sep - aristotle's logic

8/12/2019 SEP - Aristotle's Logic

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2. Aristotle's Logical Works: The OrganonThe ancient commentators grouped together several of Aristotle's treatises under the title Organon("Instrument") and regarded them as comprising his logical works:

1. Categories

. On Interpretation !. Prior Analytics

. Posterior Analytics #. Topics $. On Sophistical Refutations

In fact% the title Organon reflects a much later controvers& a out whether logic is a part of philosoph&(as the toics maintained) or merel& a tool used & philosoph& (as the later eripatetics thought)*calling the logical works "The Instrument" is a wa& of taking sides on this point. Aristotle himselfnever uses this term% nor does he give much indication that these particular treatises form some kind ofgroup% though there are fre+uent cross,references etween the Topics and the Analytics . -n the otherhand% Aristotle treats the Prior and Posterior Analytics as one work% and On Sophistical Refutations is afinal section% or an appendi % to the Topics ). To these works should e added the Rhetoric % whiche plicitl& declares its reliance on the Topics .

3. The Subject of Logic: "Syllogisms"All Aristotle's logic revolves around one notion: the deductio ( sullogismos ). A thorough e planationof what a deduction is% and what the& are composed of% will necessaril& lead us through the whole ofhis theor&. /hat% then% is a deduction0 Aristotle sa&s:

A deduction is speech ( logos ) in which% certain things having een supposed% somethingdifferent from those supposed results of necessit& ecause of their eing so. ( Prior

Analytics I. % 1 , 2)

3ach of the "things supposed" is a !remise ( protasis ) of the argument% and what "results of necessit&"is the co clusio ( sumperasma ).

The core of this definition is the notion of "resulting of necessit&" ( ex ananks sumbainein ). Thiscorresponds to a modern notion of logical conse+uence: 4 results of necessit& from 5 and 6 if it would

e impossi le for 4 to e false when 5 and 6 are true. /e could therefore take this to e a generaldefinition of "valid argument".

3. # ductio a d $eductio

7eductions are one of two species of argument recogni8ed & Aristotle. The other species is i ductio(epagg ). 9e has far less to sa& a out this than deduction% doing little more than characteri8e it as"argument from the particular to the universal". 9owever% induction (or something ver& much like it)

pla&s a crucial role in the theor& of scientific knowledge in the Posterior Analytics : it is induction% or atan& rate a cognitive process that moves from particulars to their generali8ations% that is the asis ofknowledge of the indemonstra le first principles of sciences.


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3.2 Aristotelia $eductio s a d %oder &alid Argume ts7espite its wide generalit&% Aristotle's definition of deduction is not a precise match for a moderndefinition of validit&. ome of the differences ma& have important conse+uences:

1. Aristotle e plicitl& sa&s that what results of necessit& must e different from what is supposed.This would rule out arguments in which the conclusion is identical to one of the premises.

odern notions of validit& regard such arguments as valid% though triviall& so.. The plural "certain things having een supposed" was taken & some ancient commentators torule out arguments with onl& one premise.

!. The force of the +ualification " ecause of their eing so" has sometimes een seen as ruling outarguments in which the conclusion is not ;relevant< to the premises% e.g.% arguments in which the

premises are inconsistent% arguments with conclusions that would follow from an& premiseswhatsoever% or arguments with superfluous premises.

-f these three possi le restrictions% the most interesting would e the third. This could e (and has een) interpreted as committing Aristotle to something like a relevance logic . In fact% there are passagesthat appear to confirm this. 9owever% this is too comple a matter to discuss here.

9owever the definition is interpreted% it is clear that Aristotle does not mean to restrict it onl& to asu set of the valid arguments. This is wh& I have translated sullogismos with ;deduction< rather than its3nglish cognate. In modern usage% ;s&llogism< means an argument of a ver& specific form. oreover%modern usage distinguishes etween valid s&llogisms (the conclusions of which follow from their

premises) and invalid s&llogisms (the conclusions of which do not follow from their premises). Thesecond of these is inconsistent with Aristotle's use: since he defines a sullogismos as an argument inwhich the conclusion results of necessit& from the premises% "invalid sullogismos " is a contradiction interms. The first is also at least highl& misleading% since Aristotle does not appear to think that the

sullogismoi are simpl& an interesting su set of the valid arguments. oreover (see elow)% Aristotlee pends great efforts to argue that ever& valid argument% in a road sense% can e "reduced" to anargument% or series of arguments% in something like one of the forms traditionall& called a s&llogism. Ifwe translate sullogismos as "s&llogism% "% this ecomes the trivial claim "3ver& s&llogism is as&llogism"%

. (remises: The Structures of Assertio s&llogisms are structures of sentences each of which can meaningfull& e called true or false:assertio s (apophanseis )% in Aristotle's terminolog&. According to Aristotle% ever& such sentence musthave the same structure: it must contain a subject (hupokeimenon ) and a !redicate and must eitheraffirm or den& the predicate of the su =ect. Thus% ever& assertion is either the affirmatio kataphasis orthe de ial (apophasis ) of a single predicate of a single su =ect.

In On Interpretation % Aristotle argues that a single assertion must alwa&s either affirm or den& a single

predicate of a single su =ect. Thus% he does not recogni8e sentential compounds% such as con=unctionsand dis=unctions% as single assertions. This appears to e a deli erate choice on his part: he argues% forinstance% that a con=unction is simpl& a collection of assertions% with no more intrinsic unit& than these+uence of sentences in a length& account (e.g. the entire Ilia % to take Aristotle's own e ample). incehe also treats denials as one of the two asic species of assertion% he does not view negations assentential compounds. 9is treatment of conditional sentences and dis=unctions is more difficult toappraise% ut it is at an& rate clear that Aristotle made no efforts to develop a sentential logic. ome ofthe conse+uences of this for his theor& of demonstration are important.
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. Termsu =ects and predicates of assertions are terms . A term ( horos ) can e either individual% e.g. Socrates %

Plato or universal% e.g. human %horse %animal %!hite . u =ects ma& e either individual or universal% ut predicates can onl& e universals: Socrates is human % Plato is not a horse %horses are animals %humansare not horses .

The word u i)ersal (katholou ) appears to e an Aristotelian coinage. >iterall&% it means "of a whole"*its opposite is therefore "of a particular" ( kath" hekaston ). ?niversal terms are those which can properl&serve as predicates% while particular terms are those which cannot.

This distinction is not simpl& a matter of grammatical function. /e can readil& enough construct asentence with " ocrates" as its grammatical predicate: "The person sitting down is ocrates". Aristotle%however% does not consider this a genuine predication. 9e calls it instead a merel& accide tal ori cide tal (kata sumbebkos ) predication. uch sentences are% for him% dependent for their truth valueson other genuine predications (in this case% " ocrates is sitting down").

