Notre Dame Journal of Formal Logic

Functoriality and Grammatical Role in Syllogisms

Marie La Palme Reyes, John Macnamara, and Gonzalo E. Reyes

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We specify two problems in syllogistic: the lack of functoriality of predicates (although a thief is a person, a good thief may not be a good person) and the change of grammatical role of the middle term, from subject to predicate, in some syllogisms. The standard semantics, the class interpretation, by-passes these difficulties but, we argue, in a manner that is at odds with logical intuition. We propose a semantics that is category theoretic to handle these difficulties. With this semantics we specify when syllogisms are valid and we set limits to the class interpretation. To perform this task we show how to construct the categorical notion of an entity in a system of kinds. We devote two brief sections to an argument that our approach is very much in the spirit of Aristotle.

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Notre Dame J. Formal Logic, Volume 35, Number 1 (1994), 41-66.

First available in Project Euclid: 22 December 2002

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Zentralblatt MATH identifier

Primary: 03B20: Subsystems of classical logic (including intuitionistic logic)
Secondary: 03B65: Logic of natural languages [See also 68T50, 91F20] 03G30: Categorical logic, topoi [See also 18B25, 18C05, 18C10]


La Palme Reyes, Marie; Macnamara, John; Reyes, Gonzalo E. Functoriality and Grammatical Role in Syllogisms. Notre Dame J. Formal Logic 35 (1994), no. 1, 41--66. doi:10.1305/ndjfl/1040609293.

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