inutest parts we can conceive are mathematical points; and
consequently this standard of equality is the same with that derived
from the equality of the number of points; which we have already
determined to be a just but an useless standard. We must therefore look
to some other quarter for a solution of the present difficulty.

There are many philosophers, who refuse to assign any standard of
equality, but assert, that it is sufficient to present two objects, that
are equal, in order to give us a just notion of this proportion. All
definitions, say they, are fruitless, without the perception of such
objects; and where we perceive such objects, we no longer stand in need
of any definition. To this reasoning, I entirely agree; and assert, that
the only useful notion of equality, or inequality, is derived from the
whole united appearance and the comparison of particular objects.

It is evident, that the eye, or rather the mind is often able at one
view to determine the proportions of bodies, and pronounce them equal
to, or greater or less than each other, without examining or comparing
the number of their minute parts. Such judgments are not only common,
but in many cases certain and infallible. When the measure of a yard and
that of a foot are presented, the mind can no more question, that the
first is longer than the second, than it can doubt of those principles,
which are the most clear and self-evident.

There are therefore three proportions, which the mind distinguishes
in the general appearance of its objects, and calls by the names of
greater, less and equal. But though its decisions concerning these
proportions be sometimes infallible, they are not always so; nor are our
judgments of this kind more exempt from doubt and error than those on
any other subject. We frequently correct our first opinion by a review
and reflection; and pronounce those objects to be equal, which at first
we esteemed unequal; and regard an object as less, though before it
appeared greater than another. Nor is this the only correction, which
these judgments of our senses undergo; but we often discover our error
by a juxtaposition of the objects; or where that is impracticable, by
the use of some common and invariable measure, which being successively
applied to each, informs us of their different proportions. And even
this correction is susceptible of a new correction, and of different
degrees of exactness, according to the nature of the in