Answer to Question #166487 in Philosophy for Ajay Kaswan

Question

Explain and illustrate all logical relationships between categorical propositions through traditional square of opposition.

Answer 1

O propositions, or particular negations take the form: Some S are not P

A propositions, or universal affirmatives take the form: All S are P.

E propositions, or universal negations take the form: No S are P.

I propositions, or particular affirmatives take the form: Some S are P.

1. A and O propositions are contradictory, as are E and I propositions. Propositions are contradictory when the truth of one implies the falsity of the other, and conversely.
2. A and E propositions are contrary. Propositions are contrary when they cannot both be true. universal negations take the form: No S are P.
3. Next, I and O propositions are sub contrary. Propositions are sub contrary when it is impossible for both to be false
4. Two propositions are said to stand in the relation of sub alternation when the truth of the first (“the superaltarn") implies the truth of the second (“the subaltern”), but not conversely