History and Philosophy of Logic 40 (1):1-11 (2019)

Authors
Justin Vlasits
University Tübingen
Abstract
How does Aristotle think about sentences like ‘Every x is y’ in the Prior Analytics? A recently popular answer conceives of these sentences as expressing a mereological relationship between x and y: the sentence is true just in case x is, in some sense, a part of y. I argue that the motivations for this interpretation have so far not been compelling. I provide a new justification for the mereological interpretation. First, I prove a very general algebraic soundness and completeness result that unifies the most important soundness and completeness results to date. Then I argue that this result vindicates the mereological interpretation. In contrast to previous interpretations, this argument shows how Aristotle’s conception of predication in mereological terms can do important logical work.
Keywords Aristotle  Logic  Algebraic Semantics  Mereology  Predication
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DOI 10.1080/01445340.2018.1474428
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References found in this work BETA

What is a Syllogism?T. 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.
Aristotle.Jonathan Barnes - 1975 - In R. M. Hare, Jonathan Barnes & Henry Chadwick (eds.), Founders of Thought. Oxford University Press.
A Mathematical Model of Aristotle’s Syllogistic.John Corcoran - 1973 - Archiv für Geschichte der Philosophie 55 (2):191-219.

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