Logica Universalis 12 (1-2):9-35 (2018)

Authors
John Corcoran
State University of New York, Buffalo
Abstract
This expository paper on Aristotle’s prototype underlying logic is intended for a broad audience that includes non-specialists. It requires as background a discussion of Aristotle’s demonstrative logic. Demonstrative logic or apodictics is the study of demonstration as opposed to persuasion. It is the subject of Aristotle’s two-volume Analytics, as its first sentence says. Many of Aristotle’s examples are geometrical. A typical geometrical demonstration requires a theorem that is to be demonstrated, known premises from which the theorem is to be deduced, and a deductive logic by which the steps of the deduction proceed. Every demonstration produces knowledge of its conclusion for every person who comprehends the demonstration. Aristotle presented a general truth-and-consequence theory of demonstration meant to apply to all demonstrations: a demonstration is an extended argumentation that begins with premises known to be truths and that involves a chain of reasoning showing by deductively evident steps that its conclusion is a consequence of its premises. In short, a demonstration is a deduction whose premises are known to be true. Aristotle’s general theory of demonstration required a prior general theory of deduction presented in the Prior Analytics. His general immediate-deduction-chaining theory of deduction was meant to apply to all deductions: any deduction that is not immediately evident is an extended argumentation that involves a chaining of immediately evident steps that shows its final conclusion to follow logically from its premises. His deductions, both direct and indirect, were rule-based and not tautology-based. The idea of tautology-based deduction, which dominated modern logic in the early years of the 1900s, is nowhere to be found in Analytics. Rule-based deduction was rediscovered by modern logicians. To illustrate his general theory of deduction, Aristotle presented a prototype: an ingeniously simple and mathematically precise special case traditionally known as the categorical syllogistic. With reference only to propositions of the four so-called categorical forms, he painstakingly worked out exactly what those immediately evident deductive steps are and how they are chained to complete deductions. In his specialized prototype theory, Aristotle explained how to deduce from a given categorical premise set, no matter how large, any categorical conclusion implied by the given set. He did not extend this treatment to non-categorical deductions, thus setting a program for future logicians. The prototype, categorical syllogistic, was seen by Boole as a “first approximation” to a comprehensive logic. Today, however it appears more as the first of the dozens of logics already created and as the first exemplification of a family that continues to expand.
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DOI 10.1007/s11787-018-0189-4
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References found in this work BETA

The Structure of Scientific Revolutions.David Bohm - 1964 - Philosophical Quarterly 14 (57):377-379.
Aristotle's Prior Analytics and Boole's Laws of Thought.John Corcoran - 2003 - History and Philosophy of Logic. 24 (4):261-288.
The Founding of Logic.John Corcoran - 1994 - Ancient Philosophy 14 (S1):9-24.
What is a Syllogism?T. J. Smiley - 1973 - Journal of Philosophical Logic 2 (1):136 - 154.
Aristotle's Demonstrative Logic.John Corcoran - 2009 - History and Philosophy of Logic 30 (1):1-20.

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Citations of this work BETA

Universal Logic: Evolution of a Project.Jean-Yves Beziau - 2018 - Logica Universalis 12 (1-2):1-8.

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