# Logic: Or, the Morphology of Knowledge - Vol. 1

By Bernard Bosanquet | Go to book overview

CHAPTER III. .
MEASUREMENT--QUANTITY AND PROPORTION

1. MEASUREMENT is the equation of any whole, by comparison, to a numerical aggregate of determinate parts. The parts may be determinate through reference either outside or within the whole to be measured; but if the reference falls within it (as when we say a man's whole height is so many times the length of his head) the whole must be complex and contain subordinate systems. The reference may also take the shape of relations which are not purely quantitative (as a tone or semitone in music, apart from its physical cause, is simply a difference between two peculiar sounds); but in that case we are passing out of the region of pure measurement. Some reference, however, there must be in measurement beyond that to the simple whole which is to be measured. It is no measurement of a line to divide it into 100 or 1000 equal parts. We must know what else they are parts of, besides being parts of the line to be measured. The length of a line is measured when it is equated to feet and inches--to the length, that is, of some actual piece of metal agreed upon as a standard--the pitch of a note is measured when we have determined its place in the scale or the number of vibrations per second that enter into it; the specific gravity of a substance is measured when we have stated the ratio of its weight to that of an equal volume of distilled water at a certain temperature. Here a verbal difficulty may be cleared away. If the weight of the substance before us is twelve times that of water, our definition of measurement applies straightforwardly. We equate the whole substance in respect of its weight to a numerical aggregate of twelve parts, each of which is determined by equation to a known

Measurement and Individuality.

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