Indicative Conditionals, Context and Disagreement

Edgington mentioned that there are two prima facie desirable properties of indicative conditionals: (i) minimal certainty that A or C is enough for certainty that if not A, C; (ii) it is not necessarily irrational to disbelieve A yet disbelieve that if A, C. Then, she argued that those claim conditionals do express propositions (or have truth conditions) cannot satisfy both. Moreover, she argued that, by introducing the notion of context set, Stalnaker's semantics may satisfy both, but on his account there will be no disagreement, which is counter-intuitive, when debating. In this paper, I will argue that Stalnaker's semantics can explain disagreement, in a sense, by introducing the notion of context.