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Indirect Proof and Inversions of Syllogisms
Bulletin of Symbolic Logic 25 (2):196-207 (2019)
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.My notes
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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.
The Place of Reduction in Aristotle's Prior Analytics.George Boger - forthcoming - History and Philosophy of Logic:1-34.
Aristotle's Proofs Through the Impossible in Prior Analytics 1.15.Riccardo Zanichelli - 2023 - History and Philosophy of Logic 44 (4):395-421.
References found in this work
A. S. Troelstra and H. Schwichtenberg. Basic proof theory. Second edition of jsl lxiii 1605. Cambridge tracts in theoretical computer science, no. 43. cambridge university press, cambridge, new York, etc., 2000, XII + 417 pp.Roy Dyckhoff - 2001 - Bulletin of Symbolic Logic 7 (2):280-280.
A Mathematical Model of Aristotle’s Syllogistic.John Corcoran - 1973 - Archiv für Geschichte der Philosophie 55 (2):191-219.
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