Indirect Proof and Inversions of Syllogisms

Bulletin of Symbolic Logic 25 (2):196-207 (2019)
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Abstract

By considering the new notion of theinversesof syllogisms such asBarbaraandCelarent, we show how the rule ofIndirect Proof, in the form (no multiple or vacuous discharges) used by Aristotle, may be dispensed with, in a system comprising four basic rules of subalternation or conversion and six basic syllogisms.

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Citations of this work

Analysis in Prior Analytics I.45.Igor Martinjak - 2022 - History and Philosophy of Logic 43 (3):207-231.
Aristotle's Proofs Through the Impossible in Prior Analytics 1.15.Riccardo Zanichelli - 2023 - History and Philosophy of Logic 44 (4):395-421.
The Place of Reduction in Aristotle's Prior Analytics.George Boger - forthcoming - History and Philosophy of Logic:1-34.

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References found in this work

What is a syllogism?Timothy J. Smiley - 1973 - Journal of Philosophical Logic 2 (1):136 - 154.
Completeness of an ancient logic.John Corcoran - 1972 - Journal of Symbolic Logic 37 (4):696-702.
Stoic Syllogistic.Susanne Bobzien - 1996 - Oxford Studies in Ancient Philosophy 14:133-92.
A Mathematical Model of Aristotle’s Syllogistic.John Corcoran - 1973 - Archiv für Geschichte der Philosophie 55 (2):191-219.

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