On Assertion and Indicative Conditionals

T he circumstances in which it is natural to assert the ordinary indicative conditional If P then are those in which it is natural to assert Either not P or, P and and conversely. For instance, the circumstances in which it is natural to assert If it rains, the match will be cancelled are precisely those in which it is natural to assert Either it won't rain or, it will and the match will be cancelled. Similarly, the circumstances in which it is natural to assert Not both P and are precisely those in which it is natural to assert Either not P or not We explain the latter coincidence of assertion conditions by a coincidence of truth conditions. Why not do the same in the case of the conditional? Why that is, hold that If P then has the same truth conditions as Either not P or, P and Q? This hypothesis-given the standard and widely accepted truth functional treatments of not, or,5 and and-amounts to the Equivalence thesis: the thesis that (P Q) is equivalent to (P D Q). (I will use for the indicative conditional, reserving 0-* for the subjunctive or counterfactual conditional.) In this paper I defend a version of the Equivalence thesis. As a rule, our intuitive judgements of assertability match up with our intuitive judgements of probability, that is, S is assertable to the extent that it has high subjective probability for its assertor. Now it has been widely noted that when (P D Q) is highly probable but both and are not highly probable, it is proper to assert (P Q).1 The problem for the Equivalence thesis is to explain away the putative counter examples to -P e (P-Q)J and Q H (P -> the only too familiar cases where despite the high probability of or of Q. and so of (P D Q), (P -* Q) is