Which of the four basic categorical forms are consistent with one another?

A-claim (universal affirmative): All S is P / All S are P

E-claim (universal negative): No S is P / No S are P

I-claim (particular affirmative): Some S is P / Some S are P

O-claim (particular negative): Some S is not P / Some S are not P

  • 2
    Hi, welcome to PSE. What does "consistent with one another" mean?
    – Conifold
    Sep 23, 2015 at 0:24
  • 1
    The answer is the following are consistent sets: {A, I} , {E, O}, {I,O} . The inconsistent sets are {E, I} and {A, O}. The contradictory set is {A, E}. This is almost definitely homework...
    – virmaior
    Sep 23, 2015 at 2:10
  • See Square of Opposition. Sep 23, 2015 at 6:59

1 Answer 1


I guess, "inconsistent" is a little ambiguous. I've just completed an online quiz whose explanation says the following: "inconsistent" means that there is no possible way for both statements to be true at the same time.

In this vein, A and E are NOT inconsistent with each other. If there is no single object P in existence, then for any attribute Q it will be both true that (i) all Ps are Q (simply because there is no P that is not Q) and (ii) that no Ps are Q (well, because there are no Ps at all).


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