248 THE GROUNDWORK OF SCIENCE

to mental states. Such we have seen to be the case with

respect to the various instances we have put forward as

examples. When we say that the number of balls in a

bag cannot at the same time be both " odd " and " even,"

we are certain that this is not a truth due to our organization,

but to the real necessary objective conditions of existence of

the balls themselves. Our reason declares that the law

of contradiction is no " form of thought " imposed on our

intellect, but is a certain and inevitable law of objective

existence independent of our intellect.

To doubt this would be to destroy all certainty, since

it is a fundamental truth on which all reasoning depends.

If we could not be sure the fact that "all men are mortal"

did not necessarily imply that none could live for ever,

we could never infer the mortality of anyone as a con-

sequence of his humanity. Thus for anyone to attempt

such a task as that of "proving" the law of contradiction

would be, in the highest degree, absurd, since he would

be compelled to already assume its certainty at the very

outset of his demonstration at the very first assertion he

made.

Our perception, therefore, of the necessary validity of

the law of contradiction, teaches us both an absolute

verity with respect to objective existences with respect

to the matter of all science as well as the existence of

our own mental perception thereof.

Another principle of universal application and self-evident

validity is the well-known axiom: "things which are equal

to the same thing are equal to each other."

As with the law of contradiction, so with this axiom it

is practically known and constantly acted on in every-day

life without advertence to its axiomatic character, and even

without any knowledge of it as a recognized truth at all.

The familiar application of a yard measure to different

to mental states. Such we have seen to be the case with

respect to the various instances we have put forward as

examples. When we say that the number of balls in a

bag cannot at the same time be both " odd " and " even,"

we are certain that this is not a truth due to our organization,

but to the real necessary objective conditions of existence of

the balls themselves. Our reason declares that the law

of contradiction is no " form of thought " imposed on our

intellect, but is a certain and inevitable law of objective

existence independent of our intellect.

To doubt this would be to destroy all certainty, since

it is a fundamental truth on which all reasoning depends.

If we could not be sure the fact that "all men are mortal"

did not necessarily imply that none could live for ever,

we could never infer the mortality of anyone as a con-

sequence of his humanity. Thus for anyone to attempt

such a task as that of "proving" the law of contradiction

would be, in the highest degree, absurd, since he would

be compelled to already assume its certainty at the very

outset of his demonstration at the very first assertion he

made.

Our perception, therefore, of the necessary validity of

the law of contradiction, teaches us both an absolute

verity with respect to objective existences with respect

to the matter of all science as well as the existence of

our own mental perception thereof.

Another principle of universal application and self-evident

validity is the well-known axiom: "things which are equal

to the same thing are equal to each other."

As with the law of contradiction, so with this axiom it

is practically known and constantly acted on in every-day

life without advertence to its axiomatic character, and even

without any knowledge of it as a recognized truth at all.

The familiar application of a yard measure to different