Abstract
Summary This paper criticizes some of the claims of the standard theories of subjective probability. The criticisms are especially oriented toward the structural axioms that cannot be regarded as axioms of pure rationality and the general results that yield exact measurement of subjective probabilities. Qualitative axioms for upper and lower probability are introduced to provide a theory of inexact measurement of subjective probability. Only minor modifications of de Finetti's qualitative axioms yield the desired theory. The paper concludes with a comparison of the measurement of belief to the measurement results characteristic of Euclidean geometry, and also examines briefly some possibilities for using learning models as simplified abstract processes for constructing belief.
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