AN ESSAY ON QUANTITY:
OCCASIONED BY READING A TREATISE IN WHICH SIMPLE AND COMPOUND RATIOS ARE APPLIED TO VIRTUE AND MERIT.
Sec. 1. What quantity is
Sec. 2. Of proper and improper quantity
Sec. 3. Corollary 1
Sec. 4. Corollary 2
Sec. 5. Corollary 3
Sec. 6. Of the Newtonian measure of force
Sec. 7. Of the Leibnitzian measure of force
Sec. 8. Reflections on this controversy
Sec. 1. What quantity is.
Since mathematical demonstration is thought to carry a peculiar evidence along with it, which leaves no room for further dispute, it may be of some use, or entertainment at least, to inquire to what subjects this kind of proof may be applied.
Mathematics contain properly the doctrine of measure; and the object of this science is commonly said to be quantity; therefore quantity ought to be defined, what may be measured. Those who have defined quantity to be whatever is capable of more or less, have given too wide a notion of it, which, I apprehend, has led some persons to apply mathematical reasoning to subjects that do not admit of it.
Pain and pleasure admit of various degrees, but who can pretend to measure them? Had this been possible, it is not to be doubted but we should have had as distinct names for their various degrees as we have for measures of length or capacity; and a patient should have been able to describe the quantity of his pain, as well as the time it began, or the part it affected. To talk intelligibly of the quantity of pain, we should have some standard to measure it by; some known degree of it, so well ascertained, that all men, when they talked of it, should mean the same thing; we should also be able to compare other degrees of pain with this, so as to perceive distinctly, not only whether they exceed or fall short of it, but how far, or in what proportion,—whether by a half, a fifth, or a tenth.
Whatever has quantity, or is measurable, must be made up of parts, which bear proportion to one another and to the whole; so that it may be increased by addition of like parts, and dimin-
- This splendid specimen of metaphysical mathematics originally appeared in the xlvth vol. of the "Philosophical Transactions," and has never before been published in conjunction with the author's other Essays.