Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 45, Number 4 (2004), 215-233.
Equivalence of Syllogisms
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.
Notre Dame J. Formal Logic, Volume 45, Number 4 (2004), 215-233.
First available in Project Euclid: 29 October 2004
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Primary: 03B99: None of the above, but in this section
Richman, Fred. Equivalence of Syllogisms. Notre Dame J. Formal Logic 45 (2004), no. 4, 215--233. doi:10.1305/ndjfl/1099238446. https://projecteuclid.org/euclid.ndjfl/1099238446