@onse+uentl&% predication for Aristotle is as much a matter of metaph&sics as a matter of grammar. Thereason that the term Socrates is an individual term and not a universal is that the entit& which itdesignates is an individual% not a universal. /hat makes !hite and human universal terms is that the&designate universals.

urther discussion of these issues can e found in the entr& on Aristotle's metaph&sics .

.2 Affirmatio s* $e ials* a d +o tradictio sAristotle takes some pains in On Interpretation to argue that to ever& affirmation there correspondse actl& one denial such that that denial denies e actl& what that affirmation affirms. The pair consistingof an affirmation and its corresponding denial is a co tradictio (antiphasis ). In general% Aristotleholds% e actl& one mem er of an& contradiction is true and one false: the& cannot oth e true% and the&cannot oth e false. 9owever% he appears to make an e ception for propositions a out future events%

though interpreters have de ated e tensivel& what this e ception might e (see further discussion elow). The principle that contradictories cannot oth e true has fundamental importance in Aristotle'smetaph&sics (see further discussion elow).

.3 All* Some* a d ,o e-ne ma=or difference etween Aristotle's understanding of predication and modern (i.e.% post, regean)logic is that Aristotle treats individual predications and general predications as similar in logical form:he gives the same anal&sis to " ocrates is an animal" and "9umans are animals". 9owever% he notesthat when the su =ect is a universal% predication takes on two forms: it can e either u i)ersal or!articular . These e pressions are parallel to those with which Aristotle distinguishes universal and

particular terms% and Aristotle is aware of that% e plicitl& distinguishing etween a term eing auniversal and a term eing universall& predicated of another.

/hatever is affirmed or denied of a universal su =ect ma& e affirmed or denied of it it u i)ersally(katholou or "of all"% kata pantos )%i !art (kata meros %en merei )% ori defi itely (a ihoristos ).

Affirmatio s $e ials

- i)ersal affirmed of all of 3ver& is %All is (are)

denied of all of Bo is
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(articular affirmed of someof

ome is (are) denied of someof

ome is not%

Bot ever& is

# defi ite affirmed of is denied of is not

.3. The "S uare of /!!ositio "

In On Interpretation % Aristotle spells out the relationships of contradiction for sentences with universalsu =ects as follows:

Affirmatio $e ial

- i)ersal 3ver& A is C Bo A is C

- i)ersal ome A is C Bot ever& A is Cimple as it appears% this ta le raises important difficulties of interpretation (for a thorough discussion%see the entr& on the s+uare of opposition ).

In the Prior Analytics % Aristotle adopts a somewhat artificial wa& of e pressing predications: instead ofsa&ing "4 is predicated of 5" he sa&s "4 elongs ( huparchei ) to 5". This should reall& e regarded as atechnical e pression. The ver huparchein usuall& means either " egin" or "e ist% e present"% andAristotle's usage appears to e a development of this latter use.

.3.2 Some +o )e ie t Abbre)iatio s

or clarit& and revit&% I will use the following semi,traditional a reviations for Aristoteliancategorical sentences (note that the predicate term comes first and the su =ect term secon ):

Abbre)iatio Se te ce

Aa a elongs to all (3ver& is a)

3a a elongs to no (Bo is a)

Ia a elongs to some ( ome is a)

-a a does not elong to all ( ome is not a)

0. The SyllogisticAristotle's most famous achievement as logician is his theor& of inference% traditionall& called thesyllogistic (though not & Aristotle). That theor& is in fact the theor& of inferences of a ver& specificsort: inferences with two premises% each of which is a categorical sentence% having e actl& one term incommon% and having as conclusion a categorical sentence the terms of which are =ust those two termsnot shared & the premises. Aristotle calls the term shared & the premises the middle term (meson )and each of the other two terms in the premises an e1treme (akron ). The middle term must e eithersu =ect or predicate of each premise% and this can occur in three wa&s: the middle term can e thesu =ect of one premise and the predicate of the other% the predicate of oth premises% or the su =ect of

oth premises. Aristotle refers to these term arrangements as figures ( schmata ):
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0. The igures

irst igure Seco d igure Third igure(redicate Subject (redicate Subject (redicate Subject

(remise a a a c(remise c a c c

+o clusio a c c aAristotle calls the term which is the predicate of the conclusion the major term and the term which isthe su =ect of the conclusion the mi or term. The premise containing the ma=or term is the major!remise % and the premise containing the minor term is the mi or !remise .

Aristotle's procedure is then a s&stematic investigation of the possi le com inations of premises in eachof the three figures. or each com ination% he seeks either to demonstrate that some conclusionnecessaril& follows or to demonstrate that no conclusion follows. The results he states are e actl&correct.

0.2 %ethods of (roof: +o )ersio a d eductioAristotle shows each valid form to e valid & showing how to construct a deduction of its conclusionfrom its premises. These deductions% in turn% can take one of two forms: direct or !robati)e ( eiktikos )deductions and deductions through the im!ossible ( ia to a unaton ).

A direct deduction is a series of steps leading from the premises to the conclusion% each of which iseither a co )ersio of a previous step or an inference from two previous steps rel&ing on a first,figurededuction. @onversion% in turn% is inferring from a proposition another which has the su =ect and

predicate interchanged. pecificall&% Aristotle argues that three such conversions are sound: 3a D 3 a Ia D I a Aa D I a

9e undertakes to =ustif& these in An# Pr# I. . rom a modern standpoint% the third is sometimes regardedwith suspicion. ?sing it we can get Some monsters are chimeras from the apparentl& true All chimerasare monsters * ut the former is often construed as impl&ing in turn There is something !hich is amonster an a chimera % and thus that there are monsters and there are chimeras. In fact% this simpl&

points up something a out Aristotle's s&stem: Aristotle in effect supposes that all terms in s&llogismsare non,empt&. ( or further discussion of this point% see the entr& on the s+uare of opposition ).

