocate the largest kind of thing under which X falls; then, divide thatkind into two parts, and decide which of the two X falls into. Repeatthis method with the part until X has been fully located. This method is part of Aristotle's Platonic legacy. His attitudetowards it, however, is complex. He adopts a view of the properstructure of definitions that is closely allied to it: a correctdefinition of X should give the genus (genos:kind or family) of X, which tells what kind of thing X is, and thedifferentia (diaphora: difference) whichuniquely identifies X within that genus. Something defined in this wayis a species (eidos: the term is one ofPlato's terms for "Form"), and the differentia is thus the "differencethat makes a species" (eidopoios diaphora, "specificdifference"). In Posterior Analytics II.13, he gives his ownaccount of the use of Division in finding definitions.However, Aristotle is strongly critical of the Platonic view ofDivision as a method for establishing definitions. InPrior Analytics I.31, he contrasts Division with thesyllogistic method he has just presented, arguing that Division cannotactually prove anything but rather assumes the very thing it issupposed to be proving. He also charges that the partisans of Divisionfailed to understand what their own method was capable of proving.7.5 Definition and DemonstrationClosely related to this is the discussion, in PosteriorAnalytics II.3-10, of the question whether there can be bothdefinition and demonstration of the same thing. Since the definitionsAristotle is interested in are statements of essences, knowing adefinition is knowing, of some existing thing, what it is.Consequently, Aristotle's question amounts to a question whetherdefining and demonstrating can be alternative ways of acquiring thesame knowledge. His reply is complex: Not everything demonstrable can be known by finding definitions,since all definitions are universal and affirmative whereas somedemonstrable propositions are negative.If a thing is demonstrable, then to know it just is to possess itsdemonstration; therefore, it cannot be known just by definition.Nevertheless, some definitions can be understood as demonstrationsdifferently arranged.As an example of case 3, Aristotle considers the definition "Thunder isthe extinction of fire in the clouds". He sees this as a compressed andrearranged form of this demonstration: Sound accompanies the extinguishing of fire.Fire is extinguished in the clouds.Therefore, a sound occurs in the clouds.We can see the connection by considering the answers to two questions:"What is thunder?" "The extinction of fire in the clouds" (definition)."Why does it thunder?" "Because fire is extinguished in the clouds"(demonstration). As with his criticisms of Division, Aristotle is arguing for thesuperiority of his own concept of science to the Platonic concept.Knowledge is composed of demonstrations, even if it may also includedefinitions; the method of science is demonstrative, even if it mayalso include the process of defining.8. Dialectical Argument and the Art of DialecticAristotle often contrasts dialectical arguments withdemonstrations. The difference, he tells us, is in the character oftheir premises, not in their logical structure: whether an argument isa sullogismos is only a matter of whether its conclusionresults of necessity from its premises. The premises of demonstrationsmust be true and primary, that is, not only true but alsoprior to their conclusions in the way explained in the PosteriorAnalytics. The premises of dialectical deductions, by contrast,must be accepted (endoxos). 8.1 Dialectical Premises: The Meaning of EndoxosRecent scholars have proposed different interpretations of the termendoxos. Aristotle often uses this adjective as a substantive:ta endoxa, "accepted things", "accepted opinions". On oneunderstanding, descended from the work of G. E. L. Owen and developedmore fully by Jonathan Barnes and especially Terence Irwin, theendoxa are a compilation of views held by various people withsome form or other of standing: "the views of fairly reflective peopleafter some reflection", in Irwin's phrase. Dialectic is then simply "amethod of argument from [the] common beliefs [held by these people]".For Irwin, then, endoxa are "common beliefs". Jonathan Barnes,noting that endoxa are opinions with a certain standing,translates with "reputable". My own view is that Aristotle's texts support a somewhat differentunderstanding. He also tells us that dialectical premises differ fromdemonstrative ones in that the former are questions, whereasthe latter are assumptions or assertions: "thedemonstrator does not ask, but takes", he says. This fits mostnaturally with a view of dialectic as argument directed at anotherperson by question and answer and consequently taking as premises thatother person's concessions. Anyone arguing in this manner will, inorder to be successful, have to ask for premises which the interlocutoris liable to accept, and the best way to be successful at that is