Bayesian probability


Bayesian decision theory is here construed as explicating a particular concept of rational choice and Bayesian probability is taken to be the concept of probability used in that theory. Bayesian probability is usually identified with the agent’s degrees of belief but that interpretation makes Bayesian decision theory a poor explication of the relevant concept of rational choice. A satisfactory conception of Bayesian decision theory is obtained by taking Bayesian probability to be an explicatum for inductive probability given the agent’s evidence.

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  1. Carnap, R. (1950). Logical foundations of probability (2nd ed., 1962). Chicago: University of Chicago Press.

  2. Carnap R. (1952) The continuum of inductive methods. University of Chicago Press, Chicago

    Google Scholar 

  3. Carnap R. (1963) Replies and systematic expositions. In: Schilpp P.A. (eds) The philosophy of Rudolf Carnap. Open Court, La Salle, IL, pp 859–1013

    Google Scholar 

  4. Kahneman, D., Slovic, P., Tversky, A. (eds) (1982) Judgment under uncertainty: Heuristics and biases. Cambridge University Press, New York

    Google Scholar 

  5. Maher P. (2006) The concept of inductive probability. Erkenntnis 65: 185–206

    Article  Google Scholar 

  6. Maher P. (2007) Explication defended. Studia Logica 86: 331–341

    Article  Google Scholar 

  7. Maher, P. (2008). Physical probability. In C. Glymour, W. Wang, & D. Westerståhl (Eds.), Logic, methodology and philosophy of science: Proceedings of the thirteenth international congress. London: Kings College Publications (To appear).

  8. Ore O. (1960) Pascal and the invention of probability theory. American Mathematical Monthly 67: 409–419

    Article  Google Scholar 

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Correspondence to Patrick Maher.

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Maher, P. Bayesian probability. Synthese 172, 119 (2010).

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  • Bayesian probability
  • Logical probability
  • Inductive probability
  • Subjective probability
  • Degrees of belief
  • Decision theory
  • Expected utility
  • Explication
  • Carnap