Ancient Logic and Its Modern Interpretations: Proceedings of by Norman Kretzmann (auth.), John Corcoran (eds.)

By Norman Kretzmann (auth.), John Corcoran (eds.)

During the final part century there was innovative growth in common sense and in logic-related components comparable to linguistics. HistoricaI wisdom of the origins of those topics has additionally elevated considerably. therefore, it's going to look that the matter of settling on the level to which historic logical and linguistic theories admit of exact interpretation in sleek phrases is now ripe for research. the aim of the symposium used to be to assemble logicians, philosophers, linguists, mathematicians and philologists to provide study effects concerning the above challenge with emphasis on common sense. shows and discussions on the symposium centred themselves into 5 parts: historic semantics, smooth examine in historical good judgment, Aristotle's good judgment, Stoic common sense, and instructions for destiny examine in old good judgment and logic-related parts. Seven of the papers which look less than have been initially awarded on the symposium. In each case, dialogue on the symposium resulted in revisions, every so often to wide revisions. The editor urged nonetheless additional revisions, yet in each case the writer was once the finaljudge of the paintings that looks lower than his name.

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Additional info for Ancient Logic and Its Modern Interpretations: Proceedings of the Buffalo Symposium on Modernist Interpretations of Ancient Logic, 21 and 22 April, 1972

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1-25,304. 8 This sort of development was suggested to me by John Corcoran, to whom I am also indebted for suggestions incorporated at several places. PART TWO MODERN RESEARCH IN ANCIENT LOGIC IAN MUELLER GREEK MATHEMATICS AND GREEK LOGIC 1. INTRODUCTION By 'logic' I mean 'the analysis of argument or proof in terms of form'. The two main examples of Greek logic are, then, Aristotle's syHogistic developed in the fint twenty-two chapters of the Prior Analytics and Stoic propositionallogic as reconstructed in the twentieth century.

Throughout antiquity, indeed down into the nineteenth century, the latter step was not seen as a matter of logic. 12 The inference was brought into the domain of logic only with the invention of the quantifier and the discovery of the rules governing it. I have analyzed Elements 1,1 in order to show that Euclid's tacit logic is at least the first order predicate calculus, nothing less. His logic may even be more than that, since representing his reasoning in the first order predicate calculus would seem to require reformulations foreign to the spirit of the Elements.

5) and (4) (a 'trivial consequence' of (l» by the second anapodeiktos. And (8) is related similarly to (6) and (7). If (2) is taken as an expression of trichotomy, then (9) follows from (2), (5), and (8) by two applications of the fifth anapodeiktos. 2 There are many other cases in the Elements which could be analyzed simiIarly. But since reasoning in accordance with the ruIes of a Iogic does not in itseIf impIy knowIedge of the Iogic, the possibiIity of anaIyzing a Euclidean proof in terms of Stoic propositional Iogic does not justify attributing to Euclid a knowledge of Stoic logic.

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