tohave an inventory of acceptable premises, i.e., premises that are infact acceptable to people of different types.In fact, we can discern in the Topics (and theRhetoric, which Aristotle says depends on the art explained inthe Topics) an art of dialectic for use in such arguments. Myreconstruction of this art (which would not be accepted by allscholars) is as follows.8.2 The Two Elements of the Art of DialecticGiven the above picture of dialectical argument, the dialectical artwill consist of two elements. One will be a method for discoveringpremises from which a given conclusion follows, while the other will bea method for determining which premises a given interlocutor will belikely to concede. The first task is accomplished by developing asystem for classifying premises according to their logical structure.We might expect Aristotle to avail himself here of the syllogistic, butin fact he develops quite another approach, one that seems lesssystematic and rests on various "common" terms. The second task isaccomplished by developing lists of the premises which are acceptableto various types of interlocutor. Then, once one knows what sort ofperson one is dealing with, one can choose premises accordingly.Aristotle stresses that, as in all arts, the dialectician must study,not what is acceptable to this or that specific person, but what isacceptable to this or that type of person, just as the doctor studieswhat is healthful for different types of person: "art is of theuniversal". 8.2.1 The "Logical System" of the TopicsThe method presented in the Topics for classifying argumentsrelies on the presence in the conclusion of certain "common" terms(koina) — common in the sense that they are not peculiar toany subject matter but may play a role in arguments about anythingwhatever. We find enumerations of arguments involving these terms in asimilar order several times. Typically, they include: Opposites (antikeimena, antitheseis) Contraries (enantia)Contradictories (apophaseis)Possession and Privation (hexis kai sterêsis)Relatives (pros ti)Cases (ptôseis)"More and Less and Likewise"The four types of opposites are the best represented.Each designates a type of term pair, i.e., a way two terms can beopposed to one another. Contraries are polar oppositesor opposed extremes such as hot and cold, dry and wet, good and bad. Apair of contradictories consists of a term and itsnegation: good, not good. A possession (or condition)and privation are illustrated by sight and blindness.Relatives are relative terms in the modern sense: apair consists of a term and its correlative, e.g. large and small,parent and child. The argumentative patterns Aristotle associated withcases generally involve inferring a sentence contaningadverbial or declined forms from another sentence containing differentforms of the same word stem: "if what is useful is good, then what isdone usefully is done well and the useful person is good". InHellenistic grammatical usage, ptôsis meant "case" (e.g.nominative, dative, accusative); Aristotle's use here is obviously anearly form of that.Under the heading more and less and likewise,Aristotle groups a somewhat motley assortment of argument patterns allinvolving, in some way or other, the terms "more", "less", and"likewise". Examples: "If whatever is A is B, then whatever is more(less) A is more (less) B"; "If A is more likely B than C is, and A isnot B, then neither is C"; "If A is more likely than B and B is thecase, then A is the case".8.2.2 The TopoiAt the heart of the Topics is a collection of what Aristotlecalls topoi, "places" or "locations". Unfortunately, though itis clear that he intends most of the Topics (Books II-VI) as acollection of these, he never explicitly defines this term.Interpreters have consequently disagreed considerably about just what atopos is. Discussions may be found in Brunschwig 1967,Slomkowski 1996, Primavesi 1997, and Smith 1997. 8.3 The Uses of Dialectic and Dialectical ArgumentAn art of dialectic will be useful wherever dialecticalargument is useful. Aristotle mentions three such uses; each meritssome comment. 8.3.1 Gymnastic DialecticFirst, there appears to have been a form of stylized argumentativeexchange practiced in the Academy in Aristotle's time. The mainevidence for this is simply Aristotle's Topics, especiallyBook VIII, which makes frequent reference to rule-governed procedures,apparently taking it for granted that the audience will understandthem. In these exchanges, one participant took the role of answerer,the other the role of questioner. The answerer began by asserting someproposition (a thesis: "position" or "acceptance"). Thequestioner then asked questions of the answerer in an attempt to secureconcessions from which a contradiction could be deduced: that is, torefute (elenchein) the answerer's position.The questioner was limited to questions that could be answered by yesor no; generally, the answerer could only respond with yes or no,though in some cases answeres could object to the form of a question.Answerers might undertake to answer in accordance with the views of aparticular type of person or a particular person (e.g. a famousphilosopher), or they might answer according to their own beliefs.There appear to have been judges or scorekeepers for the process.Gymnastic dialectical contests were sometimes, as the name suggests,for the sake of exercise in developing argumentative skill, but theymay also have been pursued as a part of a process of inquiry. 