As an e ample of the procedure% we ma& take Aristotle's proof of Camestres . 9e sa&s:

If elongs to ever& B ut to no 4% then neither will B elong to an& 4. or if elongsto no 4% then neither does 4 elong to an& * ut elonged to ever& B* therefore% 4 will

elong to no B (for the first figure has come a out). And since the privative converts%neither will B elong to an& 4. ( An# Pr# I.#% EaF,1 )

rom this te t% we can e tract an e act formal proof% as follows:

Ste! 4ustificatio Aristotle's Te1t1. aB If $ belongs to e%ery & . e4 but to no '(To prove: then neither !ill & belong to any '#
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Be4!. e4 ( % premise) )or if $ belongs to no '(. 4e (!% conversion of e) then neither oes ' belong to any $*#. aB (1% premise) but $ belonge to e%ery &*$. 4eB ( % #%Celarent ) therefore( ' !ill belong to no & +for the first figure has come about,#

E. Be4 ($% conversion of e) An since the pri%ati%e con%erts( neither !ill & belong to any '#

0.3 %ethods of $is!roof: +ou tere1am!les a d TermsAristotle proves invalidit& & constructing countere amples. This is ver& much in the spirit of modernlogical theor&: all that it takes to show that a certain form is invalid is a single instance of that formwith true premises and a false conclusion. 9owever% Aristotle states his results not & sa&ing thatcertain premise,conclusion com inations are invalid ut & sa&ing that certain premise pairs do not"s&llogi8e": that is% that% given the pair in +uestion% e amples can e constructed in which premises ofthat form are true and a conclusion of an& of the four possi le forms is false.

/hen possi le% he does this & a clever and economical method: he gives two triplets of terms% one ofwhich makes the premises true and a universal affirmative "conclusion" true% and the other of whichmakes the premises true and a universal negative "conclusion" true. The first is a countere ample for anargument with either an 3 or an - conclusion% and the second is a countere ample for an argument witheither an A or an I conclusion.

0. The $eductio s i the igures 5"%oods"6In Prior Analytics I. ,$% Aristotle shows that the premise com inations given in the following ta le&ield deductions and that all other premise com inations fail to &ield a deduction. In the terminolog&traditional since the middle ages% each of these com inations is known as a mood (from >atin mo us %"wa&"% which in turn is a translation of Greek tropos ). Aristotle% however% does not use this e pression

and instead refers to "the arguments in the figures".In this ta le% " " separates premises from conclusion* it ma& e read "therefore". The second column lists the medieval mnemonic name associated with the inference (these are still widel& used% and eachis actuall& a mnemonic for Aristotle's proof of the mood in +uestion). The third column riefl&summari8es Aristotle's procedure for demonstrating the deduction.

Table of the $eductio s i the igures

orm % emo ic (roof

Aa % A c Aac -arbara erfect

3a % A c 3ac Celarent erfectAa % I c Iac .arii erfect* also & impossi ilit&% from Camestres

3a % I c -ac )erio erfect* also & impossi ilit&% from Cesare

3@-B7 IG?H3

3a % Aac 3 c Cesare (3a % Aac)D(3 a% Aac) @el3 c


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Aa % 3ac 3 c Camestres (Aa % 3ac)D(Aa % 3ca) (3ca% Aa ) @el3c D3 c

3a % Iac - c )estino (3a % Iac)D(3 a% Iac) er - c

Aa % -ac - c -aroco (Aa % -ac JA c) Car (Aac% -ac) Imp - c

T9IH7 IG?H3

Aac% A c Ia .arapti (Aac% A c)D(Aac% Ic ) 7ar Ia

3ac% A c -a )elapton (3ac% A c)D(3ac% Ic ) er -a

Iac% A c Ia .isamis (Iac% A c)D(Ica% A c) (A c% Ica) 7ar I aDIa

Aac% I c Ia .atisi (Aac% I c)D(Aac% Ic ) 7ar Ia

-ac% A c -a -ocar o (-ac% JAa % A c) Car (Aac% -ac) Imp-a

3ac% I c -a )erison (3ac% I c)D(3ac% Ic ) er -a

0.0 %etatheoretical esults9aving esta lished which deductions in the figures are possi le% Aristotle draws a num er ofmetatheoretical conclusions% including:

1. Bo deduction has two negative premises. Bo deduction has two particular premises!. A deduction with an affirmative conclusion must have two affirmative premises. A deduction with a negative conclusion must have one negative premise.#. A deduction with a universal conclusion must have two universal premises

9e also proves the following metatheorem:All deductions can e reduced to the two universal deductions in the first figure.

9is proof of this is elegant. irst% he shows that the two particular deductions of the first figure can ereduced% & proof through impossi ilit&% to the universal deductions in the second figure:

( .arii )K(Aa % I c% J3ac) @amestres(3 c% I c) ImpIac

( )erio )K(3a % I c% JAac) @esare(3 c% I c) Imp -ac

9e then o serves that since he has alread& shown how to reduce all the particular deductions in theother figures e cept Caroco and Cocardo to .arii and )erio % these deductions can thus e reduced to

-arbara and Celarent . This proof is strikingl& similar oth in structure and in su =ect to modern proofsof the redundanc& of a ioms in a s&stem.

an& more metatheoretical results% some of them +uite sophisticated% are proved in Prior AnalyticsI. # and in Prior Analytics II. As noted elow% some of Aristotle's metatheoretical results are appealedto in the epistemological arguments of the Posterior Analytics .

0.7 Syllogisms 8ith %odalitiesAristotle follows his treatment of "arguments in the figures" with a much longer% and much more


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pro lematic% discussion of what happens to these figured arguments when we add the +ualifications"necessaril&" and "possi l&" to their premises in various wa&s. In contrast to the s&llogistic itself (or% ascommentators like to call it% the assertoric s&llogistic)% thismo al s&llogistic appears to e much lesssatisfactor& and is certainl& far more difficult to interpret. 9ere% I onl& outline Aristotle's treatment ofthis su =ect and note some of the principal points of interpretive controvers&.

0.7. The $efi itio s of the %odalitiesodern modal logic treats necessit& and possi ilit& as interdefina le: "necessaril& " is e+uivalent to"not possi l& not "% and "possi l& " to "not necessaril& not ". Aristotle gives these samee+uivalences in On Interpretation . 9owever% in Prior Analytics % he makes a distinction etween twonotions of possi ilit&. -n the first% which he takes as his preferred notion% "possi l& " is e+uivalent to"not necessaril& and not necessaril& not ". 9e then acknowledges an alternative definition of

possi ilit& according to the modern e+uivalence% ut this pla&s onl& a secondar& role in his s&stem.

