LOGIC AND SCIENTIFIC KNOWLBDGE IN r . ARISTOTLE AN EVALUATION OF TEE RELATIONSHIP BE'l'WEEN THE SYLLOGISTIC IMPLICATION AND THE SCIENTIFIC SYLLOGISM OF ARISTOTLE By LAURENCE BRENDAN HANEVY, B.Ac A Thesis -I . Suomit-tea.-totne -FacuTtY-oT Grs:dtiateS-tud1.es I I i in Partial Fulfilment of the Requirements for the Degree Master of Arts McMaster University October 1967 MASTER OF PHILOSOPHY 1967 McMASTER UNIVERSITY Philosophy Hamilton, Ontario. TITLE: An Evaluation of the Relationship Between the Syllogistic Implication and the Scientific Syllogism of Aristotle. AUTHOR: Laurence Brendan Hanevy, B.A., University College. Dublin. SUPERVISOR: Professor A. Shalom. NUIvlBER OF PAGES: iv, 81. SCOPE AND CONTENTS: In Aristotle's Frior Analytics he develops his doctrine of syllogistic implication. In the Posterior Analytics he presents his doctrine of the scientific syllogism which. for him. is productive of scientific knowledge. My concern in this work is to analyse the relationship between his doctrine of syllogistiC implication and his doctrine of scientific syllogism • . ----- ------- - I-t--w-ou-l-d -seBm-tha-t-t-l1ere-l-s-an--irreCiucioly -a.T~rnhc'Grve- .. difference between the roles performed by the syllogistic . -lmprlce:tlonal -Tarm 'ana:--tne-sClent~Tlc--syIlo,glstrc-forn1~-­ Consequently. the syllogistic implicational form cannot be used as the form of the scientific syllogism and, hence, the value of the syllogistic implication does not depend on any relationship it might have to' the scientific syllogism. The syllogistiC implication is valuable as a body of theor- etical knowledgeo . I ~ ~ \ \J.J./ ACKNOWLEDGMENTS It is a great pleasure for me to record my sincerest gratitude to Professor A. Shalom who directed this thesis. While in its preparatory stages Professor Shalom read this work, discussed it at length and offered many invaluable suggestions and criticisms~ I also wish. to express my sincere thanks to Mr. S. Ajzenstat who recommended valuable reading material and discussed and evaluaOted some of the material with me .. Finally,. I could never adequately express my gratitude to my wife. Patricia, for the constant encouragement and unfailing assistance she afforded me while I was engaged in ( ii1) CONTENTS INTRODUCTION 1 1. ARISTOTLE'S SYLLOGISTIC DOCTRINE 9 20 SCIENTIFIC KNOWLEDGE AND PRE-EXIS'I'ING KNOWLEDGE 16 3. KNOWLEDGE, TRUTH AND THE SCIENTIFIC SYLLOGISM 32 4. SYLLOGISTIC IMPLICATION AND THE SCIENTIFIC SYLLOGISM 56 59 VALUE ASSESSMENT AND THE ARISTOTELIAN SYLLOGISTIC 71 BIBLI QGRAPH'i 79 --I ! (1v) INTRODUCTION As its originator and first systematic proponent Aristotle occupies a unique and controversial niche in the chamber of logice His logical theory has instigated many and varied problems and disputations down through the steps of history. In ancient times it was a matter of argument- ation as to what position ought to be assigned to his 199ic - was it a section of his philosophy or was it propaedeutic i- to his philosophy? There was the problem as to whether f his logical theory, as expounded in the Prior Analytics, preceded or was consequent upon his theory of scientific knowledge, as elaborated in the Posterior Analytics. Was the Posterior Analytics written first and then, stimulated bi this work, did Aristotle proceed to elaborate his Prior Analytics? Or was the process the reverse? Ross tells us that Solmsen's view as to the order of the Analytics is that "having formulated the method of dialectic in the topics, Aristotle, next formulated the method of strict science in the Posterior Analytics, and finally reached in the Prior Analytics the general.account of the syllogism as being the method lying at the base both of dialectical argument and of 1 scientific reasoning". 1. Ross, W.D., Aristotle's Prior and Posterior Analytics, page 7. 1 2 Solmsen attributes this order of the Analytics to the influence of Platonism on Aristotle. He sees the syllogism in the Posterior Analytics as the kind of syllogism that would have been suggested to Aristotle by meditating on Plato's diaeresis, whereas the syllogism in the Prior Analytics indicates that as Aristotle moved away from Platonic influence his ideas widened so that he thought no syllogism unworthy of attention 1 so long as the conclusion follows from the premisses. Ross says that the value of Solmsen's view depends on whether or not the "detailed contents of the two Analytics 2 tell in favour of or against this view". Ross argues that the Prior Analytics was 'composed before the Posterior Analytics and used by Aristotle in his composition of the Posterior Analytlcs8 He bases his argument on a comparison of the contents of both books. He says "it may probably be said without fear of contradiction that none of the contents of the Prior Analytics certainly presuppose the Posterior. Let us see whether any of the contents of the Posterior AnalytiCs presuppos~ the Prior". 