8.3.2 Dialectic That Puts to the TestAristotle also mentions an "art of making trial", or a variety ofdialectical argument that "puts to the test" (the Greek word is theadjective peirastikê, in the feminine: such expressionsoften designate arts or skills, e.g. rhêtorikê,"the art of rhetoric"). Its function is to examine the claims of thosewho say they have some knowledge, and it can be practiced by someone whodoes not possess the knowledge in question. The examination is a matterof refutation, based on the principle that whoever knows a subject musthave consistent beliefs about it: so, if you can show me that mybeliefs about something lead to a contradiction, then you have shownthat I do not have knowledge about it. This is strongly reminiscent of Socrates' style of interrogation,from which it is almost certainly descended. In fact, Aristotle oftenindicates that dialectical argument is by nature refutative.8.3.3 Dialectic and PhilosophyDialectical refutation cannot of itself establish any proposition(except perhaps the proposition that some set of propositions isinconsistent). More to the point, though deducing a contradiction frommy beliefs may show that they do not constitute knowledge, failure todeduce a contradiction from them is no proof that they are true. Notsurprisingly, then, Aristotle often insists that "dialectic does notprove anything" and that the dialectical art is not some sort ofuniversal knowledge. In Topics I.2, however, Aristotle says that the art ofdialectic is useful in connection with "the philosophical sciences".One reason he gives for this follows closely on the refutativefunction: if we have subjected our opinions (and the opinions of ourfellows, and of the wise) to a thorough refutative examination, we willbe in a much better position to judge what is most likely true andfalse. In fact, we find just such a procedure at the start of many ofAristotle's treatises: an enumeration of the opinions current about thesubject together with a compilation of "puzzles" raised by theseopinions. Aristotle has a special term for this kind of review: adiaporia, a "puzzling through".He adds a second use that is both more difficult to understand andmore intriguing. The Posterior Analytics argues that ifanything can be proved, then not everything that is known is known as aresult of proof. What alternative means is there whereby the firstprinciples of sciences are known? Aristotle's own answer as found inPosterior Analytics II.19 is difficult to interpret, andrecent philosophers have often found it unsatisfying since (as oftenconstrued) it appears to commit Aristotle to a form of apriorism orrationalism both indefensible in itself and not consonant with his owninsistence on the indispensability of empirical inquiry in naturalscience.Against this background, the following passage in TopicsI.2 may have special importance:It is also useful in connection with the first thingsconcerning each of the sciences. For it is impossible to say anythingabout the science under consideration on the basis of its ownprinciples, since the principles are first of all, and we must work ourway through about these by means of what is generally accepted abouteach. But this is peculiar, or most proper, to dialectic: for since itis examinative with respect to the principles of all the sciences, ithas a way to proceed.A number of interpreters (beginning with Owen 1961) have built on thispassage and others to find dialectic at the heart of Aristotle'sphilosophical method. Further discussion of this issue would take usfar beyond the subject of this article (the fullest development is inIrwin 1988; see also Nussbaum 1986 and Bolton 1990; for criticism, Hamlyn 1990,Smith 1997). 9. Dialectic and RhetoricAristotle says that rhetoric, i.e., the study of persuasive speech, isa "counterpart" (antistrophos) of dialectic and that therhetorical art is a kind of "outgrowth" (paraphues ti) ofdialectic and the study of character types. The correspondence withdialectical method is straightforward: rhetorical speeches, likedialectical arguments, seek to persuade others to accept certainconclusions on the basis of premises they already accept. Therefore,the same measures useful in dialectical contexts will, mutatismutandis, be useful here: knowing what premises an audience of a giventype is likely to believe, and knowing how to find premises from whichthe desired conclusion follows. The Rhetoric does fit this general description: Aristotleincludes both discussions of types of person or audience (withgeneralizations about what each type