Aristotle's Modal Syllogisms

ARISTOTLE’S MODAL SYLLOGISMS S T O R R S McCALL Assistant Professor of Philosophy McGill University 1963 NORTH-HOLLAND P U B L I S H I N G COMPANY AMSTERDAM No part of this book may be reproduced in any form by print, microfilm 01 any other means without written permission from the publisher PRINTED IN THE NETHERLANDS PREFACE “Who would desire now to oppress the Student with the heavy burden of modals?” So wrote Manse1 in the preface to Aldrich’s Logic in 1849, and if any excuse be needed, one hundred years later, for adding to this burden it could be found in the modern revival of interest in modal logic. Nor is the book directed at the already-oppressed Student in any case : it represents simply a desire on the part of the author to get straight about a rather obscure segment of Aristotle’s logic. To my colleagues at McGill I am indebted for discussion of many points, and for the patience which they showed in dealing with the many mimeographed drafts of this book. Among those who helped me, I wish particularly to thank Professors Raymond Klibansky of McGill, Arthur Prior of Manchester, Nicholas Rescher of Pittsburgh, and Mr. Michael Dummett of Oxford, all of whom made helpful suggestions on parts of the manuscript, and Mr. Andr6 Gombay, of McGill, who read the proofs. Lastly I salute the work of W. D. Ross and Jan Lukasiewicz on the Prior Analytics. Without it, this book could scarcely have been written. Montreal 18 Jane 1962 STORRS MCCALL NOTATION The logical symbolism used in this book is based on that of the Polish school. Thus we have: N p for not # C#q if p then q KPq Pmdq p if and only if q EPq it is possible that P MP it is necessary that fi L$ it is contingent that p. QP In addition, for the premisses of Aristotle’s syllogisms we use: Aab for all a i s b Eab noais b lab some a is b some a is not b. Oab For clarity, separations will be made in formulae containing the latter expressions. Thus E Eab NIab is to be read: “ ‘No a is b’ is equivalent to ‘It is not the case that some u is b’ ”. CHAPTER I T H E PROBLEM O F T H E A P O D E I C T I C M O O D S 1. Introduction Aristotle’s system of modal syllogisms, to be found in chapters 3 and 8-22 of the first book of the Prior Arzulytics, has been open to public inspection for over 2300 years. And yet perhaps no other piece of philosophical writing has had such consistently bad reviews. Beginning with Aristotle’s successor Theophrastus (“he of the graceful style”), and continuing through to the modern logician Jan Lukasiewicz, this part of the Philosopher’s teachings has been alternately the subject of enthusiastic rebuttal and unjustified neglect. In extenuation, two things must be admitted. Firstly, the subject is of extreme difficulty: there is a mediaeval saying warning that “De modalibus non gustabit asinus”. Secondly, Aristotle’s treatment of modal syllogisms has its share of what may with charity be called obscurities, without charity errors. The present author does no more than claim to find a smaller number of errors and a greater degree of consistency in the work than the majority of his predecessors. 2. Historical survey The fate which Aristotle’s modal syllogisms have suffered at the hands of their expositors and critics has not in general been a kind one. Eukasiewicz’s judgement is that, in contrast to his assertoric syllogistic, “Aristotle’s modal syllogistic is almost incomprehensible because of its many faults and inconsistencies” 1, and this, or something milder, must have been the opinion of the numerous 1 Aristotle‘s Syllogistic, 2nd ed., Oxford 1957, p. 133. 2 T H E PROBLEM OF T H E APODEICTIC MOODS philosophers who have tried to reform the system since its appe