90 THE GROUNDWORK OF SCIENCE

of this chapter has been said to consist of careful measure-

ments; and there is much truth in the saying, if a sufficiently

wide meaning be assigned to the term " measurement." For

science has to consider, as everyone knows, not only spatial

dimensions or the extent and directions in which any body

is extended or, in popular phraseology, " occupies space "-

but also differences of quality, differences of energy, and of

qualities as well as quantities of energy, and differences in

respect to all those qualities which the different senses we

possess enable us, though in radically diverse ways, to be

subjectively affected by, and, through the intervention of the

intellect, to perceive the objective existence of.

But for the apprehension of all these matters, measurement

is an indispensable and also an efficient aid. Thus inquiries

as to matters seemingly so purely qualitative as different

degrees of warmth, are answered by thermometric measure-

ments ; differences of velocity are estimated by the aid of the

chronometer, and differences in the action of gravity, under

various conditions, by the measurement of weight. Our own

past history and the history of mankind are to be understood

only by measurements of time. Moreover, to know anything,

as we said before,* is to know that it is distinct from some-

thing else, which is to know numerical difference, which is

again counting, and that, to a certain degree, is measure-

ment.

But, though the inquiries of physical science may be gene-

rally described as various kinds of measurements, such a

phrase is obviously inapplicable to the investigations of mental

science. It is true that our own existence does not become

known to us save through successive changes in conscious-

ness (successive "states of consciousness''), that is, through

"relations" which exist between them, and all mental facts

become known through relations in which they stand to other

* Sec ante, p. 18.

of this chapter has been said to consist of careful measure-

ments; and there is much truth in the saying, if a sufficiently

wide meaning be assigned to the term " measurement." For

science has to consider, as everyone knows, not only spatial

dimensions or the extent and directions in which any body

is extended or, in popular phraseology, " occupies space "-

but also differences of quality, differences of energy, and of

qualities as well as quantities of energy, and differences in

respect to all those qualities which the different senses we

possess enable us, though in radically diverse ways, to be

subjectively affected by, and, through the intervention of the

intellect, to perceive the objective existence of.

But for the apprehension of all these matters, measurement

is an indispensable and also an efficient aid. Thus inquiries

as to matters seemingly so purely qualitative as different

degrees of warmth, are answered by thermometric measure-

ments ; differences of velocity are estimated by the aid of the

chronometer, and differences in the action of gravity, under

various conditions, by the measurement of weight. Our own

past history and the history of mankind are to be understood

only by measurements of time. Moreover, to know anything,

as we said before,* is to know that it is distinct from some-

thing else, which is to know numerical difference, which is

again counting, and that, to a certain degree, is measure-

ment.

But, though the inquiries of physical science may be gene-

rally described as various kinds of measurements, such a

phrase is obviously inapplicable to the investigations of mental

science. It is true that our own existence does not become

known to us save through successive changes in conscious-

ness (successive "states of consciousness''), that is, through

"relations" which exist between them, and all mental facts

become known through relations in which they stand to other

* Sec ante, p. 18.