Notre Dame Journal of Formal Logic

Equivalence of Syllogisms

Fred Richman


We consider two categorical syllogisms, valid or invalid, to be equivalent if they can be transformed into each other by certain transformations, going back to Aristotle, that preserve validity. It is shown that two syllogisms are equivalent if and only if they have the same models. Counts are obtained for the number of syllogisms in each equivalence class. For a more natural development, using group-theoretic methods, the space of syllogisms is enlarged to include nonstandard syllogisms, and various groups of transformations on that space are studied.

Article information

Notre Dame J. Formal Logic, Volume 45, Number 4 (2004), 215-233.

First available in Project Euclid: 29 October 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03B99: None of the above, but in this section

categorical syllogism


Richman, Fred. Equivalence of Syllogisms. Notre Dame J. Formal Logic 45 (2004), no. 4, 215--233. doi:10.1305/ndjfl/1099238446.

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