Analysis of Conditional Expressions Public Deposited

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  • March 20, 2019
  • Presting, Kenneth A.
    • Affiliation: College of Arts and Sciences, Department of Philosophy
  • What David Lewis proved in 1976 was stronger than he realized. Not only can no system of logic can have a conditional connective with non-trivial conditional probability, but also no probability space can have even a single non-trivial conditional event. However, Lewis' definition of conditional connective is flawed, and does not apply to his original target, the Stalnaker/Thomasson C2 logic. Lewis assumed a property which Stalnaker's system does not have - McGee's export-import law. Modal models of Stalnaker's C2 exist for every first-order model. Stalnaker's corner connectives, when interpreted as Lycan-style quantified conditionals, do have nontrivial conditional probability. Interpreting propositions as indicator functions instead of sets of possible worlds, the modern Kolmogorov theory of conditional expectation opens new possibilities for simultaneously modeling both objective and subjective probability as the expectation of truth. I use the new interpretation to defend Lycan's theory of conditionals against an objection from Dorothy Edgington.
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  • Simmons, Keith
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