Toward the end of his classic treatise An Essay on Free Will, Peter van Inwagen offers a modal argument against the Principle of Sufficient Reason which he argues shows that the principle “collapses all modal distinctions.” In this paper, a critical flaw in this argument is shown to lie in van Inwagen’s beginning assumption that there is such a thing as the conjunction of all contingently true propositions. This is shown to follow from Cantor’s theorem and a property of conjunction (...) with respect to contingent propositions. Given the failure of this assumption, van Inwagen’s argument against the Principle of Sufficient Reason cannot succeed, at least not without the addition of some remarkable and previously unacknowledged qualifications. (shrink)

Propositional contingentism is the view that what propositions there are is a contingent matter—certain propositions ontologically depend on objects which themselves only contingently exist. Possible worlds are, loosely, complete ways the world could have been. That is to say, the ways in which everything in its totality could have been. Propositional contingentists make use of possible worlds frequently. However, a neglected, but important, question concerns whether there are any notions of worlds which are both theoretically adequate and consistent with propositional (...) contingentism. Some notion of a possible world is adequate if the systematic connection between, at least, possibility and truth at some possible world holds. Here, I argue that no adequate notion of a possible world is available to at least those who subscribe to one natural formulation of propositional contingentism. I also show that this result contrasts with a simple and adequate definition of a possible world available to the necessitist—those who hold that necessarily everything necessarily exists. (shrink)

Allen s has proposed a new approach to possible worlds, designed explicitly to overcome Cantorian difficulties for possible worlds construed as maximal consistent set of propositions. I emphasize some of the distinctive features of Hazenworlds, some of their weaknesses, and some further Cantorian problems for worlds against which they seem powerless.

The authors provide an object-theoretic analysis of two paradoxes in the theory of possible worlds and propositions stemming from Russell and Kaplan. After laying out the paradoxes, the authors provide a brief overview of object theory and point out how syntactic restrictions that prevent object-theoretic versions of the classical paradoxes are justified philosophically. The authors then trace the origins of the Russell paradox to a problematic application of set theory in the definition of worlds. Next the authors show that an (...) object-theoretic analysis of the Kaplan paradox reveals that there is no genuine paradox at all, as the central premise of the paradox is simply a logical falsehood and hence can be rejected on the strongest possible grounds—not only in object theory but for the very framework of propositional modal logic in which Kaplan frames his argument. The authors close by fending off a possible objection that object theory avoids the Russell paradox only by refusing to incorporate set theory and, hence, that the object-theoretic solution is only a consequence of the theory’s weakness. (shrink)

I formulate and defend two sceptical theses on specific parts of our modal knowledge (unqualified and absolute modalities). My main point is that unqualified modal sentences are defective in that they fail to belong unambiguously to specific modal kinds and thus cannot be evaluated; hence, we must be sceptical of beliefs involving them.