AN ESSAY ON QUANTITY
a relation of things measurable by lines or numbers. All proper quantity may be measured by these, and improper quantities must be measured by those that are proper.
There are many things capable of more and less, which perhaps are not capable of mensuration. Tastes, smells, the sensation of heat and cold, beauty, pleasure, all the affections and appetites of the mind, wisdom, folly, and most kinds of probability, with many other things too tedious to enumerate, admit of degrees, but have not yet been reduced to measure, nor, as I apprehend, ever can be. I say, most kinds of probability, because one kind of it, viz., the probability of chances, is properly measurable by number, as is above observed.
Although attempts have been made to apply mathematical reasoning to some of these things, and the quantity of virtue and merit in actions has been measured by simple and compound ratios; yet I do not think that any real knowledge has been struck out this way: it may perhaps, if discreetly used, be a help to discourse on these subjects, by pleasing the imagination, and illustrating what is already known; but until our affections and appetites shall themselves be reduced to quantity, and exact measures of their various degrees be assigned, in vain shall we essay to measure virtue and merit by them. This is only to ring changes upon words, and to make a show of mathematical reasoning, without advancing one step in real knowledge.
Sec. 5. Coroll. 3.
I apprehend the account that hath been given of the nature of proper and improper quantity, may also throw some light upon the controversy about the force of moving bodies, which long exercised the pens of many mathematicians, and, for what I know, is rather dropped than ended; to the no small scandal of mathematics, which hath always boasted of a degree of evidence, inconsistent with debates that can be brought to no issue.
Though philosophers on both sides agree with one another, and with the vulgar in this, That the force of a moving body is the same while its velocity is the same, is increased when its velocity is increased, and diminished when that is diminished. But this vague notion of force, in which both sides agree, though perhaps sufficient for common discourse, yet is not sufficient to make it a subject of mathematical reasoning. In order to that, it must be more accurately defined, and so defined as to give us a measure of it, that we may understand what is meant by a double or a triple force. The ratio of one force to another cannot be perceived but by a measure; and that measure must be settled not by mathematical reasoning, but by a definition. Let any one consider force without relation to any other quantity, and see whether he can conceive one force exactly double to another; I am sure I cannot, nor shall, till I shall be endowed