0.7.2 Aristotle's 9e eral A!!roach

Aristotle uilds his treatment of modal s&llogisms on his account of non,modal ( assertoric )

s&llogisms: he works his wa& through the s&llogisms he has alread& proved and considers theconse+uences of adding a modal +ualification to one or oth premises. ost often% then% the +uestionshe e plores have the form: "9ere is an assertoric s&llogism* if I add these modal +ualifications to the

premises% then what modall& +ualified form of the conclusion (if an&) follows0". A premise can haveone of three modalities: it can e necessar&% possi le% or assertoric. Aristotle works through thecom inations of these in order:

Two necessar& premises -ne necessar& and one assertoric premise Two possi le premises -ne assertoric and one possi le premise

-ne necessar& and one possi le premiseThough he generall& considers onl& premise com inations which s&llogi8e in their assertoric forms% hedoes sometimes e tend this* similarl&% he sometimes considers conclusions in addition to those whichwould follow from purel& assertoric premises.

ince this is his procedure% it is convenient to descri e modal s&llogisms in terms of the correspondingnon,modal s&llogism plus a triplet of letters indicating the modalities of premises and conclusion: B "necessar&"% "possi le"% A "assertoric". Thus% "Car ara BAB" would mean "The form -arbarawith necessar& ma=or premise% assertoric minor premise% and necessar& conclusion". I use the letters"B" and " " as prefi es for premises as well* a premise with no prefi is assertoric. Thus% -arbara

BAB would e BAa % A c BAac.

0.7.3 %odal +o )ersio s

As in the case of assertoric s&llogisms% Aristotle makes use of conversion rules to prove validit&. Theconversion rules for necessar& premises are e actl& analogous to those for assertoric premises:

B3a DB3 a BIa DBI a BAa DBI a

ossi le premises ehave differentl&% however. ince he defines "possi le" as "neither necessar& nor


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impossi le"% it turns out that x is possibly ) entails% and is entailed &% x is possibly not ) . Aristotlegenerali8es this to the case of categorical sentences as follows:

Aa D 3a 3a D Aa Ia D -a -a D Ia

In addition% Aristotle uses the intermodal principle BDA: that is% a necessar& premise entails thecorresponding assertoric one. 9owever% ecause of his definition of possi ilit&% the principle AD doesnot generall& hold: if it did% then BD would hold% ut on his definition "necessaril& " and "possi l&" are actuall& inconsistent ("possi l& " entails "possi l& not ").

This leads to a further complication. The denial of "possi l& " for Aristotle is "either necessaril& ornecessaril& not ". The denial of "necessaril& " is still more difficult to e press in terms of acom ination of modalities: "either possi l& (and thus possi l& not ) or necessaril& not " This isimportant ecause of Aristotle's proof procedures% which include proof through impossi ilit&. If wegive a proof through impossi ilit& in which we assume a necessar& premise% then the conclusion weultimatel& esta lish is simpl& the denial of that necessar& premise% not a "possi le" conclusion inAristotle's sense. uch propositions do occur in his s&stem% ut onl& in e actl& this wa&% i.e.% asconclusions esta lished & proof through impossi lit& from necessar& assumptions. omewhatconfusingl&% Aristotle calls such propositions "possi le" ut immediatel& adds " not in the sensedefined": in this sense% "possi l& -a " is simpl& the denial of "necessaril& Aa ". uch propositionsappear onl& as premises% never as conclusions.

0.7. Syllogisms 8ith ,ecessary (remises

Aristotle holds that an assertoric s&llogism remains valid if "necessaril&" is added to its premises andits conclusion: the modal pattern BBB is alwa&s valid. 9e does not treat this as a trivial conse+uence

ut instead offers proofs* in all ut two cases% these are parallel to those offered for the assertoric case.

The e ceptions are -aroco and -ocar o % which he proved in the assertoric case through impossi ilit&:attempting to use that method here would re+uire him to take the denial of a necessar& - proposition ash&pothesis% raising the complication noted a ove% and he must resort to a different form of proofinstead.

0.7.0 ,A A, +ombi atio s: The (roblem of the "T8o ;arbaras" a d /ther $ifficulties

ince a necessar& premise entails an assertoric premise% ever& AB or BA com ination of premises willentail the corresponding AA pair% and thus the corresponding A conclusion. Thus% ABA and BAAs&llogisms are alwa&s valid. 9owever% Aristotle holds that some% ut not all% ABB and BABcom inations are valid. pecificall&% he accepts -arbara BAB ut re=ects -arbara ABB. Almost fromAristotle's own time% interpreters have found his reasons for this distinction o scure% or unpersuasive%or oth. Theophrastus% for instance% adopted the simpler rule that the modalit& of the conclusion of as&llogism was alwa&s the "weakest" modalit& found in either premise% where B is stronger than A andA is stronger than (and where pro a l& has to e defined as "not necessaril& not"). -ther difficultiesfollow from the pro lem of the "Two Car aras"% as it is often called% and it has often een maintainedthat the modal s&llogistic is inconsistent.

This su =ect +uickl& ecomes too comple for summari8ing in this rief article. or further discussion%see Cecker% c@all% atterson% van Hi=en% triker% Bortmann% Thom% and Thomason.


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7. $emo stratio s a d $emo strati)e Scie cesA demo stratio (apo eixis ) is "a deduction that produces knowledge". Aristotle's Posterior Analyticscontains his account of demonstrations and their role in knowledge. rom a modern perspective% wemight think that this su =ect moves outside of logic to epistemolog&. rom Aristotle's perspective%however% the connection of the theor& of sullogismoi with the theor& of knowledge is especiall& close.

7. Aristotelia Scie cesThe su =ect of the Posterior Analytics is epistm . This is one of several Greek words that canreasona l& e translated "knowledge"% ut Aristotle is concerned onl& with knowledge of a certain t&pe(as will e e plained elow). There is a long tradition of translating epistm in this technical sense asscie ce % and I shall follow that tradition here. 9owever% readers should not e misled & the use of thatword. In particular% Aristotle's theor& of science cannot e considered a counterpart to modern

philosoph& of science% at least not without su stantial +ualifications.

/e have scientific knowledge% according to Aristotle% when we know:

the cause wh& the thing is% that it is the cause of this% and that this cannot e otherwise.( Posterior Analytics I. )

This implies two strong conditions on what can e the o =ect of scientific knowledge:

1. -nl& what is necessaril& the case can e known scientificall&. cientific knowledge is knowledge of causes

9e then proceeds to consider what science so defined will consist in% eginning with the o servationthat at an& rate one form of science consists in the possession of a demo stratio (apo eixis )% whichhe defines as a "scientific deduction":

& "scientific" ( epistmonikon )% I mean that in virtue of possessing it% we have knowledge.

