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 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.