Various theories have explored the hypothesis that ordinary matter- of-fact conditionals (as contrasted with counterfactual conditionals) are probability conditionals. David Lewis showed that given certain natural assumptions, there could be no probability conditional except in certain trivial probability distributions, but others have shown that on different assumptions nontrivial probability conditionals are possible. Drs. Stalnaker and Jeffrey are working together to develop a semantics for a probability conditional that avoids Lewis's trivialization, to explore its formal properties and intuitive plausibility, and to relate it to other proposals for the development of a probability conditional. In the proposed semantics, the values of sentences are random variables, functions assigning values between 0 and 1 to "possible worlds", points in probability spaces. A simple semantic rule for the conditional ensures that it is a probability conditional, but questions remain about the interpretation of complex sentences with conditionals as parts -- both about conjunctions and disjunctions of conditionals, and about nested conditionals. There are also interesting questions to be explored about the relation between this semantic framework and truth-conditional semantics for conditionals developed in the possible worlds framework. This research could contribute to clarifying the role of conditionals in inductive reasoning and concept formation in science.
