In the sixth and eighth lectures of this course I dealt with two inevitable beliefs which lie at the root of all science and all practice—the beliefs that an independent, or, as it is commonly called, an “external” world exists, and the belief that the world, whether external or internal, has at least a measure of regularity. In the seventh lecture I interpolated a discussion upon probability; and showed, or attempted to show, that we must take account of a kind of probability other than that which, in the hands of mathematicians, has so greatly contributed to knowledge. If, now, we consider these subjects in their mutual relation, we perceive that an “inevitable” belief is one which possesses the highest degree of this intuitive probability. These are two descriptions of the same quality—one emphasising the objective, the other the subjective, aspects of a single fact. But this at once suggests a further inquiry. Probability is evidently a matter of degree. A belief may be more probable or less probable. Inevitableness, on the other hand, seems at first sight to be insusceptible of gradation. It is, or it is not. Yet this extreme definiteness vanishes if we regard it as a limiting case—as the last term of a series whose earlier members represent varying degrees of plausibility. On this view we should regard our beliefs about the universe as moulded by formative forces, which vary from irresistible coercion to faint and doubtful inclination. Beliefs in the reality of the external world and in its regularity are important products of the first. I now propose to call attention to some beliefs which are due to the less obvious action of the second. Both kinds, whether capable of proof or not, are more or less independent of it. Both are to be regarded rather as the results of tendencies than as the conclusions of logic. I am well aware that a doctrine like this will find few admirers among systematic thinkers. Inevitable beliefs which are fundamental without being axiomatic; which lack definiteness and precision; which do not seem equally applicable to every field of experience; which do not claim to be of the essence of our understanding, like the categories of the critical philosophy, or the so-called laws of thought, have little to recommend them to philosophers. And when inevitableness is treated as merely an extreme form of plausibility, when guidance is discovered in tendencies which are weak and of uncertain application, leading to error as well as to truth, their objections will scarcely be mitigated.