## Notre Dame Journal of Formal Logic

### Equivalence of Syllogisms

Fred Richman

#### Abstract

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

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

Dates
First available in Project Euclid: 29 October 2004

https://projecteuclid.org/euclid.ndjfl/1099238446

Digital Object Identifier
doi:10.1305/ndjfl/1099238446

Mathematical Reviews number (MathSciNet)
MR2130479

Zentralblatt MATH identifier
1123.03018

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

Keywords
categorical syllogism

#### Citation

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

#### References

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• [7] Richards, D., "Categorical Syllogisms", Master's thesis, Florida Atlantic University, Boca Raton, 2000.