better proposal to regard their denotation and connotation as
coinciding; though open to the objection that 'connote' means 'to mark
along with' something else, and this plan leaves nothing else. Mill
thought that abstract terms are connotative when, besides denoting a
quality, they suggest a quality of that quality (as 'fault' implies
'hurtfulness'); but against this it may be urged that one quality cannot
bear another, since every qualification of a quality constitutes a
distinct quality in the total ('milk-whiteness' is distinct from
'whiteness,' _cf._ chap. iii. § 4). After all, if it is the most
consistent plan, why not say that abstract, like proper, terms have no
connotation?

But if abstract terms must be made to connote something, should it not
be those things, indefinitely suggested, to which the qualities belong?
Thus 'whiteness' may be considered to connote either snow or vapour, or
any white thing, apart from one or other of which the quality has no
existence; whose existence therefore it implies. By this course the
denotation and connotation of abstract and of general names would be
exactly reversed. Whilst the denotation of a general name is limited by
the qualities connoted, the connotation of an abstract name includes all
the things in which its denotation is realised. But the whole difficulty
may be avoided by making it a rule to translate, for logical purposes,
all abstract into the corresponding general terms.

§ 4. If we ask how the connotation of a term is to be known, the answer
depends upon how it is used. If used scientifically, its connotation is
determined by, and is the same as, its definition; and the definition is
determined by examining the things to be denoted, as we shall see in
chap. xxii. If the same word is used as a term in different sciences, as
'property' in Law and in Logic, it will be differently defined by them,