and which already implies
a confusion of ideas. We apply the conception of justice in a sphere
where it is not applicable, and naturally fail to get any intelligible
answer.

It is impossible to combine the conceptions of God as the creator and
God as the judge; and the logical straits into which the attempt leads
are represented by the endless free-will controversy. I will not now
enter that field of controversy: and I will only indicate what seems to
me to be the position which we must accept in any scientific discussion
of our problem. Hume, as I think, laid down the true principle when he
said that there could be no _a priori_ proof of a matter of fact.
An _a priori_ truth is a truth which cannot be denied without
self-contradiction, but there can never be a logical consideration in
supposing the non-existence of any fact whatever. The ordinary appeal
to the truths of pure mathematics is, therefore, beside the question.
All such truths are statements of the precise equivalence of two
propositions. To say that there are four things is also to say that
there are two pairs of things: to say that there is a plane triangle is
also to say that there is a plane trilateral. One statement involves
the other, because the difference is not in the thing described, but in
our mode of contemplating it. We, therefore, cannot make one assertion
and deny the other without implicit contradiction. From such results,
again, is evolved (in the logical sense of evolution) the whole vast
system of mathematical truths. The complexity of that system gives the
erroneous idea that we can, somehow, attain a knowledge of facts,
independently of experience. We fail to observe that even the most
complex mathematical formula is simply a statement of an exact
equivalence of two assertions; and that, till we know by experience the
truth of one statement, we can never infer the truth, in fact, of the
other. However elaborate may be the evolutions of mathematical truth,
they can never get beyond the germs out of which they are evolved. They
are valid precisely because the most complex statement is always the
exact equivalent of the simpler, out of which it is constructed. They
remain to the end truths of number or truths of geometry. They cannot,
by themselves, tell us that things exist which can be counted or which
can be measured. The whole claim, however elaborate, still requires its
point of suspension. We may put their claims to absolute or neces