Logic and Gambling


This paper outlines a formal recursive wager resolution calculus (WRC) that provides a novel conceptual framework for sentential logic via bridge rules that link wager resolution with truth values. When paired with a traditional truth-centric criterion of logical soundness WRC generates a sentential logic that is broadly truth-conditional but not truth-functional, supports the rules of proof employed in standard mathematics, and is immune to the most vexing features of their traditional implementation. WRC also supports a novel probabilistic criterion of logical soundness, the fair betting probability criterion (FBP). It guarantees that the conclusion of an FBP-valid argument is at least as credible as a conjunction of premises, and also that the conclusion is true if the premises are. In addition, WRC provides a platform for a novel non-probabilistic, computationally simpler criterion of logical soundness – the criterion of Super-validity - that issues the same logical appraisals as FBP, and hence the same guarantees.



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Stephen Spielman
University of Pennsylvania (PhD)

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References found in this work

On conditionals.Dorothy Edgington - 1995 - Mind 104 (414):235-329.
Two Recent Theories of Conditionals.Allan Gibbard - 1981 - In William Harper, Robert C. Stalnaker & Glenn Pearce (eds.), Ifs. Reidel. pp. 211-247.

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