Functoriality and grammatical role in syllogisms. (English) Zbl 0801.03003

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

Notre Dame J. Formal Logic 35, No. 1, 41-66 (1994).

Summary: 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.

MSC:

03A05

Philosophical and critical aspects of logic and foundations

Keywords:

syllogistic; functoriality; change of grammatical role; semantics; syllogisms

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