e one in the many, the
same amidst the different, the identity signified by the common name.
The name of an attribute as thought of by itself without reference to
any individual or class possessing it, is called an ABSTRACT name. By
contradistinction, the name of an individual or a class is CONCRETE.

Technical terms are wanted also to express the relation of the
individuals and the attributes to the general name. The individuals
jointly are spoken of as the DENOTATION, or EXTENSION or SCOPE of
the name; the common attributes as its CONNOTATION, INTENSION,
COMPREHENSION, or GROUND. The whole denotation, etc., is the class;
the whole connotation, etc., is the concept.[1] The limits of a
"class" in Logic are fixed by the common attributes. Any individual
object that possesses these is a member. The statement of them is the
DEFINITION.

To predicate a general name of any object, as, "This is a cat," "This
is a very sad affair," is to refer that object to a class, which is
equivalent to saying that it has certain features of resemblance with
other objects, that it reminds us of them by its likeness to them.
Thus to say that the predicate of every proposition is a general name,
expressed or implied, is the same as to say that every predication may
be taken as a reference to a class.

Ordinarily our notion or concept of the common features signified by
general names is vague and hazy. The business of Logic is to make them
clear. It is to this end that the individual objects of the class are
summoned before the mind. In ordinary thinking there is no definite
array or muster of objects: when we think of "dog" or "cat,"
"accident," "book," "beggar," "ratepayer," we do not stop to call
before the mind a host of representatives of the class, nor do we take
precise account of their common attributes. The concept of "house" is
what all houses have in common. To make this explicit would be no
easy matter, and yet we are constantly referring objects to the
class "house". We shall see presently that if we wish to make the
connotation or concept clear we must run over the denotation or class,
that is to say, the objects to which the general name is applied in
common usage. Try, for example, to conceive clearly what is meant
by house, tree, dog, walking-stick. You think of individual objects,
so-called, and of what they have in common.

A class may be constituted on one property or on many. There are
several points common to all hou