Subalternation .-- Opposition being the relation of propositions that have the same matter and differ only in form (as A., E., I., O.), propositions of the forms A.and I.are said to be Subalterns in relation to one another, and so are E.and O.; the universal of each quality being distinguished as 'subalternans,' and the particular as 'subalternate.' It follows from the principle of Identity that, the matter of the propositions being the same, if A.is true I.is true, and that if E.is true O.is true; for A.and E.predicate something of _All S_ or _All men_; and since I.and O.make the same predication of _Some S_ or _Some men_, the sense of these particular propositions has already been predicated in A.or E.If _All S is P, Some S is P_; if _No S is P, Some S is not P_; or, if _All men are fond of laughing, Some men are_; if _No men are exempt from ridicule, Some men are not_.
Similarly, if I.is false A.is false; if O.is false E.is false.

If we deny any predication about _Some S_, we must deny it of _All S_; since in denying it of _Some_, we have denied it of at least part of _All_; and whatever is false in one form of words is false in any other.
On the other hand, if I.is true, we do not know that A.is; nor if O.
is true, that E.is; for to infer from _Some_ to _All_ would be going beyond the evidence.

We shall see in discussing Induction that the great problem of that part of Logic is, to determine the conditions under which we may in reality transcend this rule and infer from _Some_ to _All_; though even there it will appear that, formally, the rule is observed.

For the present it is enough that I.is an immediate inference from A., and O.from E.; but that A.is not an immediate inference from I., nor E.from O.
Sec.3.Connotative Subalternation .-- We have seen (chap.iv.Sec.

6) that if the connotation of one term is only part of another's its denotation is greater and includes that other's.