nd _apple_.

Again, as a rule, if you increase the connotation you contract the
area within which the name is applicable. Take any group of things
having certain attributes in common, say, _men of ability_: add
_courage_, _beauty_, _height of six feet_, _chest measurement of 40
inches_, and with each addition fewer individuals are to be found
possessing all the common attributes.

This is obvious enough, and yet the expression inverse variation is
open to objection. For the denotation may be increased in a sense
without affecting the connotation. The birth of an animal may be said
to increase the denotation: every year thousands of new houses are
built: there are swarms of flies in a hot summer and few in a cold.
But all the time the connotation of _animal_, _house_, or _fly_
remains the same: the word does not change its meaning.

It is obviously wrong to say that they vary in inverse proportion.
Double or treble the number of attributes, and you do not necessarily
reduce the denotation by one-half or one-third.

It is, in short, the meaning or connotation that is the main thing.
This determines the application of a word. As a rule if you increase
meaning, you restrict scope. Let your idea, notion, or concept of
_culture_ be a knowledge of Mathematics, Latin and Greek: your _men of
culture_ will be more numerous than if you require from each of them
these qualifications _plus_ a modern language, an acquaintance with
the Fine Arts, urbanity of manners, etc.

It is just possible to increase the connotation without decreasing the
denotation, to thicken or deepen the concept without diminishing
the class. This is possible only when two properties are exactly
co-extensive, as equilaterality and equiangularity in triangles.

SINGULAR and PROPER NAMES. A Proper or Singular name is a name used to
designate an individual. Its function, as distinguished from that of
the general name, is to be used purely for the purpose of distinctive
reference.

A man is not called Tom or Dick because he is like in certain respects
to other Toms or other Dicks. The Toms or the Dicks do not form a
logical class. The names are given purely for purposes of distinction,
to single out an individual subject. The Arabic equivalent for a
Proper name, _alam_, "a mark," "a sign-post," is a recognition of
this.

In the expressions "a Napoleon," "a Hotspur," "a Harry," the names
are not singular names logically, but general names logically, used