Square of Opposition:

Both A and I are affirmative propositions; they differ only in quantity. A is the more sweeping statement, because it makes a claim about all Ss -- that they are P.

I is more cautious. When we say that some S are P, we are not committing ourselves to any claim about the whole class of Ss.


We can see that if A is true, I must be true as well. If all Ss are P, then it is safe to say that some Ss are P -- though we usually wouldn't bother to say it.

For exactly the same reasons, the O proposition is subalternate to the E proposition. In this case, both propositions are negative; still, the universal one always implies the particular.

This illustrates the concept of subalternates with true universals.

When we consider false statements, the tables are turned. If the I proposition is false, then the A must be false as well. If not even one S is P, then it is certainly false that all S are P.

In the same way, on the negative side of the square, if not even one S is not P, then it is certainly false that no S is P; if O is false, E is false as well.


Suppose that A is false, Does that mean I must be false as well? No. Even if it isn't true that all politicians are honest, it might still be true that some are. Similarly, the falsity of an E proposition leaves the truth or falsity of the O undetermined. It would be false, for example, to say that no natural substances cause cancer, but it is still possible that some do not.

This illustrates the concept of subalternates with false particulars.

Contraries | Contradictories |
Subalternates | Subcontraries

Square of Opposition

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