The theme of the dissertation is that we should not be too cautious about engaging in metaphysics of modality; what may appear to be a refusal to engage in metaphysical speculation may instead involve a commitment to epistemic consequences that we should not accept. In Part I, I argue that David Lewis's modal realism implies that scepticism towards induction is rationally unavoidable. I conclude that his theory must be rejected. ;While not endorsing Lewis's account of the nature of possible worlds, (...) I argue that the recombination principle is what is causing the problems, and that this principle will cause problems when combined with any theory of modality according to which there are objective matters of fact as to what is possible or necessary. ;I conclude that we must reject the recombination principle, and that any principle we accept in its place must be one which will not lead to inductive scepticism. This suggests that we cannot countenance any objective possibilities that contravene actual natural laws. ;In Part II, I argue that one sort of explanation is closely connected with objective possibility: A fundamental explanation for some state of affairs involves saying something about its nature that has implications for what is objectively possible. I defend a weak form of the principle of sufficient reason, according to which every state of affairs has a fundamental explanation ;I go on to recast and defend a version of the Cosmological Argument for the existence of God. This argument, on my view, is plausible only when taken as an inductive argument, and indeed, as an inference to the best explanation. I argue that the theistic hypothesis deserves to be taken seriously on its merits as an explanation; more generally, I claim that it is not sufficient grounds for rejecting any hypothesis simply to say that it involves commitments as to what is possible or necessary. A willingness to accept some such commitments is an unavoidable consequence of what we normally take to be rational ways of forming beliefs. (shrink)