The remainder of Posterior Analytics I is largel& concerned with two tasks: spelling out the nature ofdemonstration and demonstrative science and answering an important challenge to its ver& possi ilit&.Aristotle first tells us that a demonstration is a deduction in which the premises are:

1. true. !rimary ( prota )!. immediate (amesa % "without a middle"). better k o8 or more familiar ( gnrimtera ) than the conclusion#. !rior to the conclusion$. causes (aitia ) of the conclusion

The interpretation of all these conditions e cept the first has een the su =ect of much controvers&.Aristotle clearl& thinks that science is knowledge of causes and that in a demonstration% knowledge ofthe premises is what rings a out knowledge of the conclusion. The fourth condition shows that theknower of a demonstration must e in some etter epistemic condition towards them% and so moderninterpreters often suppose that Aristotle has defined a kind of epistemic =ustification here. 9owever% asnoted a ove% Aristotle is defining a special variet& of knowledge. @omparisons with discussions of

=ustification in modern epistemolog& ma& therefore e misleading.

The same can e said of the terms "primar&"% "immediate" and " etter known". odern interpreterssometimes take "immediate" to mean "self,evident"* Aristotle does sa& that an immediate proposition is


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that scientific knowledge is onl& possi le & demonstration from premises scientificall& known:instead% he claims% there is another form of knowledge possi le for the first premises% and this providesthe starting points for demonstrations.

To solve this pro lem% Aristotle needs to do something +uite specific. It will not e enough for him toesta lish that we can have knowledge of some propositions without demonstrating them: unless it is inturn possi le to deduce all the other propositions of a science from them% we shall not have solved the

regress pro lem. oreover (and o viousl&)% it is no solution to this pro lem for Aristotle simpl& toassert that we have knowledge without demonstration of some appropriate starting points. 9e doesindeed sa& that it is his position that we have such knowledge ( An# Post# I. %)% ut he owes us anaccount of wh& that should e so.

7. = o8ledge of irst (ri ci!les: NousAristotle's account of knowledge of the indemonstra le first premises of sciences is found in Posterior

Analytics II.1F% long regarded as a difficult te t to interpret. Criefl&% what he sa&s there is that it isanother cognitive state% nous (translated variousl& as "insight"% "intuition"% "intelligence")% whichknows them. There is wide disagreement among commentators a out the interpretation of his account

of how this state is reached* I will offer one possi le interpretation. irst% Aristotle identifies his pro lem as e plaining how the principles can " ecome familiar to us"% using the same term "familiar"( gnrimos ) that he used in presenting the regress pro lem. /hat he is presenting% then% is not a methodof discover& ut a process of ecoming wise. econd% he sa&s that in order for knowledge of immediate

premises to e possi le% we must have a kind of knowledge of them without having learned it% ut thisknowledge must not e as "precise" as the knowledge that a possessor of science must have. The kindof knowledge in +uestion turns out to e a capacit& or power ( unamis ) which Aristotle compares to thecapacit& for sense,perception: since our senses are innate% i.e.% develop naturall&% it is in a wa& correctto sa& that we know what e.g. all the colors look like efore we have seen them: we have the capacit&to see them & nature% and when we first see a color we e ercise this capacit& without having to learnhow to do so first. >ikewise% Aristotle holds% our minds have & nature the capacit& to recogni8e the

starting points of the sciences.In the case of sensation% the capacit& for perception in the sense organ is actuali8ed & the operation onit of the percepti le o =ect. imilarl&% Aristotle holds that coming to know first premises is a matter of a

potentialit& in the mind eing actuali8ed & e perience of its proper o =ects: "The soul is of such anature as to e capa le of undergoing this". o% although we cannot come to know the first premiseswithout the necessar& e perience% =ust as we cannot see colors without the presence of colored o =ects%our minds are alread& so constituted as to e a le to recogni8e the right o =ects% =ust as our e&es arealread& so constituted as to e a le to perceive the colors that e ist.

It is considera l& less clear what these o =ects are and how it is that e perience actuali8es the relevant potentialities in the soul. Aristotle descri es a series of stages of cognition. irst is what is common to

all animals: perception of what is present. Be t is memor&% which he regards as a retention of asensation: onl& some animals have this capacit&. 3ven fewer have the ne t capacit&% the capacit& toform a single e perience ( empeiria ) from man& repetitions of the same memor&. inall&% man&e periences repeated give rise to knowledge of a single universal ( katholou ). This last capacit& is

present onl& in humans.

ee ection E of the entr& on Aristotle's ps&cholog& for more on his views a out mind.
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with 4 is its definition. "@apa le of laughing"% for e ample% counterpredicates with "human" ut failsto e its definition. uch a predicate (non,essential ut counterpredicating) is a !eculiar !ro!erty or!ro!rium (i ion ).

inall&% if 4 is predicated of 5 ut is neither essential nor counterpredicates% then 4 is an accide t( sumbebkos ) of 5.

Aristotle sometimes treats genus% peculiar propert&% definition% and accident as including all possi le predications (e.g. Topics I). >ater commentators listed these four and the differentia as the five!redicables % and as such the& were of great importance to late ancient and to medieval philosoph&(e.g.% orph&r&).

>.3 The +ategoriesThe notion of essential predication is connected to what are traditionall& called the categories(katgoriai ). In a word% Aristotle is famous for having held a "doctrine of categories". Lust what thatdoctrine was% and indeed =ust what a categor& is% are considera l& more ve ing +uestions. The& also+uickl& take us outside his logic and into his metaph&sics. 9ere% I will tr& to give a ver& generaloverview% eginning with the somewhat simpler +uestion "/hat categories are there0"

/e can answer this +uestion & listing the categories. 9ere are two passages containing such lists:

/e should distinguish the kinds of predication ( ta gen tn katgorin ) in which the four predications mentioned are found. These are ten in num er: what,it,is% +uantit&% +ualit&%relative% where% when% eing,in,a,position% having% doing% undergoing. An accident% agenus% a peculiar propert& and a definition will alwa&s e in one of these categories.(Topics I.F% 12! 2, #)

-f things said without an& com ination% each signifies either su stance or +uantit& or+ualit& or a relative or where or when or eing,in,a,position or having or doing orundergoing. To give a rough idea% e amples of su stance are man% horse* of +uantit&: four,foot% five,foot* of +ualit&: white% literate* of a relative: dou le% half% larger* of where: in the>&ceum% in the market,place* of when: &esterda&% last &ear* of eing,in,a,position: is,l&ing%is,sitting* of having: has,shoes,on% has,armor,on* of doing: cutting% urning* of undergoing:

eing,cut% eing, urned. ( Categories % 1 #, a % tr. Ackrill% slightl& modified)

These two passages give ten,item lists% identical e cept for their first mem ers. /hat are the& lists of 09ere are three wa&s the& might e interpreted:

The word "categor&" ( katgoria ) means "predication". Aristotle holds that predications and predicatescan e grouped into several largest "kinds of predication" ( gen tn katgorin ). 9e refers to thisclassification fre+uentl&% often calling the "kinds of predication" simpl& "the predications"% and this ( &wa& of >atin) leads to our word "categor&".

irst% the categories ma& e kin s of pre icate : predicates (or% more precisel&% predicatee pressions) can e divided into ten separate classes% with each e pression elonging to =ust oneclass. This comports well with the root meaning of the word katgoria ("predication"). -n thisinterpretation% the categories arise out of considering the most general t&pes of +uestion that can

e asked a out something: " /hat is it0"* " 0o! much is it0"* "/hat sort is it0"* "/here is it0"*"/hat is it oing 0" Answers appropriate to one of these +uestions are nonsensical in response toanother ("/hen is it0" "A horse"). Thus% the categories ma& rule out certain kinds of +uestion asill,formed or confused. This pla&s an important role in Aristotle's metaph&sics.


