Sec. 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.

Many of the things noticed in this chapter, especially in this section and the preceding, will be discussed at greater length in the chapters on Classification and Definition.

Sec. 7.  Contradictory Relative Terms.—­Every term has, or may have, another corresponding with it in such a way that, whatever differential qualities (Sec. 5) it connotes, this other connotes merely their absence; so that one or the other is always formally predicable of any Subject, but both these terms are never predicable of the same Subject in the same relation:  such pairs of terms are called Contradictories.  Whatever Subject we take, it is either visible or invisible, but not both; either human or non-human, but not both.