None of these observations apply to the kind of probability on whose importance I am now insisting. If calculable probability be indeed “common sense reduced to calculation,” intuitive probability lies deeper. It supports common sense, and it supplies the ultimate ground—be it secure or insecure—of all work-a-day practice and all scientific theory. It has nothing to do with “randomness”; it knows nothing of averages; it obeys no formal laws; no light is thrown on it by cards or dice; it cannot be reduced to calculation. How, then, is it to be treated? What place is it to occupy in our general scheme? These are all important questions. But no answer to them can be given till we have pressed somewhat further the line of thought which the discussion in this present lecture has for a moment interrupted. Before I began this long parenthesis on the theory of chance, I was occupied with a most important example of a belief which possesses the highest degree of intuitive probability, but no calculable probability at all. I mean the belief in an independent physical universe. In the next lecture I shall resume the general thread of my argument, and consider another belief of the same kind which is not less—some would say even more—essential to natural science than the one with which I have already dealt. I mean a belief in the regularity of nature. FOOTNOTES: [9] Although, as a matter of fact, I do speak of it in the next lecture. [10] Maxwell, as all who interest themselves in physics are aware, arrived at very interesting conclusions by considering what would happen if little demons interfered with the random motions of the molecules constituting a gas. LECTURE VIII UNIFORMITY AND CAUSATION I In my last lecture but one I dwelt upon the interplay of causes and reasons in one special case—the case of our immediate experiences of the external world, the world in which we move, the world investigated by the physical sciences. No case can indeed be more important; for these immediate experiences are deemed by every man to be his guide through all the hours of his waking life, and by every man of science to supply the evidence on which depends all our knowledge of natural laws. Yet this very statement suggests the existence of another series of problems not less important and not less closely connected with my general argument. For, how do we get from particular experiences to general laws—from beliefs about individual occurrences to beliefs about the ordering of the universe? These beliefs, looked at from the scientific point of view, are, as I have so often observed, a natural product. They have a history like other natural products. They are the effects of a long train of causes; and among those causes are some which claim, rightly or wrongly, to be reasons, an uncounted multitude which make no such claim, and others, again, which occupy a doubtful position between the two.