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Document Details : Title: Aristotelian Diagrams for the Ancient Discussion on Privative and Infinite Negation Author(s): GARCIA-CRUZ, José David , DEMEY, Lorenz Journal: Logique et Analyse Volume: 263 Date: 2023 Pages: 159-203 DOI: 10.2143/LEA.263.0.3293992 Abstract : This paper is concerned with the ancient discussion on privative negation (e.g., ‘unjust’) and infinite negation (e.g., ‘not-just’). We formalize and compare the positions of Aristotle and Alexander of Aphrodisias, of Proclus and Ammonius Hermiae, and of Porphyry (as presented by Boethius). Each of these formalizations takes the form of a logical system, which is intended to capture the main tenets of the position it formalizes. As an additional point of reference, we also discuss the system of contemporary, Boolean predicate logic. Our comparison focuses on the diagrams that each position gives rise to, and we show how our formalizations provide a unified and systematic perspective on these diagrams. In particular, we argue that the ancient discussion on privative and infinite negation can be understood through the lens of the so-called ‘logic-sensitivity’ of Aristotelian diagrams. |
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