B. De Finetti's "Fundamental Theorem of Probability" is reformulated as a computable linear programming problem. The theorem is substantially extended, and shown to have fundamental implications for the theory and practice of statistics. It supports an operational meaning for the partial assertion of prevision via asserted bounds. The theorem is expanded to apply to general quantities; to allow bounds and orderings on previsions as input to the programming problem; and to yield bounds, even on conditional previsions, as output. Consequences include the ultimate strengthening of any probability inequality based on linear constraints, such as the Bienayme-P. L. Chebyshev inequality and an inequality related to Kolmogorov's inequality, but based only on the judgment of a sequence of quantities as exchangeable. Included in the wide variety of potential applications are the safety assessment of complex engineering systems, the analysis of agricultural production statistics, and a synthesis of subjective judgments in macro-economic forecasting. Prevision is explicitly recognized as a completion of the notion of logical assertion, introduced by Frege. (Author/SLD)