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econd% the categories ma& e seen as classifications of pre ications % that is% kinds of relationthat ma& hold etween the predicate and the su =ect of a predication. To sa& of ocrates that heis human is to sa& what he is% whereas to sa& that he is literate is not to sa& what he is ut ratherto give a +ualit& that he has . or Aristotle% the relation of predicate to su =ect in these twosentences is +uite different (in this respect he differs oth from lato and from modernlogicians). The categories ma& e interpreted as ten different wa&s in which a predicate ma& e

related to its su =ect. This last division has importance for Aristotle's logic as well as hismetaph&sics. Third% the categories ma& e seen as kin s of entity % as highest genera or kinds of thing that are.

A given thing can e classified under a series of progressivel& wider genera: ocrates is ahuman% a mammal% an animal% a living eing. The categories are the highest such genera. 3achfalls under no other genus% and each is completel& separate from the others. This distinction isof critical importance to Aristotle's metaph&sics.

/hich of these interpretations fits est with the two passages a ove0 The answer appears to edifferent in the two cases. This is most evident if we take note of point in which the& differ: theCategories lists substa ce (ousia ) in first place% while the Topics list 8hat?it?is (ti esti ). A su stance%for Aristotle% is a t&pe of entit&% suggesting that the Categories list is a list of t&pes of entit&.

-n the other hand% the e pression "what,it,is" suggests most strongl& a t&pe of predication. Indeed% theTopics confirms this & telling us that we can "sa& what it is" of an entity falling under an& of thecategories:

an e pression signif&ing what,it,is will sometimes signif& a su stance% sometimes a+uantit&% sometimes a +ualit&% and sometimes one of the other categories.

As Aristotle e plains% if I sa& that ocrates is a man% then I have said what ocrates is and signified asu stance* if I sa& that white is a color% then I have said what white is and signified a +ualit&* if I sa&that some length is a foot long% then I have said what it is and signified a +uantit&* and so on for theother categories. /hat,it,is% then% here designates a kind of predication% not a kind of entit&.

This might lead us to conclude that the categories in the Topics are onl& to e interpreted as kinds of predicate or predication% those in the Categories as kinds of eing. 3ven so% we would still want to askwhat the relationship is etween these two nearl&,identical lists of terms% given these distinctinterpretations. 9owever% the situation is much more complicated. irst% there are do8ens of other

passages in which the categories appear. Bowhere else do we find a list of ten% ut we do find shorterlists containing eight% or si % or five% or four of them (with su stanceMwhat,it,is% +ualit&% +uantit&% andrelative the most common). Aristotle descri es what these lists are lists of in different wa&s: the& tell us"how eing is divided"% or "how man& wa&s eing is said"% or "the figures of predication" (ta schNmatatNs katNgorias). The designation of the first categor& also varies: we find not onl& "su stance" and"what it is" ut also the e pressions "this" or "the this" ( to e ti %to to e %to ti ). These latter e pressionsare closel& associated with% ut not s&non&mous with% su stance. 9e even com ines the latter with"what,it,is" ( $etaphysics 6 1% 12 a12: "O one sense signifies what it is and the this% one signifies+ualit& O").

oreover% su stances are for Aristotle fundamental for predication as well as metaph&sicall&fundamental. 9e tells us that ever&thing that e ists e ists ecause su stances e ist: if there were nosu stances% there would not e an&thing else. 9e also conceives of predication as reflecting ametaph&sical relationship (or perhaps more than one% depending on the t&pe of predication). Thesentence " ocrates is pale" gets its truth from a state of affairs consisting of a su stance ( ocrates) anda +ualit& (whiteness) which is in that su stance. At this point we have gone far outside the realm of


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Aristotle's logic into his metaph&sics% the fundamental +uestion of which% according to Aristotle% is"/hat is a su stance0". ( or further discussion of this topic% see the entr& on Aristotle's metaph&sics %and in particular% ection on the categories.)

ee rede 1F 1% 3 ert 1F # for additional discussion of Aristotle's lists of categories.

or convenience of reference% I include a ta le of the categories% along with Aristotle's e amples andthe traditional names often used for them. or reasons e plained a ove% I have treated the first item inthe list +uite differentl&% since an e ample of a su stance and an e ample of a what,it,is are necessaril&(as one might put it) in different categories.

Traditio al ame Literally 9reek ocation /here pou in the >&ceum% in the marketplace

Time when pote &esterda&% last &ear

osition eing situated keisthai lies% sits

9a it having% possession echein is shod% is armed

Action doing poiein cuts% urns

assion undergoing paschein is cut% is urned

>. The %ethod of $i)isioIn the Sophist % lato introduces a procedure of "7ivision" as a method for discovering definitions. Tofind a definition of 4% first locate the largest kind of thing under which 4 falls* then% divide that kindinto two parts% and decide which of the two 4 falls into. Hepeat this method with the part until 4 has

een full& located.

This method is part of Aristotle's latonic legac&. 9is attitude towards it% however% is comple . 9eadopts a view of the proper structure of definitions that is closel& allied to it: a correct definition of 4should give the ge us ( genos : kind or famil&) of 4% which tells what kind of thing 4 is% and thediffere tia ( iaphora : difference) which uni+uel& identifies 4 within that genus. omething defined inthis wa& is a s!ecies (ei os : the term is one of lato's terms for " orm")% and the differentia is thus the"difference that makes a species" ( ei opoios iaphora % "specific difference"). In Posterior AnalyticsII.1!% he gives his own account of the use of 7ivision in finding definitions.9owever% Aristotle is strongl& critical of the latonic view of 7ivision as a method for establishingdefinitions. In Prior Analytics I.!1% he contrasts 7ivision with the s&llogistic method he has =ust

presented% arguing that 7ivision cannot actuall& prove an&thing ut rather assumes the ver& thing it issupposed to e proving. 9e also charges that the partisans of 7ivision failed to understand what theirown method was capa le of proving.
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>.0 $efi itio a d $emo stratio@losel& related to this is the discussion% in Posterior Analytics II.!,12% of the +uestion whether therecan e oth definition and demonstration of the same thing. ince the definitions Aristotle is interestedin are statements of essences% knowing a definition is knowing% of some e isting thing% what it is.@onse+uentl&% Aristotle's +uestion amounts to a +uestion whether defining and demonstrating can ealternative wa&s of ac+uiring the same knowledge. 9is repl& is comple :

1. Bot ever&thing demonstra le can e known & finding definitions% since all definitions areuniversal and affirmative whereas some demonstra le propositions are negative.

