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• W2485752670 abstract "Abstract 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." @default.
• W2485752670 created "2016-08-23" @default.
• W2485752670 creator A5030966548 @default.
• W2485752670 date "2014-02-27" @default.
• W2485752670 modified "2023-10-18" @default.
• W2485752670 title "Quantifying Predicates, Singular Term Predicates, Negative Terms" @default.
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• W2485752670 doi "https://doi.org/10.1093/acprof:oso/9780199688845.003.0003" @default.
• W2485752670 hasPublicationYear "2014" @default.
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