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 _à priori_ proof of a matter of fact. An _à 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 necessary truth as high as we please; but they cannot give us by themselves a single fact. I can show, for example, that a circle has an infinite number of properties, all of which are virtually implied in the very existence of a circle. But that the circle or that space itself exists, is not a necessary truth, but a datum of experience. It is quite true that such truths are not, in one sense, empirical; they can be discovered without any change of experience; for, by their very nature, they refer to the constant element of experience, and are true on the