Open Access
Translator Disclaimer
Winter 1994 Functoriality and Grammatical Role in Syllogisms
Marie La Palme Reyes, John Macnamara, Gonzalo E. Reyes
Notre Dame J. Formal Logic 35(1): 41-66 (Winter 1994). DOI: 10.1305/ndjfl/1040609293


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.


Download Citation

Marie La Palme Reyes. John Macnamara. Gonzalo E. Reyes. "Functoriality and Grammatical Role in Syllogisms." Notre Dame J. Formal Logic 35 (1) 41 - 66, Winter 1994.


Published: Winter 1994
First available in Project Euclid: 22 December 2002

zbMATH: 0801.03003
MathSciNet: MR1271697
Digital Object Identifier: 10.1305/ndjfl/1040609293

Primary: 03B20
Secondary: 03B65 , 03G30

Rights: Copyright © 1994 University of Notre Dame


Vol.35 • No. 1 • Winter 1994
Back to Top