tends to believe) and a summaryversion (in II.23) of the argument patterns discussed in theTopics. For further discussion of his rhetoric see Aristotle's rhetoric.10. Sophistical ArgumentsDemonstrations and dialectical arguments are both forms of validargument, for Aristotle. However, he also studies what he callscontentious (eristikos) orsophistical arguments: these he defines as argumentswhich only apparently establish their conclusions. In fact, Aristotledefines these as apparent (but not genuine) dialecticalsullogismoi. They may have this appearance in either of twoways: Arguments in which the conclusion only appears to follow ofnecessity from the premises (apparent, but not genuine,sullogismoi).Genuine sullogismois the premises of which are merelyapparently, but not genuinely, acceptable.Arguments of the first type in modern terms, appear to be valid but arereally invalid. Arguments of the second type are at first moreperplexing: given that acceptability is a matter of what peoplebelieve, it might seem that whatever appears to be endoxosmust actually be endoxos. However, Aristotle probably has inmind arguments with premises that may at first glance seem tobe acceptable but which, upon a moment's reflection, we immediatelyrealize we don not actually accept. Consider this example fromAristotle's time: Whatever you have not lost, you still have.You have not lost horns.Therefore, you still have hornsThis is transparently bad, but the problem is not that it is invalid:the problem is rather that the first premise, though superficiallyplausible, is false. In fact, anyone with a little ability to follow anargument will realize that at once upon seeing this very argument. Aristotle's study of sophistical arguments is contained in OnSophistical Refutations, which is actually a sort of appendix tothe Topics.To a remarkable extent, contemporary discussions of fallaciesreproduce Aristotle's own classifications. See Dorion 1995 for furtherdiscussion.11. Non-Contradiction and MetaphysicsTwo frequent themes of Aristotle's account of science are (1) that thefirst principles of sciences are not demonstrable and (2) that there isno single universal science including all other sciences as its parts."All things are not in a single genus", he says, "and even if theywere, all beings could not fall under the same principles" (OnSophistical Refutations 11). Thus, it is exactly the universalapplicability of dialectic that leads him to deny it the status of ascience. In Metaphysics IV (Γ), however, Aristotle takes whatappears to be a different view. First, he argues that there is, in away, a science that takes being as its genus (his name for it is "firstphilosophy"). Second, he argues that the principles of this sciencewill be, in a way, the first principles of all (though he does notclaim that the principles of other sciences can be demonstrated fromthem). Third, he identifies one of its first principles as the "mostsecure" of all principles: the principle of non-contradiction. As hestates it,It is impossible for the same thing to belong and notbelong simultaneously to the same thing in the same respect(Met. )This is the most secure of all principles, Aristotle tells us, because"it is impossible to be in error about it". Since it is a firstprinciple, it cannot be demonstrated; those who think otherwise are"uneducated in analytics". However, Aristotle then proceeds to givewhat he calls a "refutative demonstration" (apodeixaielenktikôs) of this principle. Further discussion of this principle and Aristotle's argumentsconcerning it belong to a treatment of his metaphysics (see Aristotle: Metaphysics). However,it should be noted that: (1) these arguments draw on Aristotle's viewsabout logic to a greater extent than any treatise outside the logicalworks themselves; (2) in the logical works, the principle ofnon-contradiction is one of Aristotle's favorite illustrations of the"common principles" (koinai archai) that underlie the art ofdialectic.See Aristotle's Metaphysics,Dancy 1975, Code 1986 for further discussion.12. Time and Necessity: The Sea-BattleThe passage in Aristotle's logical works which has received perhaps themost intense discussion in recent decades is On Interpretation9, where Aristotle discusses the question whether every propositionabout the future must be either true or false. Though something of aside issue in its context, the passage raises a problem of greatimportance to Aristotle's near contemporaries (and perhapscontemporaries). A contradiction (antiphasis) is a pair ofpropositions one of which asserts what the other denies. A major goalof On Interpretation is to discuss the thesis that, of everysuch contradiction, one member must be true and the other false. In thecourse of his discussion, Aristotle allows for some exceptions. Onecase is what he calls indefinite propositions such as"A man is walking": nothing prevents both this proposition and "A manis not walking" being simultaneously true. This exception can beexplained on relatively simple grounds.A