Square of opposition

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Image:Square of Opposition.png

The Square of Opposition is a term from the study of Aristotelian logic or Term Logic in which the logical relationship between various types of sentences is spelled out.

Contents 1 Summary 2 Problem of existential import 3 See also 4 External links

Summary

For any subject S and predicate P, these rules explicitly stated by Aristotle (in his work, De Interpretatione) are supposed to apply:

1. Contraries cannot both be true. (At least one of the Universals must be false)
2. Contradictory statements have opposite truth values.

From the above, it follows that:

1. Universal statements entail their subalterns.
2. Subcontraries cannot both be false (At least one of the particular statements must be true).

Problem of existential import

The Square of Opposition has largely fallen out of favour in modern times, and indeed is incompatible with modern predicate calculus. This is because, in modern logic, "every S is a P" does not actually imply the existence of any S's. Therefore, the Aristotelian move to "some S is a P" (which does imply the existence of an S) does not follow in modern logic. The question as to how properly to interpret Aristotelian logic on this point was known as the problem of existential import. Some approaches include:

1. Dismissing the Aristotelian syllogistic as fundamentally flawed
2. Restricting the Aristotelian syllogistic to cases where all predicates have members
3. Removing existential suppositions from the Particular Negative.

See also

• Boole's syllogistic
• Free logic

External links

• Stanford Encyclopedia of Philosophy article
• History of the Problem of Existential Importzh:对立四边形