The Beginnings of Formal Logic: Deduction in Aristotle’s Topics vs. Prior Analytics

in Phronesis
Restricted Access
Get Access to Full Text
Rent on DeepDyve

Have an Access Token?



Enter your access token to activate and access content online.

Please login and go to your personal user account to enter your access token.



Help

Have Institutional Access?



Access content through your institution. Any other coaching guidance?



Connect

It is widely agreed that Aristotle’s Prior Analytics, but not the Topics, marks the beginning of formal logic. There is less agreement as to why this is so. What are the distinctive features in virtue of which Aristotle’s discussion of deductions (syllogismoi) qualifies as formal logic in the one treatise but not in the other? To answer this question, I argue that in the Prior Analytics—unlike in the Topics—Aristotle is concerned to make fully explicit all the premisses that are necessary to derive the conclusion in a given deduction.

The Beginnings of Formal Logic: Deduction in Aristotle’s Topics vs. Prior Analytics

in Phronesis

Sections

References

AckrillJ.L. Aristotle’s Categories and De Interpretatione 1963 Oxford

AllenJ. ‘The Development of Aristotle’s Logic: Part of an Account in Outline’ Proceedings of the Boston Area Colloquium in Ancient Philosophy 1995 11 177 205

AllenJ. Inference from Signs: Ancient Debates about the Nature of Evidence 2001 Oxford

AllenJ. ‘Aristotle on the Disciplines of Argument: Rhetoric, Dialectic, Analytic’ Rhetorica 2007 25 87 108

AllenJ. ‘Syllogism, Demonstration, and Definition in Aristotle’s Topics and Posterior Analytics Oxford Studies in Ancient Philosophy 2011 40 63 90

AnagnostopoulosG. Aristotle on the Goals and Exactness of Ethics 1994 Berkeley

AthertonC. The Stoics on Ambiguity 1993 Cambridge

BarnesJ. SchofieldM.BurnyeatM.F.BarnesJ. ‘Proof Destroyed’ Doubt and Dogmatism: Studies in Hellenistic Epistemology 1980 Oxford 161 81

BarnesJ. BertiE. ‘Proof and the Syllogism’ Aristotle on Science: The Posterior Analytics 1981 Padua 17 59

BarnesJ. AlbertiA. ‘Logical Form and Logical Matter’ Logica Mente e Persona 1990 Florence 7 119

BarnesJ. Aristotle’s Posterior Analytics 1994 2nd edn Oxford

BarnesJ. FredeM.StrikerG. ‘Grammar on Aristotle’s Terms’ Rationality in Greek Thought 1996 Oxford 175 202

BarnesJ. GüntherH.-C.RengakosA. ‘Proof and the Syllogistic Figures’ Beiträge zur antiken Philosophie: Festschrift für Wolfgang Kullmann 1997 Stuttgart 153 66

BarnesJ. IerodiakonouK. ‘Syllogistic in the anon Heiberg’ Byzantine Philosophy and its Ancient Sources 2002 Oxford 97 137

BarnesJ. Truth etc. Six Lectures on Ancient Logic 2007 Oxford

BeaneyM. Frege: Making Sense 1996 London

BekkerI. Aristoteles Graece 1831 Vol. 1 Berlin

BobzienS. ‘The Development of Modus Ponens in Antiquity: From Aristotle to the 2nd Century ad Phronesis 2002 47 359 94

BobzienS. FredeD.InwoodB. ‘The Stoics on Fallacies of Equivocation’ Language and Learning: Philosophy of Language in the Hellenistic Age 2005 Cambridge 239 73

BobzienS. ScottD. ‘Aristotle’s De Interpretatione 8 is about Ambiguity’ Maieusis: Essays in Ancient Philosophy in Honour of Myles Burnyeat 2007 Oxford 301 21

BocheńskiI.M. ‘On the Categorical Syllogism’ Dominican Studies 1948 1 35 57

BocheńskiI.M. Ancient Formal Logic 1951 Amsterdam

BocheńskiI.M. Formale Logik 1956 Freiburg and Munich

BoltonR. ‘The Problem of Dialectical Reasoning (Συλλογισμός) in Aristotle’ Ancient Philosophy 1994 14 99 132

