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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 22 December 2002

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1040609293

Digital Object Identifier
doi:10.1305/ndjfl/1040609293

Mathematical Reviews number (MathSciNet)
MR1271697

Zentralblatt MATH identifier
0801.03003

Subjects
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]

Citation

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. https://projecteuclid.org/euclid.ndjfl/1040609293


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References

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