different exception arises for more complex reasons. Considerthese two propositions:There will be a sea-battle tomorrowThere will not be a sea-battle tomorrowIt seems that exactly one of these must be true and the other false.But if (1) is now true, then there must be asea-battle tomorrow, and there cannot fail to be a sea-battletomorrow. The result, according to this puzzle, is that nothing ispossible except what actually happens: there are no unactualizedpossibilities. Such a conclusion is, as Aristotle is quick to note, a problem bothfor his own metaphysical views about potentialities and for thecommonsense notion that some things are up to us. He therefore proposesanother exception to the general thesis concerning contradictorypairs.This much would probably be accepted by most interpreters. What therestriction is, however, and just what motivates it are matters of widedisagreement. It has been proposed, for instance, that Aristotleadopted, or at least flirted with, a three-valued logic for futurepropositions, or that he countenanced truth-value gaps, or that hissolution includes still more abstruse reasoning. The literature is muchtoo complex to summarize: see Anscombe, Hintikka, D. Frede, Whitaker,Waterlow.Historically, at least, it is likely that Aristotle is responding toan argument originating in the Megarian School. He ascribes the viewthat only that which happens is possible to the Megarians inMetaphysics IX (Θ). The puzzle with which he isconcerned strongly recalls the "Master Argument" of Diodorus Cronus,especially in certain further details. For instance, Aristotle imaginesthe statement about tomorrow's sea battle having been uttered tenthousand years ago. If it was true, then its truth was a fact about thepast; if the past is now unchangeable, then so is the truth value ofthat past utterance. This recalls the Master Argument's premise that"what is past is necessary". Diodorus Cronus was active a little afterAristotle, and he was a Megarian (see Dorion 1995 for criticism ofDavid Sedley's attempt to reject this). It seems to me reasonable toconclude that Aristotle's target here is some Megarian argument,perhaps an earlier version of the Master.13. Glossary of Aristotelian TerminologyAccept: tithenai (in a dialectical argument)Accepted: endoxos (also ‘reputable’‘common belief’)Accident: sumbebêkos (see incidental)Accidental: kata sumbebêkosAffirmation: kataphasisAffirmative: kataphatikosAssertion: apophansis (sentence with a truth value,declarative sentence)Assumption: hupothesisBelong: huparcheinCategory: katêgoria (see the discussion in Section7.3).Contradict: antiphanaiContradiction: antiphasis (in the sense "contradictorypair of propositions" and also in the sense "denial of aproposition")Contrary: enantionDeduction: sullogismosDefinition: horos, horismosDemonstration: apodeixisDenial (of a proposition): apophasisDialectic: dialektikê (the art ofdialectic)Differentia: diaphora; specific difference, eidopoiosdiaphoraDirect: deiktikos (of proofs; opposed to "through theimpossible")Essence: to ti esti, to ti ên einaiEssential: en tôi ti esti (of predications)Extreme: akron (of the major and minor terms of adeduction)Figure: schêmaForm: eidos (see also Species)Genus: genosImmediate: amesos ("without a middle")Impossible: adunaton; "through the impossible" (diatou adunatou), of some proofs.Incidental: see AccidentalInduction: epagôgêMiddle, middle term (of a deduction): mesonNegation (of a term): apophasisObjection: enstasisParticular: en merei, epi meros (of aproposition); kath'hekaston (of individuals)Peculiar, Peculiar Property: idios, idionPossible: dunaton, endechomenon;endechesthai (verb: "be possible")Predicate: katêgorein (verb);katêegoroumenon ("what is predicated")Predication: katêgoria (act or instance ofpredicating, type of predication)Primary: prôtonPrinciple: archê (starting point of ademonstration)Quality: poionReduce, Reduction: anagein,anagôgêRefute: elenchein; refutation, elenchosScience: epistêmêSpecies: eidosSpecific: eidopoios (of a differentia that "makes aspecies", eidopoios diaphora)Subject: hupokeimenonSubstance: ousiaTerm: horosUniversal: katholou (both of propositions and ofindividuals)BibliographyAckrill, J. 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Oxford: Clarendon Press.Other Internet Resources[Please contact the author with suggestions.] Related Entries Aristotle, General Topics: metaphysics | Aristotle, General Topics: poetics | Aristotle, General Topics: rhetoric | Aristotle, Special Topics: mathematics | Chrysippus | Diodorus Cronus | future contingents | logic: ancient | logic: relevance | Megarian School | square of opposition | StoicismAcknowledgmentsI am indebted to Alan Code, Marc Cohen, and Theodor Ebert for helpfulcriticisms of earlier versions of this article. I thank FranzFritsche, Nikolai Biryukov, Ralph E. Kenyon, Johann Dirry, and BenGreenberg for calling my attention to errors. Copyright © 2007 byRobin Smith<rasmith@tamu.edu> |
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