BrandisC. ‘Über die Reihenfolge der Bücher des Aristotelischen Organons und ihre Griechischen Ausleger, nebst Beiträgen zur Geschichte des Textes jener Bücher des Aristoteles und ihrer Ausgaben’ Hist.-Phil. Abhandlungen der königlichen Akademie der Wissenschaften zu Berlin (Jahr 1833) 1835 249 99

BrunschwigJ. Aristote: Topiques iv 1967 Paris

BrunschwigJ. OwenG.E.L. ‘Observations sur les manuscrits parisiens des Topiques Aristotle on Dialectic: The Topics 1968 Oxford 3 21

BrunschwigJ. ‘La proposition particulière et les preuves de non-concluance chez Aristote’ Cahiers pour l’Analyse 1969 10 3 26

BurnyeatM. BarnesJ.BrunschwigJ.BurnyeatM.SchofieldM. ‘The Origins of Non-Deductive Inference’ Science and Speculation: Studies in Hellenistic Theory and Practice 1982 Cambridge 193 238

BurnyeatM. FurleyD.J.NehamasA. ‘Enthymeme: Aristotle on the Logic of Persuasion’ Aristotle’s Rhetoric: Philosophical Essays 1994 Princeton 3 55

BurnyeatM. A Map of Metaphysics Zeta 2001 Pittsburgh

ByrneP.H. Analysis and Science in Aristotle 1997 Albany

CodeA. FurleyD. ‘Aristotle’s Logic and Metaphysics’ Routledge History of Philosophy From Aristotle to Augustine 1999 Vol. 2 London and New York 40 75

CookeH.P.TedennickH.ForsterE.S. Aristotle: The Organon. The Categories On Interpretation Prior Analytics 1938 Vol. 1 Cambridge, MA Loeb Classical Library

CorcoranJ. CorcoranJ. ‘Aristotle’s Natural Deduction System’ Ancient Logic and its Modern Interpretations 1974 Dordrecht 85 131

CornfordF.M. Plato’s Theory of Knowledge: The Theaetetus and the Sophist of Plato 1935 London

CrivelliP. Aristotle on Truth 2004 Cambridge

CrivelliP. LongoA. ‘Aristotle on Syllogisms from a Hypothesis’ Argument from Hypothesis in Ancient Philosophy 2011 Naples 95 184

CrivelliP. ShieldsC. ‘Aristotle’s Logic’ The Oxford Handbook of Aristotle 2012 Oxford 113 49

CrivelliP.CharlesD. ‘ “ΠΡΟΤΑΣΙΣ” in Aristotle’s Prior Analytics Phronesis 2011 56 193 203

Di LascioE.V. SheffieldF.WarrenJ. ‘Aristotle: Logic’ The Routledge Companion to Ancient Philosophy 2014 New York / Abingdon 272 89

DorionL.-A. Aristote: Les réfutations sophistiques 1995 Paris

Dutilh NovaesC. ‘The Different Ways in which Logic is (said to be) Formal’ History and Philosophy of Logic 2011 32 303 32

EbertT.NortmannU. Aristoteles: Analytica Priora Buch 1 2007 Berlin

FaitP. Aristotele: Le confutazioni sofistiche 2007 Rome

FaitP. RappC.HasperP.S. ‘The “False Validating Premiss” in Aristotle’s Doctrine of Fallacies: An Interpretation of Sophistical Refutations 8’ Logical Analysis and History of Philosophy 2013 15 238 66

FredeM. ‘Stoic vs. Aristotelian Syllogistic’ Archiv für Geschichte der Philosophie 1974a 56 1 32

FredeM. Die stoische Logik 1974b Göttingen

FregeG. Begriffsschrift eine der arithmetischen nachgebildete Formelsprache des reinen Denkens 1879 Halle

FregeG. Die Grundlagen der Arithmetik eine logisch mathematische Untersuchung über den Begriff der Zahl 1884 Breslau

FregeG. Grundgesetze der Arithmetik begriffsschriftlich abgeleitet 1893 Vol. 1 Jena

