Generalising the probabilistic semantics of conditionals

Abstract

If assertibility rules are to be important in semantic theory, hypotheses such as this one will need to beiinvestigated. And Slote's observation (see note 12) that what matters for assertibility is not belief but knowledge will turn out to have powerful consequences. Adams' rule is the first well understood assertibility rule in philosophical semantics. I think we should be led by its successes to look for more. In this paper, I have built on his assertibility rule and offered two more. But it is worth observing, finally, that their interest lies, in part, in the contrast with semantic rules stated in terms of truth conditions. Much recent discussion of assertibility conditions derives from Dummett's “anti-realist” claim that we should perhaps substitute assertibility conditions for truth conditions in general; see Dummett (1973), Wright (1976). This notion of assertibility is not the one I have been working with here: for the anti-realist notion of an assertibility condition is of a condition whose obtaining provides epistemic warrant for the sentence asserted. Dummett and Wright's assertibility conditions are thus to do with the justification of the belief expressed by a sentence and not directly with the justification for asserting it. 17 But realists may be interested in a more modest role for assertibility conditions — in my sense — which are not derived, by way of ASS, from truth conditions. Realism need not be the claim that all declarative sentences can be given truth conditions; it requires only the view that truth conditions account for the central class of cases. The proposals in this paper presuppose a realist treatment of the antecedents and consequents of unembedded conditionals, and a realist view of the sentences within the scope of the epistemic modality. What could be more central than that?