An Essay on Quantity

Whatever can be measured, and not, as some had said, whatever admits of more and less. A true quantity is made of parts that bear proportion to one another, so it can be added to, subtracted from, doubled or halved. The narrower definition matters because the wider one invited people to apply mathematical reasoning to things that have degrees but cannot be measured.

Proper quantity is measured by its own kind: a line by known lines, a stretch of time by known times. Reid finds four kinds, extension, duration, number and proportion. Improper quantity, such as velocity, density or force, cannot be measured by itself, so a measure is assigned to it through some related proper quantity, as velocity is measured by the space passed over in a given time.

Because it belongs only to propositions about things measurable by lines or numbers. Quantity admits a greater variety of exactly definable relations than any other subject, which is why mathematics can follow long trains of reasoning without danger of mistake. Where that condition is missing, as with tastes, pleasures, beauty or most probabilities, the same certainty cannot be had, however mathematical the notation looks.

The long dispute over how to measure the force of a moving body: Newton's followers measured it by velocity, Leibniz's by the square of velocity. Reid argues that force becomes a mathematical quantity only once a definition assigns it a measure. Each side had laid down a different definition and then tried to prove it by experiment, a task that could never succeed, since no definition can be false.