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Aristotle and Aquinas

Aristotle and Aquinas The Principle of Excluded Middle Fernando Inciarte, Universität Münster There are people who never make a mistake because they never undertake anything sensible. Opinions we dare to form are like draughts which we move forward on the board: they themselves may be lost, but they have started a game which will be won. Goethe, Maximen und Reflexionen (342, 413) In his Commentary on Aristotle’s Metaphysics Aquinas introduces the Principle of Excluded Middle as complementary to the Principle of Non-Contradiction in the following way: “After having argued against those for whom both contra- dictory propositions can be true, Aristotle argues against those for whom there can be a middle between the contradictories: for them not always either part of the contradiction is true” (Postquam disputavit contra ponentes contradictoria simul esse vera, hic disputat contra ponentes esse medium inter contradictionem: hi enim dicunt non semper alteram partem contradictionis esse veram, ed. Cathala/ Spiazzi, n. 720). If so, then it is the conjunction of both principles that yields the meaning of propositional negation: if p is true, then not-p is false, and vice versa. But inasmuch as modern logic bases both principles on propositional negation, it must define them differently. Let’s explain http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png History of Philosophy and Logical Analysis Brill

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Publisher
Brill
Copyright
Copyright © Koninklijke Brill NV, Leiden, The Netherlands
ISSN
2666-4283
eISSN
2666-4275
DOI
10.30965/26664275-00201010
Publisher site
See Article on Publisher Site

Abstract

The Principle of Excluded Middle Fernando Inciarte, Universität Münster There are people who never make a mistake because they never undertake anything sensible. Opinions we dare to form are like draughts which we move forward on the board: they themselves may be lost, but they have started a game which will be won. Goethe, Maximen und Reflexionen (342, 413) In his Commentary on Aristotle’s Metaphysics Aquinas introduces the Principle of Excluded Middle as complementary to the Principle of Non-Contradiction in the following way: “After having argued against those for whom both contra- dictory propositions can be true, Aristotle argues against those for whom there can be a middle between the contradictories: for them not always either part of the contradiction is true” (Postquam disputavit contra ponentes contradictoria simul esse vera, hic disputat contra ponentes esse medium inter contradictionem: hi enim dicunt non semper alteram partem contradictionis esse veram, ed. Cathala/ Spiazzi, n. 720). If so, then it is the conjunction of both principles that yields the meaning of propositional negation: if p is true, then not-p is false, and vice versa. But inasmuch as modern logic bases both principles on propositional negation, it must define them differently. Let’s explain

Journal

History of Philosophy and Logical AnalysisBrill

Published: Apr 5, 1999

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