“Tensions in the Theory of the Conditional”

I will begin by developing a theory of the conditional based on the idea that conditionals are mechanisms for talking about (possibly non-actual) worlds. I argue that credence judgments tell against the Lewis-Kratzer Duality principle and in favor of Conditional Excluded Middle. The main theory which validates the latter is  Stalnaker’s; but Stalnaker’s theory cannot account for conditionals with overt modals, which seem to require a Lewis-Kratzer restrictor approach. The latter as it stands validates Duality, not Conditional Excluded Middle; I develop a version which validates Conditional Excluded Middle, not Duality. Doing this not only better conforms with intuitions, but also allows us to dispense with one of the restrictor theory’s least attractive features: the need to posit covert modals in apparently bare conditionals. Bare conditionals, on my view, are truly bare: they conceal neither a modal meaning in ‘if’ nor a covert modal in the consequent, but rather are mechanisms for talking directly about (possibly non-actual) worlds. In the second part of the talk, I show that this way of thinking about the conditional, natural though it is, is in direct tension with another very natural thought: namely, that, if p entails q, then ‘If p, q’ is a theorem—in other words, that the conditional is bounded from above by the strict (logical) conditional.