. If a thing is demonstra le% then to know it =ust is to possess its demonstration* therefore% itcannot e known =ust & definition.

!. Bevertheless% some definitions can e understood as demonstrations differentl& arranged.

As an e ample of case !% Aristotle considers the definition "Thunder is the e tinction of fire in theclouds". 9e sees this as a compressed and rearranged form of this demonstration:

ound accompanies the e tinguishing of fire. ire is e tinguished in the clouds.

Therefore% a sound occurs in the clouds./e can see the connection & considering the answers to two +uestions: "/hat is thunder0" "Thee tinction of fire in the clouds" (definition). "/h& does it thunder0" "Cecause fire is e tinguished inthe clouds" (demonstration).

As with his criticisms of 7ivision% Aristotle is arguing for the superiorit& of his own concept of scienceto the latonic concept. Qnowledge is composed of demonstrations% even if it ma& also includedefinitions* the method of science is demonstrative% even if it ma& also include the process of defining.

@. $ialectical Argume t a d the Art of $ialectic

Aristotle often contrasts ialectical arguments with demonstrations. The difference% he tells us% is in thecharacter of their premises% not in their logical structure: whether an argument is a sullogismos is onl& amatter of whether its conclusion results of necessit& from its premises. The premises of demonstrationsmust e true an primary % that is% not onl& true ut also prior to their conclusions in the wa& e plainedin the Posterior Analytics . The premises of dialectical deductions% & contrast% must e acce!ted(en oxos ).

@. $ialectical (remises: The %ea i g of EndoxosHecent scholars have proposed different interpretations of the term en oxos . Aristotle often uses thisad=ective as a su stantive: ta en oxa % "accepted things"% "accepted opinions". -n one understanding%descended from the work of G. 3. >. -wen and developed more full& & Lonathan Carnes andespeciall& Terence Irwin% the en oxa are a compilation of views held & various people with some formor other of standing: "the views of fairl& reflective people after some reflection"% in Irwin's phrase.7ialectic is then simpl& "a method of argument from RtheS common eliefs Rheld & these peopleS". orIrwin% then%en oxa are "common eliefs". Lonathan Carnes% noting that en oxa are opinions with acertain standing% translates with "reputa le".

& own view is that Aristotle's te ts support a somewhat different understanding. 9e also tells us thatdialectical premises differ from demonstrative ones in that the former are 1uestions % whereas the latterare assumptions or assertions : "the demonstrator does not ask% ut takes"% he sa&s. This fits most


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?nder the heading more a d less a d like8ise % Aristotle groups a somewhat motle& assortment ofargument patterns all involving% in some wa& or other% the terms "more"% "less"% and "likewise".3 amples: "If whatever is A is C% then whatever is more (less) A is more (less) C"* "If A is more likel&C than @ is% and A is not C% then neither is @"* "If A is more likel& than C and C is the case% then A isthe case".

@.2.2 The Topoi At the heart of the Topics is a collection of what Aristotle calls topoi % "places" or "locations".?nfortunatel&% though it is clear that he intends most of the Topics (Cooks II,UI) as a collection ofthese% he never e plicitl& defines this term. Interpreters have conse+uentl& disagreed considera l&a out =ust what a topos is. 7iscussions ma& e found in Crunschwig 1F$E% lomkowski 1FF$%rimavesi 1FFE% and mith 1FFE.

@.3 The -ses of $ialectic a d $ialectical Argume tAn art of dialectic will e useful wherever dialectical argument is useful. Aristotle mentions three suchuses* each merits some comment.

@.3. 9ym astic $ialectic

irst% there appears to have een a form of st&li8ed argumentative e change practiced in the Academ&in Aristotle's time. The main evidence for this is simpl& Aristotle's Topics % especiall& Cook UIII% whichmakes fre+uent reference to rule,governed procedures% apparentl& taking it for granted that theaudience will understand them. In these e changes% one participant took the role of answerer% the otherthe role of +uestioner. The answerer egan & asserting some proposition (a thesis : "position" or"acceptance"). The +uestioner then asked +uestions of the answerer in an attempt to secure concessionsfrom which a contradiction could e deduced: that is% to refute (elenchein ) the answerer's position. The+uestioner was limited to +uestions that could e answered & &es or no* generall&% the answerer could

onl& respond with &es or no% though in some cases answeres could o =ect to the form of a +uestion.Answerers might undertake to answer in accordance with the views of a particular t&pe of person or a particular person (e.g. a famous philosopher)% or the& might answer according to their own eliefs.There appear to have een =udges or scorekeepers for the process. G&mnastic dialectical contests weresometimes% as the name suggests% for the sake of e ercise in developing argumentative skill% ut the&ma& also have een pursued as a part of a process of in+uir&.

@.3.2 $ialectic That (uts to the Test

Aristotle also mentions an "art of making trial"% or a variet& of dialectical argument that "puts to thetest" (the Greek word is the ad=ective peirastik % in the feminine: such e pressions often designate artsor skills% e.g. rhtorik % "the art of rhetoric"). Its function is to e amine the claims of those who sa&the& have some knowledge% and it can e practiced & someone who does not possess the knowledge in+uestion. The e amination is a matter of refutation% ased on the principle that whoever knows asu =ect must have consistent eliefs a out it: so% if &ou can show me that m& eliefs a out somethinglead to a contradiction% then &ou have shown that I do not have knowledge a out it.

This is strongl& reminiscent of ocrates' st&le of interrogation% from which it is almost certainl&descended. In fact% Aristotle often indicates that dialectical argument is & nature refutative.


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@.3.3 $ialectic a d (hiloso!hy

7ialectical refutation cannot of itself esta lish an& proposition (e cept perhaps the proposition thatsome set of propositions is inconsistent). ore to the point% though deducing a contradiction from m&

eliefs ma& show that the& do not constitute knowledge% failure to deduce a contradiction from them isno proof that the& are true. Bot surprisingl&% then% Aristotle often insists that "dialectic does not provean&thing" and that the dialectical art is not some sort of universal knowledge.

