§ 6. From such examples of terms whose connotations are related as whole
and part, it is easy to see the general truth of the doctrine that as
connotation decreases, denotation increases: for 'animal,' with less
connotation than man or chamois, denotes many more objects; 'white,'
with less connotation than snow or silver, denotes many more things, It
is not, however, certain that this doctrine is always true in the
concrete: since there may be a term connoting two or more qualities, all
of which qualities are peculiar to all the things it denotes; and, if
so, by subtracting one of the qualities from its connotation, we should
not increase its denotation. If 'man,' for example, has among mammals
the two peculiar attributes of erect gait and articulate speech, then,
by omitting 'articulate speech' from the connotation of man, we could
not apply the name to any more of the existing mammalia than we can at
present. Still we might have been able to do so; there might have been
an erect inarticulate ape, and perhaps there once was one; and, if so,
to omit 'articulate' from the connotation of man would make the term
'man' denote that animal (supposing that there was no other difference
to exclude it). Hence, potentially, an increase of the connotation of
any term implies a decrease of its denotation. And, on the other hand,
we can only increase the denotation of a term, or apply it to more
objects, by decreasing its connotation; for, if the new things denoted
by the term had already possessed its whole connotation, they must
already have been denoted by it. However, we may increase the _known_
denotation without decreasing the connotation, if we can discover the
full connotation in things not formerly supposed to have it, as when
dolphins were discovered to be mammals; or if we can impose the
requisite qualities upon new individuals, as when by annexing some
millions of Africans we extend the denotation of 'British subject'
without altering its connotation.