philosophic doubt; but even the plain man is not always cocksure. Sometimes he even doubts and suspends his judgment; but even when he believes and positively affirms, many of his beliefs and affirmations—most of those relating to the future—are intended to be taken as not certain but probable. By a ‘probable’ belief I do not now mean a belief relating to probabilities; for this may be as certain as any other—as for instance the belief that the chances are even that a penny I toss will come down tails. The theory of chances has been described as a method of extracting knowledge out of ignorance; it is undoubtedly a method of converting probable judgments into certain ones—though the certainty is of a peculiar kind, and its verification presents a special epistemological problem of some interest. But the probable beliefs that I now wish to distinguish from certain ones are beliefs which involve no attempt at a quantitative estimate of ‘amount of probability’; and they are often in form of expression indistinguishable from beliefs held with certitude:—thus when a man affirms in conversation that the new plan of international arbitration will have no practical effect, or that the Liberal Party must return to power after the next general election; it will be generally understood that though the speaker may appear to express certitude on these points, he only means that the events are extremely probable. I draw attention to this ambiguity of expression, because it facilitates an indeterminateness of thought, of which we have to take note in applying the distinction that I now draw between “certain” and “probable” beliefs. Often in ordinary thought we do not know whether we are sure of what we affirm unless we are led to reflect on the point; sometimes we do not know after reflection; sometimes we are conscious of elements of uncertainty which we decide to disregard, and then we say that we are “morally certain”—meaning that we should unhesitatingly act as if we were certain. This last state of mind I shall consider hereafter; at present I wish to confine attention to beliefs which present themselves in ordinary thought as certain without qualification. Of these I may roughly distinguish three chief classes: (1) particular beliefs about the present and recent past of the changing world of which we are part; (2) general beliefs more or less systematised in the sciences, especially the exact sciences, which we may happen to know; (3) beliefs that primâ facie relate not to mere matter of fact but to moral or æsthetic valuation—to what we ought to do as individuals, or what government
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