re_; 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. Hence genus and species stand in
subaltern relation, and whatever is true of the genus is true of the
species: If _All animal life is dependent on vegetation, All human life
is dependent on vegetation_. On the other hand, whatever is not true of
the species or narrower term, cannot be true of the whole genus: If it
is false that '_All human life is happy_,' it is false that '_All animal
life is happy_.'

Similar inferences may be drawn from the subaltern relation of
predicates; affirming the species we affirm the genus. To take Mill's
example, if _Socrates is a man, Socrates is a living creature_. On the
other hand, denying the genus we deny the species: if _Socrates is not
vicious, Socrates is not drunken_.

Such cases as these are recognised by Mill and Bain as immediate
inferences under the principle of Identity. But some Logicians might
treat them as imperfect syllogisms, requiring another premise to
legitimate the conclusion, thus:

_All animal life is dependent on vegetation;
All human life is animal life;
.'. All human life is dependent on vegetation._

Or again:

_All men are living creatures;
Socrates is a man;
.'. Socrates is a living creature._

The decision of this issue turns upon the question (_cf._ chap. vi. Sec. 3)
how far a Logician is entitled to assume that the terms