THE METHODS OF SCIENCE 103

must admit that valid inference is not only a possibility, but

a fact. He must admit that inferences which are perfectly

valid and certain have been drawn ; since, otherwise, there

could be no science about the certainty of which we could

rest secure. He also knows (as we have already seen) that

there is such a thing as scientific certainty, and that to some

scientific propositions we can assent without the least fear

of error. But this implies that we may, and that we must,

place confidence in the principles of deduction in that

perception of the mind which we express by the word

"therefore." When we use that word we mean to express

by it that there is a truth, the certainty of which is shown

through the help of different facts or principles, which

themselves are antecedently known to be true. The validity

of inference is then the fourth of those truths which we

desire here to call attention to as being convictions implied

in physical science and in all the methods by which that

science is pursued. Of the process of inference itself, we

shall have more to say hereafter ; all we desire here to

insist upon is that to deny its validity is absolutely to

stultify the whole of human science.

But though inferences are necessary for science, our

readers will not forget that (as we before pointed out) all

reasoning reposes upon a knowledge of facts antecedently

known to be true. However long our processes of reason-

ing may be they must stop somewhere. If we were bound

to prove everything, the process would never end, and in

this way again we should be reduced to a regressus ad

infinitum, and no single proposition could ever be proved.

It is therefore certain that if any inferences are true and

valid they must ultimately repose on facts directly known

to us without reasoning ; and our fifth conviction, implicitly

contained in every method by which science is pursued, is,

and must be, the truth that there are some propositions

must admit that valid inference is not only a possibility, but

a fact. He must admit that inferences which are perfectly

valid and certain have been drawn ; since, otherwise, there

could be no science about the certainty of which we could

rest secure. He also knows (as we have already seen) that

there is such a thing as scientific certainty, and that to some

scientific propositions we can assent without the least fear

of error. But this implies that we may, and that we must,

place confidence in the principles of deduction in that

perception of the mind which we express by the word

"therefore." When we use that word we mean to express

by it that there is a truth, the certainty of which is shown

through the help of different facts or principles, which

themselves are antecedently known to be true. The validity

of inference is then the fourth of those truths which we

desire here to call attention to as being convictions implied

in physical science and in all the methods by which that

science is pursued. Of the process of inference itself, we

shall have more to say hereafter ; all we desire here to

insist upon is that to deny its validity is absolutely to

stultify the whole of human science.

But though inferences are necessary for science, our

readers will not forget that (as we before pointed out) all

reasoning reposes upon a knowledge of facts antecedently

known to be true. However long our processes of reason-

ing may be they must stop somewhere. If we were bound

to prove everything, the process would never end, and in

this way again we should be reduced to a regressus ad

infinitum, and no single proposition could ever be proved.

It is therefore certain that if any inferences are true and

valid they must ultimately repose on facts directly known

to us without reasoning ; and our fifth conviction, implicitly

contained in every method by which science is pursued, is,

and must be, the truth that there are some propositions