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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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 Quantifying Predicates, Singular Term Predicates, Negative Terms

 Quantifying Predicates, Singular Term Predicates, Negative Terms

Chapter:
(p.56) 3 Quantifying Predicates, Singular Term Predicates, Negative Terms
Source:
Articulating Medieval Logic
Author(s):

Terence Parsons

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199688845.003.0003

Medieval logicians expanded Aristotle’s notation; some rules naturally come along with the expansions. Predicates are quantified, as in ‘No donkey is every animal’, and negations are sprinkled throughout sentences, so quantifier equipollences are introduced, such as ‘not some P’ is equivalent to ‘every P not’. One can now say that prefixing ‘not’ to any proposition produces its contradictory; this makes reductio proofs widely applicable. When singular terms occur, new rules are needed to let them permute with each other, with negations, and with denoting phrases. Conversion “by contraposition” is discussed; an example is converting ‘Every P is a Q’ to and from ‘Every non-Q is a non-P’; this is valid except for counterexamples involving empty terms. (‘Every chimera is an animal’ is false, but ‘Every non-animal is a non-chimera’ is true.) A set of rules of inference are given which are complete for the notation developed up to this point.

Keywords:   contraposition, equipollence, conversion, Aristotle

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