Considering the exceptions: on the failure of cumulative transitivity for indicative conditionals

Abstract

According to existing accounts of indicative conditionals, any argument of the following form is valid: Here, I present a set of counterexamples to show that there exist invalid arguments of this form. I argue that this data poses serious problems to variably strict accounts of conditionals (Lewis 1973; Stalnaker 1968), as such accounts are structurally unable to accommodate it. Dynamic strict accounts (von Fintel 2001; Gillies, 2007; Willer 2017), however, are a different story. While existing dynamic strict accounts do not accommodate the data, they are in principle able to, and I propose a modified dynamic strict account, drawing from von Fintel (2001), that does. The key modification is this: whereas existing dynamic strict accounts take into account only the effects of conditional antecedents in changing the semantic context, the data shows that we must also take into account the effects of conditional consequents in changing the semantic context.