lity.

Again, in respect of concurrent truth and falsehood there is a certain
symmetry.

Contradictories cannot both be true, nor can they both be false.

Contraries may both be false, but cannot both be true.

Sub-contraries may both be true, but cannot both be false.

Subalterns may both be false and both true. If the Universal is true,
its subalternate Particular is true: but the truth of the Particular
does not similarly imply the truth of its Subalternating Universal.

This last is another way of saying that the truth of the Contrary
involves the truth of the Contradictory, but the truth of the
Contradictory does not imply the truth of the Contrary.

There, however, the symmetry ends. The sides and the diagonals of the
Square do not symmetrically represent degrees of incompatibility, or
opposition in the ordinary sense.

There is no incompatibility between two Sub-contraries or a Subaltern
and its Subalternant. Both may be true at the same time. Indeed, as
Aristotle remarked of I and O, the truth of the one commonly implies
the truth of the other: to say that some of the crew were drowned,
implies that some were not, and _vice versa_. Subaltern and
Subalternant also are compatible, and something more. If a man has
admitted A or E, he cannot refuse to admit I or O, the Particular of
the same Quality. If All poets are irritable, it cannot be denied
that some are so; if None is, that Some are not. The admission of the
Contrary includes the admission of the Contradictory.

Consideration of Subalterns, however, brings to light a nice ambiguity
in Some. It is only when I is regarded as the Contradictory of E,
that it can properly be said to be Subalternate to A. In that case the
meaning of Some is "not none," _i.e._, "Some at least". But when Some
is taken as the sign of Particular quantity simply, _i.e._, as meaning
"not all," or "some at most," I is not Subalternate to A, but opposed
to it in the sense that the truth of the one is incompatible with the
truth of the other.

Again, in the diagram Contrary opposition is represented by a side and
Contradictory by the diagonal; that is to say, the stronger form of
opposition by the shorter line. The Contrary is more than a denial: it
is a counter-assertion of the very reverse, [Greek: to enantion].
"Are good administrators always good speakers?" "On the contrary, they
never are." This is a much stronger opposition, in the ordinary sense,
than a modest contradict