FregeG. BartlettJ.M. ‘On the Scientific Justification of a Concept-Script’ Mind 1964 73 155 60

FregeG. HermesH.KambartelF.KaulbachF. LongP.WhiteR. Posthumous Works 1979 Oxford

HarrisR. Rationality and the Literate Mind 2009 New York / Abingdon

HeathT. A History of Greek Mathematics From Thales to Euclid 1921 Vol. 1 Oxford

JonesR.E. ‘Truth and Contradiction in Aristotle’s De Interpretatione 6-9’ Phronesis 2010 55 26 67

KahnC. The Verb ‘Be’ Ancient Greek 1973 Dordrecht

KeytD. AnagnostopoulosG. ‘Deductive Logic’ A Companion to Aristotle 2009 Chichester / Malden, MA 31 50

KnealeW.KnealeM. The Development of Logic 1962 Oxford

LearJ. Aristotle and Logical Theory 1980 Cambridge

LennoxJ. Aristotle: On the Parts of Animals 2001 Oxford

LeunissenM. Explanation and Teleology in Aristotle’s Science of Nature 2010 Cambridge

ŁukasiewiczJ. Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic 1957 2nd edn Oxford

MacFarlaneJ. What Does it Mean to Say that Logic is Formal? 2000 PhD Dissertation. University of Pittsburgh

MacFarlaneJ. ‘Abelard’s Argument for Formality’ Proceedings of the 19th European Symposium on Medieval Logic and Semantics forthcoming Turnhout

MaierH. Die Syllogistik des Aristoteles Die logische Theorie des Urteils bei Aristoteles 1896 Vol. 1 Tübingen

MaierH. Die Syllogistik des Aristoteles Formenlehre und Technik des Syllogismus 1900 Vol. 2.1 Tübingen

MalinkM. ‘ΤΩΙ vs ΤΩΝ in Prior Analytics 1.1-22’ Classical Quarterly 2008 58 519 36

MalinkM. Aristotle’s Modal Syllogistic 2013 Cambridge MA

MalinkM. LeeMi-Kyoung ‘Deduction in Sophistici Elenchi 6’ Strategies of Argument: Essays in Ancient Greek Ethics Epistemology and Logic 2014 New York 149 74

McKirahanR.D. Principles and Proofs: Aristotle’s Theory of Demonstrative Science 1992 Princeton

MendellH. ‘Making Sense of Aristotelian Demonstration’ Oxford Studies in Ancient Philosophy 1998 16 161 225

MignucciM. Canto-SperberM.PellegrinP. ‘Syllogism and Deduction in Aristotle’s Logic’ Le style de la pensée: Recueil de textes en hommage à Jacques Brunschwig 2002 Paris 244 66

MorisonB. MorisonB.IerodiakonouK. ‘What was Aristotle’s Concept of Logical Form?’ Episteme etc. Essays in Honour of Jonathan Barnes 2012 Oxford 172 88

MuellerI. ‘Stoic and Peripatetic Logic’ Archiv für Geschichte der Philosophie 1969 51 173 87

MuellerI. CorcoranJ. ‘Greek Mathematics and Greek Logic’ Ancient Logic and its Modern Interpretations 1974 Dordrecht 35 70

MuellerI. Philosophy of Mathematics and Deductive Structure in Euclid’s Elements 1981 Cambridge MA

MuellerI. Alexander of Aphrodisias: On Aristotle’s Prior Analytics 1 2006 London 32 46

OliverA.SmileyT. Plural Logic 2013 Oxford

OwenG.E.L. Owen ‘Dialectic and Eristic in the Treatment of the Forms’ Aristotle on Dialectic: The Topics 1968 Oxford 103 25

OwenO.F. The Organon or Logical Treatises of Aristotle 1889 Vol. 1 London

PerinC. ‘Substantial Universals in Aristotle’s Categories’ Oxford Studies in Ancient Philosophy 2007 33 125 43

PaciusJ. Aristotelis Stagiritae Peripateticorum Principis Organum 1597a 2nd edn Frankfurt

