Described in technical language, it would seem to be _a priori_ without being necessary, and synthetic without being empirical—qualities which, in combination, scarcely fit into any familiar philosophic classification. According to the view which I desire to press in these lectures, this marks a philosophic omission. I regard the belief in an external world as one of a class whose importance has been ignored by philosophy, though all science depends on them. They refuse to be lost in the common herd of empirical beliefs; though they have no claim to be treated as axioms. We are inclined to accept them, but not rationally compelled. The inclination may be so strong as practically to exclude doubt; and it may diminish from this maximum to a faint feeling of probability. But, whatever be the strength of these beliefs, and whatever the nature of their claims, the importance of the part they play in the development and structure of our current creed cannot easily be exaggerated. Before, however, I consider other specimens of this class, I must interpolate a long parenthesis upon probability. I have just described these fundamental beliefs as being “probable” in varying degrees. Gradations of probability are familiar to the mathematical theorist. Are we, then, here concerned with probability as conceived by the mathematician? It is evidently essential to settle this question before proceeding with the main argument; and I propose, therefore, to turn aside and devote the next lecture to its consideration. LECTURE VII PROBABILITY, CALCULABLE AND INTUITIVE I I wish I were a mathematician. There is in the history of the mathematical sciences, as in their substance, something that strangely stirs the imagination even of the most ignorant. Its younger sister, Logic, is as abstract, and its claims are yet wider. But it has never shaken itself free from a certain pretentious futility: it always seems to be telling us, in language quite unnecessarily technical, what we understood much better before it was explained. It never helps to discover, though it may guarantee discovery; it never persuades, though it may show that persuasion has been legitimate; it never aids the work of thought, it only acts as its auditor and accountant-general. I am not referring, of course, to what I see described in recent works as “modern scientific logic.” Of this I do not presume to speak. Still less am I referring to so-called Inductive Logic. Of this it is scarce worth while to speak.[9] I refer to their more famous predecessor, the formal logic of the schools.