# Lewis Carroll's Diagram and Categorical Syllogisms

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Aristotelian logic, or the traditional study of deduction, deals with four so-called categorical or subject-predicate propositions, which can be defined by S a P ⇔ All S is P (universal affirmative or A proposition), S i P ⇔ Some S is P (particular affirmative or I proposition), S e P ⇔ No S is P (universal negative or E proposition), S o P ⇔ Some S is not P (particular negative or O proposition).

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Contributed by: Izidor Hafner (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The so-called figure of a categorical syllogism is determined by the possible position of middle term. There are four figures:

M x P, S x M ⊨ S x P, P x M, S x M ⊨ S x P, M x P, M x S ⊨ S x P, P x M, M x S ⊨ S x P, where x is a, i, e, or o.

This version of Carroll's diagrams was found in [2], p. 112. See also the Wikipedia entry for Categorical proposition.

[1] R. Audi, ed., *The Cambridge Dictionary of Philosophy*, Cambridge: Cambridge University Press, 1995 pp. 780–782.
[2] L. Borkowski, *Elementy logiki formalnej* (*Elements of Formal Logic*, in Polish), 3rd ed., Warsaw: Wyd, 1976.
[3] L. Carroll, *Symbolic Logic and the Game of Logic*, New York: Dover, 1958.
[4] I. M. Copi and C. Cohen, *Introduction to Logic*, 9th ed., New York: Macmillan, 1994 pp. 214–218.

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"Lewis Carroll's Diagram and Categorical Syllogisms"

http://demonstrations.wolfram.com/LewisCarrollsDiagramAndCategoricalSyllogisms/

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Published: March 7 2011