PaciusJ. In Porphyrii Isagogen et Aristotelis Organum Commentarius Analyticus 1597b Frankfurt

PosteE. Aristotle: On Fallacies or the Sophistici Elenchi 1866 London

PrimavesiO. Die aristotelische Topik 1996 Munich

RappC. SchirrenT.UedingG. ‘Topos und Syllogismus bei Aristoteles’ Topik und Rhetorik 2000 Tübingen 15 35

RappC. Aristoteles: Rhetorik 2002 Berlin

RiniA.A. Aristotle’s Modal Proofs: Prior Analytics A8-22 in Predicate Logic 2011 Dordrecht

RossD.W. ‘The Discovery of the Syllogism’ Philosophical Review 1939 48 251 72

RossD.W. Aristotle’s Prior and Posterior Analytics 1949 Oxford

RossD.W. Aristotelis Topica et Sophistici Elenchi 1958 Oxford

RussellB. History of Western Philosophy and its Connection with Political and Social Circumstances from the Earliest Times to the Present Day 1946 London

SainatiV. Storia dell’ ‘Organon aristotelico 1968 Vol. 1 Florence

SlomkowskiP. Aristotle’s Topics 1997 Leiden

SlugaH. Gottlob Frege 1980 London

SmileyT. ‘The Schematic Fallacy’ Proceedings of the Aristotelian Society (1982/83) 83 1 17

SmithR. ‘What is Aristotelian Ecthesis?’ History and Philosophy of Logic 1982 3 113 27

SmithR. Aristotle: Prior Analytics 1989 Indianapolis

SmithR. ‘Aristotle on the Uses of Dialectic’ Synthese 1993 96 335 58

SmithR. BarnesJ. ‘Logic’ The Cambridge Companion to Aristotle 1995 Cambridge 27 65

SmithR. Aristotle’s Topics: Books 1 and 8 1997 Oxford

SpecaA.N. Hypothetical Syllogistic and Stoic Logic 2001 Leiden

StracheI.WalliesM. Aristotelis Topica cum libro de Sophisticis Elenchis 1923 Leipzig

StrikerG. FredeM.Striker ‘Perfection and Reduction in Aristotle’s Prior Analytics Rationality in Greek Thought 1996 Oxford 203 19

StrikerG. GentzlerJ. ‘Aristotle and the Uses of Logic’ Method in Ancient Philosophy 1998 Oxford 209 26

StrikerG. Aristotle’s Prior Analytics: Book 1 2009 Oxford

ThomP. The Syllogism 1981 Munich

TredennickH.ForsterE.S. Aristotle Organon Posterior Analytics and Topica 1960 Vol. 2 Cambridge, MA Loeb Classical Library

von KirchmannJ.H. Aristoteles’ erste Analytiken oder: Lehre vom Schluss 1877 Leipzig

von KirchmannJ.H. Erläuterungen zu Aristoteles’ sophistischen Widerlegungen 1883 Heidelberg

WagnerT. RappC.CorciliusK. ‘Topos’ Aristoteles-Handbuch: Leben Werk Wirkung 2011 Stuttgart / Weimar 355 7

WagnerT.RappC. Aristoteles: Topik 2004 Stuttgart

WaitzT. Aristotelis Organon Graece 1844 Vol. 1 Leipzig

WaitzT. Aristotelis Organon Graece 1846 Vol. 2 Leipzig

WeidemannH. Aristoteles: Peri Hermeneias 2002 2nd edn Berlin

WeidemannH. ShieldsC. De Interpretatione The Oxford Handbook of Aristotle 2012 Oxford 81 112

WeinerJ. Frege in Perspective 1990 Ithaca, NY

WeinerJ. Frege Explained 2004 Chicago

WeinerJ. PotterM.RickettsT. ‘Understanding Frege’s Project’ The Cambridge Companion to Frege 2010 Cambridge 32 62

WhitakerC.W.A. Aristotle’s De Interpretatione: Contradiction and Dialectic 1996 Oxford

WoodsJ.IrvineA. GabbayD.M.WoodsJ. ‘Aristotle’s Early Logic’ Handbook of the History of Logic 2004 Vol. 1 Amsterdam 27 99 Greek Indian and Arabic Logic

1

See e.g. Cornford 1935264; Russell 1946 219; Ross 1949 29; Bocheński 1956 74; Allen 2001 13; Ebert and Nortmann 2007 106-7; Striker 2009 p. xi.

