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Articulating Medieval Logic$
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Terence Parsons

Print publication date: 2014

Print ISBN-13: 9780199688845

Published to Oxford Scholarship Online: June 2014

DOI: 10.1093/acprof:oso/9780199688845.001.0001

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Aristotle’s Proofs of Conversions and Syllogisms

Aristotle’s Proofs of Conversions and Syllogisms

(p.21) 2 Aristotle’s Proofs of Conversions and Syllogisms
Articulating Medieval Logic

Terence Parsons

Oxford University Press

In Prior Analytics Aristotle proves the conversion principles, using three logical techniques: reductio (indirect derivation), exposition (a kind of existential instantiation: given ‘Some S is a P’, introduce a previously unused name m, and write ‘m is an S’ and ‘m is a P’), and expository syllogism (given ‘m is a P’ and ‘m is an S’ infer ‘Some S is a P’). He assumes four basic forms of syllogism, and uses them together with reductio, exposition, and expository syllogisms to prove the remaining forms. The four basic forms can be proved too, though this was unknown to him or to medieval logicians. Monotonicity properties of the determiners ‘every’, ‘no’, and ‘some’ are explained; Aristotle’s four basic argument forms allow easy proofs of their monotonicity properties. By the 13th century a memorizable verse was developed that encodes Aristotle’s validation of all syllogistic forms from the basic four.

Keywords:   Aristotle, conversion, exposition, reduction, monotonicity, syllogism

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