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Keynes as a conceptualist

Peirce would have classified Keynes as a conceptualist. For Keynes "the terms certain and probable describe the various degrees of rational belief about a proposition which different amounts of knowledge authorize us to entertain" (TP, p. 3.) To call the degrees of belief "rational" is to indicate that the "degree of belief" is that degree to which it is rational for X to entertain an hypothesis given the information or evidence available to X.

X is supposed to have a body of "direct" knowledge of logical relations between propositions that includes deductive entailments and judgements concerning the probability relations between data and hypothesis as well general principles characterizing the consistency of probability judgements with each other.

If we strip away the dubious elements of Russellian epistemology that surface in the first two chapters of Keynes's Treatise on Probability, the principles of probability logic as Keynes conceived it constitute constraints on the rational coherence of belief. Principles of deductive closure and consistency cover judgements of certainty. Principles of probability logic are constraints of rational coherence imposed on judgements of degree of belief.

Thus, Keynes suggests that if X has a set of exclusive and exhaustive hypotheses given X's background information (or certainties, evidence, or knowledge), and if "[t]here [is] no relevant evidence relating to one alternative, unless there is corresponding evidence relating to the other," one should assign equal probabilities to each alternative (TP, p. 60). Keynes suggested that the judgements of relevance and irrelevance of the evidence required to apply the principle should be based on direct judgement. Such judgements seem to be judgements of a relation of probability between evidence and hypotheses of the sort that Keynes compared to the relation of deductive entailment. Frank Plumpton Ramsey (1990a, pp. 57-9) justly worried about whether one could ground such judgments directly. Nonetheless, Keynes's principle of insufficient reason or "Indifference," as Keynes called it, is a constraint on the coherence or consistency of such judgements of relevance and judgements of equality and inequality in probability judgement. As such it could be considered a "logical principle" in a sense akin to that according to which the requirement that judgements of probability obey the calculus of probability was taken by Ramsey to be a logical principle belonging to a "logic of consistency" for probability judgement.

Keynes's second principle requires the probability of ab given h to be less than the probability of a given h unless the probability of b given ah equals 1. Keynes offered a third principle stating that the probability of a given h is comparable with the probability of a given hh1 as long as h1 contains no independent parts relevant to a.

The important point to notice here is that Keynes thought of probability logic as imposing constraints on coherent probability judgement that did not always or, indeed, typically require rational agents to adopt a unique probability distribution over some domain given the evidence. Many systems of quantitative probability judgement might satisfy the constraints given the inquirer's "evidence" or body of certainties. Sometimes numerically determinate probability judgements are mandated. For example, when the principle of insufficient reason is applicable, a rational agent is constrained to adopt degrees of belief on his or her evidence that is representable quantitatively. But probability logic cannot constrain quantitative probability judgement uniquely. According to Keynes, as I understand him, the inquirer is then obliged as a rational agent to adopt a state of probability judgement representable by the set of all the probability functions permissible according to the constraints or, alternatively, by the judgements of comparative probability judgement that are implied by all such logically permissible probability judgements. The principles of probability logic need not mandate numerical degrees of belief that a and that ab on the evidence h but only that X is required to be no less certain that a than that ab. According to Keynes, probabilities of hypotheses on given information could even be non-comparable.1

Here then is one point of agreement between Peirce and Keynes: belief probability judgements can be and often are indeterminate. If we ask, however, how the indeterminacy arises in rational probability judgement, Peirce would respond by saying that whenever there is not sufficiently precise information about statistical or physical probabilities on which to base a derivation of belief probabilities via direct inference (and the calculus of probabilities), probability judgement should be indeterminate. Keynes, as I understand him, insisted that his principles, in particular Insufficient Reason or Indifference, could often warrant assigning determinate probabilities on evidence even though indeterminacy can prevail when the requisite conditions are not met.

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