4

See Barnes 199039-40; 2007 277-82. As Burnyeat (2001 8) points out Aristotle’s distinction between matter and form is absent from the Organon.

6

This has been pointed out by Barnes 2007274.

7

Morison 2012172-3 and 186-7; pace Smiley 1982/83 1.

8

See Brunschwig 19693-5.

10

See Łukasiewicz 195715-19; Frede 1974a 13-15; 1974b 198-201; Morison 2012 186-7.

12

Similarly Bocheński 1956113 and 124; Mueller 1974 51.

14

Alexanderin Top. ii.2 3.25-4.10 and 5.4-13 Wallies; Smith 1993 338-9; Code 1999 45. Aristotle holds that dialectic is ‘concerned with things which are in a way common for all to know not for any separate science’ (Rhet. 1.1 1354a1-3; similarly APo. 1.11 77a31). Accordingly Aristotle’s account of dialectical deductions in the Topics is sometimes called ‘formal’ on the grounds that its topoi are topic-neutral and provide general argument forms applicable to a large number of particular cases (Allen 2001 15-16 and 69-72; Smith 1997 pp. xxiv and xxvi; Wagner and Rapp 2004 8; Wagner 2011 356).

15

For example Cornford 1935264-5; Ross 1949 29; Łukasiewicz 1957 7-8 and 13-14; Striker 2009 p. xii.

16

See Barnes 2007286-92 and 358.

18

For example Owen 188980; Smith 1989 1; Striker 2009 1; Crivelli 2012 113.

20

See Crivelli and Charles 2011194; Crivelli 2012 113-14.

22

See Ammoniusin APr. iv.6 18.15-38 Wallies; Ross 1949 289; Łukasiewicz 1957 4; Smith 1989 107; Striker 2009 77.

24

See Brunschwig 1967p. lx.

28

Striker 2009194; see also Slomkowski 1997 24 27 and 134.

30

See Alexanderin Top. ii.2 158.31-160.3 Wallies; Primavesi 1996 152-4. Similarly Aristotle writes in the Categories: ‘If you will call the individual man grammatical it follows that you will call both man and animal [i.e. the species man and the genus animal] grammatical’ (Cat. 5 3a4-5; see Perin 2007 135).

32

See Whitaker 199691-4; Weidemann 2002 206-7; Jones 2010 42-5.

33

Kneale and Kneale 196237.

35

See Alexanderin Top. ii.2 288.12-289.31 Wallies; Maier 1900 79-80 n. 1; Brunschwig 1967 pp. lix-lxi and 163-4; 1968 16-18. This alternative sense of ‘indeterminate’ is also found in the Prior Analytics (APr. 1.4 26b14-16; 1.5 27b20-2 27b28; 1.6 28b28-30 29a6; 1.15 35b11; see Alexander in APr. ii.1 66.2-18 67.3-7 88.6-8 88.31-3 105.22-6 Wallies; Waitz 1844 383; Maier 1896 162-3; Brunschwig 1969 13 and 19; Crivelli 2004 245 n. 21; Striker 2009 98-9).

40

See Alexanderin APr. ii.1 266.32-267.5 Wallies; Philoponus in APr. xiii.2 252.31-5 Wallies; Pacius 1597b 155-6; Waitz 1844 434; Mendell 1998 185; Striker 2009 179. It seems clear that Aristotle regards the major premiss of A1 as indeterminate in the sense defined in Prior Analytics 1.1 (24a19-22). Aristotle describes this major premiss as being ‘without universality’ (ἄνευ τοῦ καθόλου 41b7); the same phrase (ἄνευ τοῦ καθόλου) is used in 1.1 to characterize indeterminate premisses (24a20). Also the major premiss of A1 is very similar to one of Aristotle’s examples of indeterminate premisses in 1.1 ‘Pleasure is not good’ (24a21-2).