In Topics I. % however% Aristotle sa&s that the art of dialectic is useful in connection with "the philosophical sciences". -ne reason he gives for this follows closel& on the refutative function: if wehave su =ected our opinions (and the opinions of our fellows% and of the wise) to a thorough refutativee amination% we will e in a much etter position to =udge what is most likel& true and false. In fact% wefind =ust such a procedure at the start of man& of Aristotle's treatises: an enumeration of the opinionscurrent a out the su =ect together with a compilation of "pu88les" raised & these opinions. Aristotlehas a special term for this kind of review: a iaporia % a "pu88ling through".

9e adds a second use that is oth more difficult to understand and more intriguing. The Posterior Analytics argues that if an&thing can e proved% then not ever&thing that is known is known as a resultof proof. /hat alternative means is there where & the first principles of sciences are known0 Aristotle's

own answer as found in Posterior Analytics II.1F is difficult to interpret% and recent philosophers haveoften found it unsatisf&ing since (as often construed) it appears to commit Aristotle to a form ofapriorism or rationalism oth indefensi le in itself and not consonant with his own insistence on theindispensa ilit& of empirical in+uir& in natural science.

Against this ackground% the following passage in Topics I. ma& have special importance:

It is also useful in connection with the first things concerning each of the sciences. or it isimpossi le to sa& an&thing a out the science under consideration on the asis of its own

principles% since the principles are first of all% and we must work our wa& through a outthese & means of what is generall& accepted a out each. Cut this is peculiar% or most

proper% to dialectic: for since it is e aminative with respect to the principles of all the

sciences% it has a wa& to proceed.

A num er of interpreters ( eginning with -wen 1F$1) have uilt on this passage and others to finddialectic at the heart of Aristotle's philosophical method. urther discussion of this issue would take usfar e&ond the su =ect of this article (the fullest development is in Irwin 1F * see also Buss aum 1F $and Colton 1FF2* for criticism% 9aml&n 1FF2% mith 1FFE).

. $ialectic a d hetoricAristotle sa&s that rhetoric% i.e.% the stud& of persuasive speech% is a "counterpart" ( antistrophos ) ofdialectic and that the rhetorical art is a kind of "outgrowth" ( paraphues ti ) of dialectic and the stud& of

character t&pes. The correspondence with dialectical method is straightforward: rhetorical speeches%like dialectical arguments% seek to persuade others to accept certain conclusions on the asis of premises the& alread& accept. Therefore% the same measures useful in dialectical conte ts will% mutatismutandis% e useful here: knowing what premises an audience of a given t&pe is likel& to elieve% andknowing how to find premises from which the desired conclusion follows.

The Rhetoric does fit this general description: Aristotle includes oth discussions of t&pes of person oraudience (with generali8ations a out what each t&pe tends to elieve) and a summar& version (in II. !)of the argument patterns discussed in the Topics . or further discussion of his rhetoric see Aristotle'srhetoric .
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B. So!histical Argume ts7emonstrations and dialectical arguments are oth forms of valid argument% for Aristotle. 9owever% healso studies what he calls co te tious (eristikos ) or so!histical arguments: these he defines asarguments which onl& apparentl& esta lish their conclusions. In fact% Aristotle defines these as apparent( ut not genuine) ialectical sullogismoi . The& ma& have this appearance in either of two wa&s:

1. Arguments in which the conclusion onl& appears to follow of necessit& from the premises(apparent% ut not genuine% sullogismoi ).

. Genuine sullogismois the premises of which are merel& apparentl&% ut not genuinel&%accepta le.

Arguments of the first t&pe in modern terms% appear to e valid ut are reall& invalid. Arguments of thesecond t&pe are at first more perple ing: given that accepta ilit& is a matter of what people elieve% itmight seem that whatever appears to e en oxos must actuall& e en oxos . 9owever% Aristotle

pro a l& has in mind arguments with premises that ma& at first glance seem to e accepta le ut which%upon a moment's reflection% we immediatel& reali8e we don not actuall& accept. @onsider this e amplefrom Aristotle's time:

/hatever &ou have not lost% &ou still have. 5ou have not lost horns. Therefore% &ou still have horns

This is transparentl& ad% ut the pro lem is not that it is invalid: the pro lem is rather that the first premise% though superficiall& plausi le% is false. In fact% an&one with a little a ilit& to follow anargument will reali8e that at once upon seeing this ver& argument.

Aristotle's stud& of sophistical arguments is contained in On Sophistical Refutations % which is actuall& asort of appendi to the Topics .

To a remarka le e tent% contemporar& discussions of fallacies reproduce Aristotle's own classifications.ee 7orion 1FF# for further discussion.

. ,o ?+o tradictio a d %eta!hysicsTwo fre+uent themes of Aristotle's account of science are (1) that the first principles of sciences are notdemonstra le and ( ) that there is no single universal science including all other sciences as its parts."All things are not in a single genus"% he sa&s% "and even if the& were% all eings could not fall underthe same principles" ( On Sophistical Refutations 11). Thus% it is e actl& the universal applica ilit& ofdialectic that leads him to den& it the status of a science.

In $etaphysics IU (V)% however% Aristotle takes what appears to e a different view. irst% he arguesthat there is% in a wa&% a science that takes eing as its genus (his name for it is "first philosoph&").

econd% he argues that the principles of this science will e% in a wa&% the first principles of all (thoughhe does not claim that the principles of other sciences can e demonstrated from them). Third% heidentifies one of its first principles as the "most secure" of all principles: the principle of non,contradiction. As he states it%

It is impossi le for the same thing to elong and not elong simultaneousl& to the samething in the same respect ( $et# )

This is the most secure of all principles% Aristotle tells us% ecause "it is impossi le to e in error a outit". ince it is a first principle% it cannot e demonstrated* those who think otherwise are "uneducated in


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re=ect this). It seems to me reasona le to conclude that Aristotle's target here is some egarianargument% perhaps an earlier version of the aster.

3. 9lossary of Aristotelia Termi ology Accept: tithenai (in a dialectical argument) Accepted: en oxos (also ;reputa le< ;common elief


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rinciple: arch (starting point of a demonstration) Pualit&: poion Heduce% Heduction: anagein %anagg Hefute: elenchein * refutation%elenchos cience: epistm pecies: ei os pecific: ei opoios (of a differentia that "makes a species"% ei opoios iaphora ) u =ect: hupokeimenon u stance: ousia Term: horos ?niversal: katholou ( oth of propositions and of individuals)

sep - aristotle's logic

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