But if it be false that _Some men are wise_, it is true that _Some men are not wise_; for, by contradiction, if _Some men are wise_ is false, _No men are wise_ is true; and, therefore, by subalternation, _Some men are not wise_ is true. § 9. The Square of Opposition.--By their relations of Subalternation, Contrariety, Contradiction, and Sub-contrariety, the forms A. I. E. O. (having the same matter) are said to stand in Opposition: and Logicians represent these relations by a square having A. I. E. O. at its corners: A. Contraries E. S Co s S u nt e u b ra i b a di r a l ct o l t ct o t e di r e r ra i r n nt e n s Co s s I. Sub-contraries O. As an aid to the memory, this diagram is useful; but as an attempt to represent the logical relations of propositions, it is misleading. For, standing at corners of the same square, A. and E., A. and I., E. and O., and I. and O., seem to be couples bearing the same relation to one another; whereas we have seen that their relations are entirely different. The following traditional summary of their relations in respect of truth and falsity is much more to the purpose: (1) If A. is true, I. is true, E. is false, O. is false. (2) If A. is false, I. is unknown, E. is unknown, O. is true. (3) If I. is true, A. is unknown, E. is false, O. is unknown. (4) If I. is false, A. is false, E. is true, O. is true. (5) If E. is true, A. is false, I. is false, O. is true. (6) If E. is false, A. is unknown, I. is true, O. is unknown. (7) If O. is true, A. is false, I. is unknown, E. is unknown. (8) If O. is false, A. is true, I. is true, E. is false. Where, however, as in cases 2, 3, 6, 7, alleging either the falsity of universals or the truth of particulars, it follows that two of the three Opposites are unknown, we may conclude further that one of them must be true and the other false, because the two unknown are always Contradictories. § 10. Secondary modes of Immediate Inference are obtained by applying the process of Conversion or Obversion to the results already obtained by the other process. The best known secondary form of Immediate Inference is the Contrapositive, and this is the converse of the obverse of a given proposition. Thus: DATUM. OBVERSE. CONTRAPOSITIVE. A. _All S is P_ ∴ _No S is not-P_ ∴ _No not-P is S_ I. _Some S is P_ ∴ _Some S is not not-P_ ∴ (none) E. _No S is P_ ∴ _All S is not-P_ ∴ _Some not-P is S_ O. _Some S is not P_ ∴ _Some S is not-P_ ∴ _Some not-P is S_