Abstract

Adams’ Thesis has much evidence in its favour, but DavidLewis famously showed that it cannot be true, in all but the most trivial of cases, if conditionals are proprositions and their probabilities are classical probabilities of truth. In this paper I show thatsimilar results can be constructed for a much wider class of conditionals. The fact that these results presupposethat the logic of conditionals is Boolean motivates a search for a non-Boolean alternative. It is arguedthat the exact proposition expressed by a conditional depends on the context in which it is uttered. Consequentlyits probability of truth will depend not only on the probabilities of the various propositions it mightexpress, but also on the probabilities of the contexts determining which proposition it does in fact express.The semantic theory developed from this is then shown to explain why agents’ degrees of belief satisfyAdams’ Thesis. Finally the theory is compared with proposals for a three-valued logic of conditionals.