Square of opposition

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:

Image:Square_of_opposition.png

These rules apply:

1. At least one of the universal statements must be false.
2. Contradictory statements have opposite truth values.
3. Universal statements entail their subalterns.
4. At least one of the particular statements must be true.

Only the first two rules are explicitly stated by Aristotle (in his work, De Interpretatione) but the other two can be inferred.

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.

External link

• Stanford Encyclopedia of Philosophy article