A Mathematical Model of Aristotle's Syllogistic

Abstract
In the present article we attempt to show that Aristotle's syllogistic is an underlying logiC which includes a natural deductive system and that it isn't an axiomatic theory as had previously been thought. We construct a mathematical model which reflects certain structural aspects of Aristotle's logic. We examine the relation of the model to the system of logic envisaged in scattered parts of Prior and Posterior Analytics. Our interpretation restores Aristotle's reputation as a logician of consummate imagination and skill. Several attributions of shortcomings and logical errors to Aristotle are shown to be without merit. Aristotle's logic is found to be self-sufficient in several senses: his theory of deduction is logically sound in every detail. (His indirect deductions have been criticized, but incorrectly on our account.) Aristotle's logic presupposes no other logical concepts, not even those of propositional logic. The Aristotelian system is seen to be complete in the sense that every valid argument expressible in his system admits of a deduction within his deductive system: every semantically valid argument is deducible.
Keywords SYLLOGISTIC  PREMISE-CONCLUSION ARGUMENT  PREMISE-CHAIN-CONCLUSION DEDUCTION  IMPLICATION/DEDUCTIBILITY  COMPLETENESS  UNDERLYING LOGIC  ARISTOTLE  LUKASIEWICZ  TIMOTHY SMILEY  DIRECT/INDIRECT DEDUCTIONS
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DOI 10.1515/agph.1973.55.2.191
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A Brief History of Natural Deduction.Francis Jeffry Pelletier - 1999 - History and Philosophy of Logic 20 (1):1-31.
What Is Aristotelian Ecthesis?Robin Smith - 1982 - History and Philosophy of Logic 3 (2):113-127.
Essay Review.Gasser James - 1991 - History and Philosophy of Logic 12 (2):235-240.

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A Reconstruction of Aristotle's Modal Syllogistic.Marko Malink - 2006 - History and Philosophy of Logic 27 (2):95-141.
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Aristotle on Mathematical Truth.Phil Corkum - 2012 - British Journal for the History of Philosophy 20 (6):1057-1076.
What Is Aristotelian Ecthesis?Robin Smith - 1982 - History and Philosophy of Logic 3 (2):113-127.

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