1 8 THE GROUNDWORK OF SCIENCE

Indeed, reason, it seems, does not permit us to concede

that any one science has an indefeasible claim to priority,

for conflicting, apparently equal, claims point in various

directions.

Our own body is the object we most intimately know,

and next might be ranked the objects most closely related

to us, and with which we are the most familiar. But such

things, taken together, do not constitute any distinct

science.

There is, however, one property which belongs to them

and to everything else we can think of likewise to every

separate object, natural or artificial, to every motion or

appearance, and even to every thought we can entertain

about any possible object.

To know anything whatever, is to know that it is distinct

from something else. Two marbles, alike in colour, size,

shape and weight, are known with perfect certainty to be

distinct, though we may not, when apart, be able to tell one

from the other. We recognize them as two things of the

same kind, and together they form "a pair." If we have

elsewhere a group of three marbles exactly like the first two,

then these two groups differ in number. "Number" is a

property possessed by every object, motion or appearance,

and even by every thought

The one thing which alike pertains to everything we

know, terrestrial or celestial, material or mental, is " number."

Probably it was this truth which underlay the system of

Pythagoras, who, more than two thousand four hundred

years ago, taught that "number" was the principle of all

things.

But the study of that which is thus common to everything

is the study of Mathematics. Therefore Mathematics, as the

science of number, would seem to have a reasonable claim to

be regarded as the most fundamental of all the sciences, since

Indeed, reason, it seems, does not permit us to concede

that any one science has an indefeasible claim to priority,

for conflicting, apparently equal, claims point in various

directions.

Our own body is the object we most intimately know,

and next might be ranked the objects most closely related

to us, and with which we are the most familiar. But such

things, taken together, do not constitute any distinct

science.

There is, however, one property which belongs to them

and to everything else we can think of likewise to every

separate object, natural or artificial, to every motion or

appearance, and even to every thought we can entertain

about any possible object.

To know anything whatever, is to know that it is distinct

from something else. Two marbles, alike in colour, size,

shape and weight, are known with perfect certainty to be

distinct, though we may not, when apart, be able to tell one

from the other. We recognize them as two things of the

same kind, and together they form "a pair." If we have

elsewhere a group of three marbles exactly like the first two,

then these two groups differ in number. "Number" is a

property possessed by every object, motion or appearance,

and even by every thought

The one thing which alike pertains to everything we

know, terrestrial or celestial, material or mental, is " number."

Probably it was this truth which underlay the system of

Pythagoras, who, more than two thousand four hundred

years ago, taught that "number" was the principle of all

things.

But the study of that which is thus common to everything

is the study of Mathematics. Therefore Mathematics, as the

science of number, would seem to have a reasonable claim to

be regarded as the most fundamental of all the sciences, since