We shall often need to illustrate the character of our knowledge of nature by the simile of a ballot-box, so often employed by mathematical writers in the theory of probability. Nature is to us like an infinite ballot-box, the contents of which are being continually drawn, ball after ball, and exhibited to us. Science is but the careful observation of the succession in which balls of various character present themselves; we register the combinations, notice those which seem to be excluded from occurrence, and from the proportional frequency of those which appear we infer the probable character of future drawings. But under such circumstances certainty of prediction depends on two conditions:-- 1. That we acquire a perfect knowledge of the comparative numbers of balls of each kind within the box. 2. That the contents of the ballot-box remain unchanged. Of the latter assumption, or rather that concerning the constitution of the world which it illustrates, the logician or physicist can have nothing to say. As the Creation of the Universe is necessarily an act passing all experience and all conception, so any change in that Universe, or, it may be, a termination of it, must likewise be infinitely beyond the bounds of our mental faculties. No science no reasoning upon the subject, can have any validity; for without experience we are without the basis and materials of knowledge. It is the fundamental postulate accordingly of all inference concerning the future, that there shall be no arbitrary change in the subject of inference; of the probability or improbability of such a change I conceive that our faculties can give no estimate. The other condition of inductive inference--that we acquire an approximately complete knowledge of the combinations in which events do occur, is in some degree within our power. There are branches of science in which phenomena seem to be governed by conditions of a most fixed and general character. We have ground in such cases for believing that the future occurrence of such phenomena can be calculated and predicted. But the whole question now becomes one of probability and improbability. We seem to leave the region of logic to enter one in which the number of events is the ground of inference. We do not really leave the region of logic; we only leave that where certainty, affirmative or negative, is the result, and the agreement or disagreement of qualities the means of inference. For the future, number and quantity will commonly enter into our processes of reasoning; but then I hold that number and quantity are but portions of the great logical domain. I venture to assert that number is wholly logical, both in its fundamental nature and in its developments. Quantity in all its forms is but a development of number. That which is mathematical is not the less logical; if anything it is more logical, in the sense that it presents logical results in a higher degree of complexity and variety.