Page:Treatise on Probability, Keynes, 1921.djvu/25

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CH. I
FUNDAMENTAL IDEAS
5

4. With the term "event," which has taken hitherto so important a place in the phraseology of the subject, I shall dispense altogether.[1] Writers on Probability have generally dealt with what they term the "happening" of "events." In the problems which they first studied this did not involve much departure from common usage. But these expressions are now used in a way which is vague and unambiguous; and it will be more than a verbal improvement to discuss the truth and the probability of propositions instead of the occurrence and the probability of events.[2]

5. These general ideas are not likely to provoke much criticism. In the ordinary course of thought and argument, we are constantly assuming that knowledge of one statement, while not proving the truth of a second, yields nevertheless some ground for believing it. We assert that we ought on the evidence to prefer such and such a belief. We claim rational grounds for assertions which are not conclusively demonstrated. We allow, in fact, that statements may be unproved, without, for that reason, being unfounded. And it does not seem on reflection that the information we convey by these expressions is wholly subjective. When we argue that Darwin gives valid grounds for our accepting his theory of natural selection, we do not simply mean that we are psychologically inclined to agree with him; it is certain that we also intend to convey our belief that we are acting rationally in regarding his theory as probable. We believe that there is some real objective relation between Darwin's evidence and his conclusions, which is independent of the mere fact of our belief, and which is just as real and objective, though of a different degree, as that which would exist if the argument were as demonstrative as a syllogism. We are claiming, in fact, to cognise correctly a logical connection between one set of propositions which we call our evidence and which we suppose ourselves to know, and another set which we call our conclusions, and to which we attach more or less weight

  1. ↑ Except in those chapters (Chap. XVII., for example) where I am dealing chiefly with the work of others.
  2. ↑ The first writer I know of to notice this was Ancillon in Doutes sur les bases du calcul des probabilités (1794): " Dire qu'un fait passé, présent ou à venir est probable, c'est dire qu'une proposition est probable." The point was emphasised by Boole, Laws of Thought, pp. 7 and 107. See also Czubor, Wahrscheinlichkeitsrechnung, vol. i. p. 5, and Stumpf, Über den Begriff der mathematischen Wahrscheinlichkeit.
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