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  • Print publication year: 2006
  • Online publication date: March 2010

7 - Vexed Convexity

Summary

THE HORSE OR THE CART?

John Maynard Keynes (Keynes 1952) proposed that probability should be legislative for rational belief. He also proposed that probabilities should form only a partial order: There were to be incomparable pairs of probabilities where the first is not larger than the second, the second not larger than the first, yet the two probabilities are not equal.

Frank Plumpton Ramsey objected (Ramsey 1931), quite correctly, that any such scheme depended on being able to relate beliefs and probabilities. He disregarded the second proposal, and so took probabilities to be numbers, so that what he took to be necessary was a way of measuring degrees of belief.

Ramsey offered a somewhat naïve operational way of measuring beliefs. He himself took it to be no more than approximate (“I have not worked out the mathematical logic of this in detail, because this would, I think, be rather like working out to seven places of decimals a result only valid to two” (ibid., p. 180). What was important about Ramsey's proposal was that it also suggested why beliefs (assuming their measurability) should satisfy the probability calculus.

Ramsey's approach became the model for later “subjectivistic” approaches. First, we think about ways in which to measure degrees of belief; second, we consider why those degrees should satisfy the probability calculus; and third, we consider how those probabilities should be updated in the light of new evidence.

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  • Online ISBN: 9780511584312
  • Book DOI: https://doi.org/10.1017/CBO9780511584312
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REFERENCES
Keynes, John Maynard. 1952. A Treatise on Probability. London: Macmillan
Kyburg, Henry E., Jr. 1990. “Theories as Mere Conventions.” In Savage, Wade (ed.), Scientific Theories, pp. 158–74. Minneapolis: University of Minnesota Press
Kyburg, Henry E. Jr. 2003. “Are There Degrees of Belief?Journal of Applied Logic 1: 139–49
Kyburg, Henry E. Jr., and Teng, Choh Man. 2001. Uncertain Inference. New York: Cambridge University Press
Levi, Isaac. 1967. Gambling with Truth. New York: Knopf
Levi, Isaac. 1999. “Value Commitments, Value Conflicts, and the Separability of Belief and Value.” Philosophy of Science 60:509–33
Ramsey, F. P. 1931. The Foundations of Mathematics and Other Essay. New York: Humanities Press
Fraassen, Bas. 1984. “Belief and the Will.” Journal of Philosophy 81: 235–56
Walley, Peter. 1991. Statistical Reasoning with Imprecise Probabilities. London: Chapman and Hall