266 THE GROUNDWORK OF SCIENCE

principle of contradiction ; (6) mathematical axioms ; (7)

the validity of the reasoning process ; and (8) the law of

causation. We hope the views here advocated concerning

these questions may have commended themselves to the

judgment of our readers. If so, we have already succeeded

in the greater part of our task. For there can be no

question that if the fundamental principles we have put

forward are necessary and universal truths, which carry with

them their own evidence and constitute the ultimate criteria

of human knowledge, they must also constitute a large part

of the groundwork of all science.

These truths we can recognize for what they are, namely,

absolutely certain and self-evident facts and principles. But

however evident they may be, it is no less evident that we

did not always recognize them. Not only in our infancy, but

during childhood and early youth we were either altogether

ignorant of them or, at any rate, did not take them for what

we now see them to be.

How, then, did we come to obtain a knowledge of them,

and is it possible that the mode in which we acquired them,

whatever it may have been, can give us reasonable cause to

mistrust them, or be half-hearted as it were in our recognition

of them as absolutely true facts and principles ? Can we

gain any light as to what may have been the causes of our

certitude, and have such causes any real bearing on that

certitude's validity?

We have already disposed of that most unreasonable of

all suppositions, namely, the supposition that what we have

represented as first principles can possibly be based on

reasoning. We have seen * that such a system results in a

regressus ad infinitum, and would necessarily emasculate

reasoning by depriving it of its indispensable premisses.

But some persons would represent our deepest convictions

* See ante, p. 103.

principle of contradiction ; (6) mathematical axioms ; (7)

the validity of the reasoning process ; and (8) the law of

causation. We hope the views here advocated concerning

these questions may have commended themselves to the

judgment of our readers. If so, we have already succeeded

in the greater part of our task. For there can be no

question that if the fundamental principles we have put

forward are necessary and universal truths, which carry with

them their own evidence and constitute the ultimate criteria

of human knowledge, they must also constitute a large part

of the groundwork of all science.

These truths we can recognize for what they are, namely,

absolutely certain and self-evident facts and principles. But

however evident they may be, it is no less evident that we

did not always recognize them. Not only in our infancy, but

during childhood and early youth we were either altogether

ignorant of them or, at any rate, did not take them for what

we now see them to be.

How, then, did we come to obtain a knowledge of them,

and is it possible that the mode in which we acquired them,

whatever it may have been, can give us reasonable cause to

mistrust them, or be half-hearted as it were in our recognition

of them as absolutely true facts and principles ? Can we

gain any light as to what may have been the causes of our

certitude, and have such causes any real bearing on that

certitude's validity?

We have already disposed of that most unreasonable of

all suppositions, namely, the supposition that what we have

represented as first principles can possibly be based on

reasoning. We have seen * that such a system results in a

regressus ad infinitum, and would necessarily emasculate

reasoning by depriving it of its indispensable premisses.

But some persons would represent our deepest convictions

* See ante, p. 103.