idea of extension, which is neither line, surface,
nor solid, neither great nor small, black, white, nor red, nor of any
other determinate colour. It is only implied that whatever particular
motion I consider, whether it be swift or slow, perpendicular,
horizontal, or oblique, or in whatever object, the axiom concerning
it holds equally true. As does the other of every particular extension,
it matters not whether line, surface, or solid, whether of this or
that magnitude or figure.

[Note 1: "TO THIS I CANNOT ASSENT, BEING OF OPINION," edit of 1710.]

[Note 2: Of the same sort.]

12. EXISTENCE OF GENERAL IDEAS ADMITTED.--By observing how ideas
become general we may the better judge how words are made so.
And here it is to be noted that I do not deny absolutely there
are general ideas, but only that there are any ABSTRACT GENERAL
IDEAS; for, in the passages we have quoted wherein there is
mention of general ideas, it is always supposed that they are formed by
ABSTRACTION, after the manner set forth in sections 8 and 9. Now, if we
will annex a meaning to our words, and speak only of what we can
conceive, I believe we shall acknowledge that an idea which, considered
in itself, is particular, becomes general by being made to represent or
stand for all other particular ideas of the SAME SORT. To make this plain
by an example, suppose a geometrician is demonstrating the method of
cutting a line in two equal parts. He draws, for instance, a black line
of an inch in length: this, which in itself is a particular line, is
nevertheless with regard to its signification general, since, as it is
there used, it represents all particular lines whatsoever; so that what
is demonstrated of it is demonstrated of all lines, or, in other words,
of a line in general. And, as that particular line becomes general by
being made a sign, so the name LINE, which taken absolutely is
PARTICULAR, by being a sign is made GENERAL. And as the former owes its
generality not to its being the sign of an abstract or general line, but
of ALL PARTICULAR right lines that may possibly exist, so the latter must
be thought to derive its generality from the same cause, namely, the
VARIOUS PARTICULAR lines which it indifferently denotes. [Note.]

[Note: "I look upon this (doctrine) to be one of the greatest and most
valuable discoveries that have been made of late years in the republic
of letters."--Treatise of Human Nature, book i, part i, sect. 7. Also
Stewar