nied)--such, namely, that one of them is false
and the other true. This is the case with the forms A. and O., and E.
and I., in the same matter. If it be true that _All men are wise_, it is
false that _Some men are not wise_ (equivalent by obversion to _Some
men are not-wise_); or else, since the 'Some men' are included in the
'All men,' we should be predicating of the same men that they are both
'wise' and 'not-wise'; which would violate the principle of
Contradiction. Similarly, _No men are wise_, being by obversion
equivalent to _All men are not-wise_, is incompatible with _Some men are
wise_, by the same principle of Contradiction.

But, again, if it be false that _All men are wise_, it is always true
that _Some are not wise_; for though in denying that 'wise' is a
predicate of 'All men' we do not deny it of each and every man, yet we
deny it of 'Some men.' Of 'Some men,' therefore, by the principle of
Excluded Middle, 'not-wise' is to be affirmed; and _Some men are
not-wise_, is by obversion equivalent to _Some men are not wise_.
Similarly, if it be false that _No men are wise_, which by obversion is
equivalent to _All men are not-wise_, then it is true at least that
_Some men are wise_.

By extending and enforcing the doctrine of relative terms, certain other
inferences are implied in the contrary and contradictory relations of
propositions. We have seen in chap. iv. that the contradictory of a
given term includes all its contraries: 'not-blue,' for example,
includes red and yellow. Hence, since _The sky is blue_ becomes by
obversion, _The sky is not not-blue_, we may also infer _The sky is not
red_, etc. From the truth, then, of any proposition predicating a given
term, we may infer the falsity of all propositions predicating the
contrary terms in the same relation. But, on the other hand, from the
falsity of a proposition predicating a given term, we cannot infer the
truth of the predication of any particular contrary term. If it be false
that _The sky is red_, we cannot formally infer, that _The sky is blue_
(_cf._ chap. iv. Sec. 8).

Sec. 8. Sub-contrariety is the relation of two propositions, concerning the
same matter that may both be true but are never both false. This is the
case with I. and O. If it be true that _Some men are wise_, it may also
be true that _Some (other) men are not wise_. This follows from the
maxim in chap. vi. Sec. 6, not to go beyond the evidence.

For if it be true that _Some men