3 And from a scrutiny of the contents of both books 4 Ross sums up his findings in the following words~ "Taking together the explicit references and the 1. Ross,· w.n., Aristotle's Prior and Posterior Analytics, page 8. 2. Ibid. page 8. 30 Ibido page 11. 4. Ibid. pages 12 and 13. 3 Casual allusions which presuppose the Prior AnalytiCs, we find that at least the present form of the following chapters must be dated after that work: i. 2, 3, 6, 7, 9. 11. 13-17, 19.21, 23-5, 29, 33; ii. 2, 3, 8, 11, 12. 17. Thus of the thirty-four chapters of the first book eighteen explicitly (leaving out doubtful cases) presuppose the doctrine of the syllogism as it is stated at length in the Prior Analytics. If the Posterior Analytics was written before the Prior, we should have to assume a very extensive rewriting of it after 1 the Prior Analytics had been written". In mediaeval times the true nature of Aristotle's logic seems to have been misunderstood. and what they thought to be the Aristotelian syllogistic implication was something essentially distinct from the Aristotelian syllogistic implication. Lukasiewicz, commenting on this difference, says: "The difference between the Aristotelian and the - -- -- - -- -- -- --- traditional syllogism is fundamental. The Aristotelian syllogism as an implication is a proposition and as a proposition must be either true or false. The traditional syllogism is not a proposition, but a set of propositions which are not unified so as to form one single proposition. The two premisses written usually in two different lines are stated without a conjunction and the connexion of these loose premisses with the conclusion by means of 'therefore' does 1. Ross, WeD., Aristotle's Prior and Posterior Analytics. page 13. not give a new compound proposition •••• Not being a proposition the traditional syllogism is neither true nor false; it can be valid or invalid". 1 Exactly why the mediaevals mis- understood the Aristotelian syllogistic implication is not easy to say. Lukasiewicz says that it is probably due to the influence of the Stoics. As we shall see later the doctrine of material implication 2 is absolutely basic to the Aristotelian syllogistic implication. I would suggest that the great error made by the mediaevals in formulating their version of Aristotle's syllogistic was that they failed to take account of this basic and essential doctrine of material implicationw In modern thought ther~ is no great unanimity on the subject of Aristotelian formal logic. For Lukasiewicz the relationship of material implication plays an essential role in Aristotle's syllogistic doctrine and he presents Aristotle's syllogistic as adeductlve syste-m. --3-- Kneale does not agree- that the impllcatlonal form 1s essential to Aristotlets syllogistic as he says that Aristotle regarded this form of the syllogism as no more than one device among others for saying that certain premisses allow inference to certain conclusions. 4 Since Aristotle uses the lmplicational form 1. Lukasiewicz, J., Aristotle's Syllogistic, page 21. 2. For an explanation of the doctrine of material implication see B. Russell's "The Principles of Mathematics", seventh impression 1956, pages 33-41. 3e Lukasiewicz, J., Aristotle's Syllogistic from the standpoint of modern formal logic 1957. 4~ Kneale~ Wo & Mg. The Development of Logic. 1962~ page 80. 5 throughout his syllogistic doctrine and, as I will try to show later, the relationship of material implication seems to play a central role in the Aristotelian syllogistic doctrine, I fail to see any evidence·to support Kneales) view. Also Kneale regards the presentation of Aristotle's syllogistic in the form of a deductive system by Lukasiewicz as something very inter- esting, but very different from Aristotle's own idea of his work. 1 By way o,f comment one might say that Lukasiewicz does not say that this is how Aristotle visualised his.work. nor is Lukasiewicz interested in Aristotle's hopes, intentions or aspirations, but is solely concerned with exhibiting the logic of what Aristotle 'presented as a system of logic. Lo S. Stebbing sees modern mathematical logic as the grandchild of Aristotle~ She says: II ••• the achievement of the ideal of logic makes it indistinguishable from pure mathematicsg It might be supposed that the science of logic thus conceived has nothing in common with Aristotle's conception of logic. ·But that would be a mistake. There are considerable grounds for supposing that, in recognising that the ideal of logic is the exhibition of form, the mathematical logicians are carrying on the work which 2 Aristotle himself in~tiated"o Do J. Allan does not agree with this view of Stebbing. He says that Aristotle " •• did 19 Kneale, W. & M., The Development of Logic, page 80. 2. Stebbing, L. S., A Modern Introduction to Logic. Preface lX: 6 not approach logic through the study of the methods employed in mathematics or other branches of the sciences, nor was it his chief intention to furnish canons of scientific procedure.