42

See Slomkowski 199726-7.

44

See Jones 201042-5; cf. Whitaker 1996 84-5.

45

See Jones 201042-5.

46

See Bolton 1994102-3; Primavesi 1996 35-7.

48

See Alexanderin APr. ii.1 53.28-54.2 379.14-380.27 Wallies; Philoponus in APr. xiii.2 46.25-47.9 Wallies. Moreover the use of schematic letters helps Aristotle to abstract from speaker meaning since the speaker meaning of a sentence on a given occasion of use will typically depend on the literal meaning of its subject and predicate terms.

52

See Anagnostopoulos 1994131-40. When some degree of inexactness is appropriate for the purposes of a given investigation Aristotle tends ‘to view exactness as something toilsome and as something that reflects the kind of pettiness or meanness that he elsewhere associates with the behavior of the illiberal person’ (Anagnostopoulos 1994 126).

53

See Alexanderin Top. ii.2 26.13-19 Wallies; similarly Smith 1997 51.

57

See Barnes 198123-4 n. 9; Rapp 2002 63 and 164. In Topics 8.11 (161b28-30) Aristotle takes the condition expressed by τῷ ταῦτα εἶναι to be part of the definition of deduction (cf. Rhet. 1.2 1356b17; se 6 168b24). This suggests that he takes this phrase to be equivalent to the one used in Topics 1.1 (διὰ τῶν κειμένων).

58

See Barnes 198123-4 n. 9; Bolton 1994 116; Primavesi 1996 59 n. 2; Rapp 2000 17-20; similarly Striker 2009 79-81.

59

See Alexanderin Top. ii.2 13.28-14.2 and 568.18-23 Wallies; Frede 1974a 22; Barnes 1980 168-9; Allen 1995 189; Smith 1997 143; Mignucci 2002 251; Ebert and Nortmann 2007 227-8; Striker 2009 81-2.

62

For such arguments see Alexanderin APr. ii.1 21.28-30 344.9-345.12 346.27-8 Wallies; Philoponus in APr. xiii.2 320.16-322.18 and 323.18-27 Wallies; Frede 1974a 20-3; Mignucci 2002 248-56.

64

Mignucci 2002254-6. The causal condition requires that the conclusion follow ‘through the things supposed’ (διὰ τῶν κειμένων Top. 1.1 100a26-7; se 1 165a2) whereas Aristotle denies that the conclusion of A3 has been deduced ‘through the things assumed’ (διὰ τῶν εἰλημμένων APr. 1.32 47a27-8).

65

Alexanderin APr. ii.1 347.5-7 Wallies. For alternative suggestions see Pacius 1597a 262; Ebert and Nortmann 2007 800-5; Striker 2009 214. Some of these commentators argue that in order to turn A3 into a deduction one must not only add a premiss but also transform the two premisses already present in A3.

69

See McKirahan 1992157-8; Ebert and Nortmann 2007 749-50.

71

See Philoponusin APr. xiii.2 254.12-23 Wallies; cf. n. 67 above.

75

Similarly Frege 1884§91; 1893 pp. vi-vii.

76

See Weiner 199052-3 and 67; 2010 43-4.

78

Alexanderin Top. ii.2 568.13-18 Wallies. Similarly Aristotle states that arguments are subject to criticism if ‘the conclusion does not come about either when some premisses are taken away or some premisses are added’ (Top. 8.11 161b22-4). Again this implies that an argument in which premisses are missing is not subject to criticism as long as it can be turned into a deduction by adding suitable premisses; see Allen 1995 189; Rapp 2000 27-32.

83

See Allen 1995189-90; 2001 53 and 69.

90

Bobzien 2005258-64; 2007 301-12.

97

See Weiner 2004102; cf. 2010 43-4.

100

See Barnes 2007362-9.

101

See e.g. Lennox 2001123-4; Leunissen 2010 79-80.

Figures

Information

Content Metrics

Content Metrics

All Time Past Year Past 30 Days
Abstract Views 33 33 14
Full Text Views 77 77 50
PDF Downloads 11 11 5
EPUB Downloads 4 4 2