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Aristotle and Logical Theory
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In this short book the author argues convincingly that many central issues of modern mathematical logic can be discussed fruitfully in the context of Aristotle's original logical system and that, once this context has been adopted, it will be possible for modern logicians to benefit more directly from Aristotle's own insights and theories. According to this book, the core concept in Aristotle's logical theory is "logical consequence" rather than "logical truth"--thus aligning Aristotle with Alfred Tarski and Alonzo Church and in opposition to Gottlob Frege and Willard Quine. Aristotle's view of deduction (logical reasoning) is seen to be closer to the more modern "natural" view attributed to Stanislaw Jaskowski and to Gerhard Gentzen than to the older "axiomatic" view advocated by Frege and Russell. In addition, the now-standard "countermodels" method of establishing independence (invalidity), which was adopted by Hilbert and opposed by Frege, is seen as an integral feature of Aristotle's methodology. The interpretation of Aristotle used in this work stems from scholarship by Timothy Smiley [J. Philos. Logic 2 (1973), 136-154] and by the reviewer [J. Symbolic Logic 37 (1972), 696-702]. Accordingly, the author disputes the widely accepted interpretation due to Jan Lukasiewicz [Aristotle's syllogistic from the standpoint of modern formal logic, Clarendon Press, Oxford, 1951]. The book is derived from the author's doctoral thesis supervised by Saul
Kripke and it is dedicated to Smiley whose views on logic and Aristotle are acknowledged. More specific features of the content of the book have been discussed by Michael Scanlan and the reviewer [Philos. Quart. 32 (1982), 76-86]. Also relevant is an article by Scanlan [Hist. Philos. Logic 4 (1983), 1-8].