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Canonical interpretation of propositions as events

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  • Alexander Zimper

Abstract

This paper establishes conditions under which Savage's (1954) informal interpretation of subjective probabilities as measures of confidence in the truth of propositions can be formally justified. For this purpose we construct, for any given propositional language, a canonical state space such that each proposition a of the language is associated with a unique event A defined on this state space. As our main result we establish a one–one onto correspondence between the canonical state space and the set of all truth conditions for the propositional logic such that proposition a is exactly true at every truth condition that corresponds to some state in A. According to our approach, an agent's degree of confidence in the truth of a proposition can, therefore, be interpreted as his or her subjective probability that some truth condition holds at which the proposition is true. Such an interpretation, however, is only valid for agents with unlimited powers of logical reasoning.

Suggested Citation

  • Alexander Zimper, 2010. "Canonical interpretation of propositions as events," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(3), pages 327-339, September.
    • Handle: RePEc:bla:ijethy:v:6:y:2010:i:3:p:327-339
    DOI: 10.1111/j.1742-7363.2010.00138.x
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    1. Robert Aumann & Adam Brandenburger, 2014. "Epistemic Conditions for Nash Equilibrium," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 5, pages 113-136, World Scientific Publishing Co. Pte. Ltd..
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    3. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2003. "A Subjective Spin on Roulette Wheels," Econometrica, Econometric Society, vol. 71(6), pages 1897-1908, November.
    4. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 263-300.
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