said “the change of motion is proportional to the impressed force,” or that “whatever has extension is divisible,” these propositions are to be understood of motion and extension in general; and nevertheless it will not follow that they suggest to my thoughts an idea of motion without a body moved, or any determinate direction and velocity, or that I must conceive an abstract general 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 Stewart’s Philosophy of the Mind, part i, chapt. iv. sect. iii. p. 99.]