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.