In the variety of logical relations, which may exist between a certain number of logical terms, we also meet a case of higher combinations. We have seen (p. 142) that with only six terms the number of possible selections of combinations is 18,446,744,073,709,551,616. Considering that it is the most common thing in the world to use an argument involving six objects or terms, it may excite some surprise that the complete investigation of the relations in which six such terms may stand to each other, should involve an almost inconceivable number of cases. Yet these numbers of possible logical relations belong only to the second order of combinations. CHAPTER X. THE THEORY OF PROBABILITY. The subject upon which we now enter must not be regarded as an isolated and curious branch of speculation. It is the necessary basis of the judgments we make in the prosecution of science, or the decisions we come to in the conduct of ordinary affairs. As Butler truly said, “Probability is the very guide of life.” Had the science of numbers been studied for no other purpose, it must have been developed for the calculation of probabilities. All our inferences concerning the future are merely probable, and a due appreciation of the degree of probability depends upon a comprehension of the principles of the subject. I am convinced that it is impossible to expound the methods of induction in a sound manner, without resting them upon the theory of probability. Perfect knowledge alone can give certainty, and in nature perfect knowledge would be infinite knowledge, which is clearly beyond our capacities. We have, therefore, to content ourselves with partial knowledge--knowledge mingled with ignorance, producing doubt. A great difficulty in this subject consists in acquiring a precise notion of the matter treated. What is it that we number, and measure, and calculate in the theory of probabilities? Is it belief, or opinion, or doubt, or knowledge, or chance, or necessity, or want of art? Does probability exist in the things which are probable, or in the mind which regards them as such? The etymology of the name lends us no assistance: for, curiously enough, *probable* is ultimately the same word as *provable*, a good instance of one word becoming differentiated to two opposite meanings.