Square of opposition
From Freepedia
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.
For any subject S and predicate P, these rules are supposed to apply:
- At least one of the universal statements must be false.
- Contradictory statements have opposite truth values.
- Universal statements entail their subalterns.
- 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.
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 know as the problem of existential import, and received a variety of proposed resolutions, as well as being regarded as a flaw of syllogistic.
