Mereology in Aristotle's Assertoric Syllogistic

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.

The Discovery of Principles in Prior Analytics 1.30

“…On the 'heterodox' reading of the dictum de omni, see Barnes 2007, 386-412;Morison 2008, 212-15;2015, 131-9;Malink 2013, 45-72. 100 Smyth 1971Malink 2013, 73-85;Vlasits 2019, 2-11. 101 Malink 20092013, 128-30.…”