Published online by Cambridge University Press: 01 April 2022
The representation theorems of expected utility theory show that having certain types of preferences is both necessary and sufficient for being representable as having subjective probabilities. However, unless the expected utility framework is simply assumed, such preferences are also consistent with being representable as having degrees of belief that do not obey the laws of probability. This fact shows that being representable as having subjective probabilities is not necessarily the same as having subjective probabilities. Probabilism can be defended on the basis of the representation theorems only if attributions of degrees of belief are understood either antirealistically or purely qualitatively, or if the representation theorems are supplemented by arguments based on other considerations (simplicity, consilience, and so on) that single out the representation of a person as having subjective probabilities as the only true representation of the mental state of any person whose preferences conform to the axioms of expected utility theory.
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I wish to thank Alan Hájek, Michael Kinyon, J. Wesley Robbins, and the participants at the Conference on Methods (New School, New York City, May 15, 1999) for helpful discussion of this essay. Thanks also to one of the anonymous referees, whose insightful comments prompted me to clarify several points.