# Lewis Carroll's Bilateral Diagram

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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

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A diagram showing the relations among categorical propositions is known as the traditional square of opposition [2, p. 217]. Two propositions are contradictories if one is the negation of the other. Propositions A and O, and propositions I and E are contradictories. Two propositions are contraries if they cannot both be true. Two propositions are subcontraries if they cannot both be false. Proposition A is called superaltern, I is called subaltern, and the coresponding relation is called subalternation. The same definitions are aplied to E and O [2, pp. 214-217]. Under the assumption that class S is not empty, propositions A and E are contraries, propositions I and O are subcontraries, and superaltern implies subaltern.

[1] L. Carroll, *Symbolic Logic and The Game of Logic*, New York: Dover, 1958.

[2] I. M. Copi and C. Cohen, *Introduction to Logic*, 9th ed., New York: Macmillan, 1994 pp. 214-218.

## Permanent Citation

"Lewis Carroll's Bilateral Diagram"

http://demonstrations.wolfram.com/LewisCarrollsBilateralDiagram/

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Published: March 7 2011