Conditional Excluded Middle in Informational Semantics

Abstract

Semantics for indicative conditionals (ICs) struggle with a problem inherited from the classical Stalnaker/Lewis debate on counterfactuals. On the one hand, ICs seem to satisfy Conditional Excluded Middle; on the other, ICs of the form φ > ¬ψ seem incompatible with might-conditionals of the form φ > 3ψ. These requirements are jointly unsatisfiable on standard notions of consequence. I show that a relative of Veltman’s data and update semantics (1985, 1996), which I call path semantics, validates both. The analysis is confined to ICs, but can in principle be extended to counterfactuals.