A Completed System for Robin Smith's Incomplete Ecthetic Syllogistic

Abstract : In this paper we first show that Robin Smith's ecthetic system SE for Aristotle's assertoric syllogistic is not complete, despite what is claimed by Smith. SE is then not adequate to establish that ecthesis allows one to dispense with indirect or per impossibile deductions in Aristotle's assertoric logic. As an alternative to SE, we then present a stronger system EC which is adequate for this purpose. EC is a nonexplosive ecthetic system which is shown to be sound and complete with respect to all valid syllogistic arguments with a consistent set of premises.
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https://hal-univ-rennes1.archives-ouvertes.fr/hal-01586049
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Submitted on : Tuesday, September 12, 2017 - 1:57:57 PM
Last modification on : Thursday, November 29, 2018 - 4:42:02 PM

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Pierre Joray. A Completed System for Robin Smith's Incomplete Ecthetic Syllogistic. Notre Dame Journal of Formal Logic, University of Notre Dame, 2017, 58 (3), pp.329--342. ⟨10.1215/00294527-3882234⟩. ⟨hal-01586049⟩

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