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Probability a logical relation

Keynes is unequivocal in his insistence that probability represents a logical relation that is objective.

[I]n the sense important to logic, probability is not subjective. It is not, that is to say, subject to human caprice. A proposition is not probable because we think it so. When once the facts are given which determine our knowledge, what is probable or improbable in these circumstances has been fixed objectively, and is independent of our opinion. The Theory of Probability is logical, therefore, because it is concerned with the degree of belief which it is rational to entertain in given conditions, and not merely with the actual beliefs of particular individuals, which may or may not be rational.

(TP, p. 4)

Having thus laid his cards on the table, Keynes at no point backs down.

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.

(TP, p. 5)

Keynes distinguishes three senses of the term "probability." In the most basic sense, it refers to "the logical relation between two sets of propositions" (TP, p. 11). Derivatively, the word applies to "the degrees of rational belief arising out of knowledge of secondary propositions which assert the existence of probability relations" (TP, p. 12). And then one can apply the term "probable" to the proposition that is so believed.

The epistemology discussed in the second chapter of the Treatise is a creation of the early twentieth century. It owes much to Russell and Moore, and is only marginally relevant to the discussion of probability. One phrase, however, is relevant to our treatment of Ramsey's criticism. The distinction is drawn between "direct knowledge" and "knowledge by argument." "In the case of every argument, it is only directly that we can know the secondary proposition which makes the argument itself valid and rational" (TP, p. 15). Applied to probability, in its fundamental sense, this entails that the probability relation between premises and conclusion of an argument must be perceived directly.

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