are wise_, it may indeed be true that
_All are_ (this being the subalternans): and if _All are_, it is (by
contradiction) false that _Some are not_; but as we are only told that
_Some men are_, it is illicit to infer the falsity of _Some are not_,
which could only be justified by evidence concerning _All men_.

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.

Sec. 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