In this paper, we give a precise characterization of the principle of recombination and argue that it need not be subject to any restrictions.

David Kaplan famously argued that mainstream semantics for modal logic, which identifies propositions with sets of possible worlds, is affected by a cardinality paradox. Takashi Yagisawa showed that a variant of the same paradox arises when standard possible worlds semantics is extended with impossible worlds to deliver a hyperintensional account of propositions. After introducing the problem, we discuss two general approaches to a possible solution: giving up on sets and giving up on worlds, either in the background semantic framework or (...) in the corresponding conception of propositions. As a result, we conclude that abandoning worlds by embracing a truthmaker-based approach offers a promising way to account for hyperintensional propositions without facing the paradoxical outcome. (shrink)

The Forrest-Armstrong argument, as reconfigured by David Lewis, is a reductio against an unrestricted principle of recombination. There is a gap in the argument which Lewis thought could be bridged by an appeal to recombination. After presenting the argument, I show that no plausible principle of recombination can bridge the gap. But other plausible principles of plenitude can bridge the gap, both principles of plenitude for world contents and principles of plenitude for world structures. I conclude that the Forrest-Armstrong argument, (...) when fortified in one of these ways, demands that unrestricted recombination be rejected. The appropriate restriction comes from a consideration of what world structures are possible. I argue that, although there are too many worlds to form a set, for any world, the individuals at that world do form a set. To defend it I invoke a principle of Limitation of Size together with an iterative conception of structure. (shrink)

Is the world internally connected by a web of necessary connections or is everything loose and independent? Followers of David Hume accept the latter by upholding Hume’s Dictum, according to which there are no necessary connections between distinct existences. Roughly put, anything can coexist with anything else, and anything can fail to coexist with anything else. Hume put it like this: “There is no object which implies the existence of any other if we consider these objects in themselves.” Since Hume’s (...) day, Hume’s Dictum has played a major role in philosophy, especially in contemporary metaphysics. In ruling out necessary connections, Hume’s Dictum implies that causal relations and the laws of nature are contingent. It makes other demands on our metaphysics of science as well; for example, it places restrictions on our metaphysics of counterfactuals, dispositions, and explanation. The principle has applications in other areas too. Hume’s Dictum places constraints on our theories of abstract objects and moral properties. For example, Hume’s Dictum rules out the view that moral properties are distinct from, but necessarily connected to, non-moral properties. While Hume’s Dictum is a prominent principle in metaphysics, few Humeans have defended the principle at length. It is assumed more often than it is argued for. As a result, Hume’s Dictum no longer enjoys the reputation it once did. It’s common to hear complaints about the lack of arguments in support of Hume’s Dictum. Moreover, philosophers are increasingly willing to defend views that are at odds with Hume’s Dictum. A striking example of this is the recent explosion of interest in views that take causal relations and the laws of nature to be necessary. Humeans can no longer afford to be complacent. An extended defense of Hume’s Dictum is called for, and that’s what this dissertation aims to offer. This dissertation has three parts. In the first part, I lay out some preliminaries and offer a precise formulation of Hume’s Dictum. In the second part, I develop three arguments in favor of Hume’s Dictum. In the final part, I defend Hume’s Dictum against objections. (shrink)

Cantor proved that no set has a bijection between itself and its power set. This is widely taken to have shown that there infinitely many sizes of infinite sets. The argument depends on the princip...

I argue for the possibility of hypergunk: that is, it is possible that there exists an x such that every part of x has a proper part and, for any set S of parts of x, there is a set S′ of parts of...

In this paper, we give a precise characterization of the principle of recombination and argue that it need not be subject to any restrictions.

Regularity is the thesis that all contingent propositions should be assigned probabilities strictly between zero and one. I will prove on cardinality grounds that if the domain is large enough, a regular probability assignment is impossible, even if we expand the range of values that probabilities can take, including, for instance, hyperreal values, and significantly weaken the axioms of probability.

This article includes a basic overview of possible world semantics and a relatively comprehensive overview of three central philosophical conceptions of possible worlds: Concretism (represented chiefly by Lewis), Abstractionism (represented chiefly by Plantinga), and Combinatorialism (represented chiefly by Armstrong).

Consider the reasonable axioms of subjunctive conditionals if p → q1 and p → q2 at some world, then p → at that world, and if p1 → q and p2 → q at some world, then → q at that world, where p → q is the subjunctive conditional. I show that a Lewis-style semantics for subjunctive conditionals satisfies these axioms if and only if one makes a certain technical assumption about the closeness relation, an assumption that is probably (...) false. I will then show how Lewisian semantics can be modified so as to assure and even when the technical assumption fails, and in fact in one sense the semantics actually becomes simpler then. (shrink)

The notion of omnipotence has proved to be quite recalcitrant to analysis. Still, during the last three decades or so, there has resurfaced a clever argument to the effect that, whatever omnipotence is, it cannot be exemplified in God: an allegedly impeccable and all-perfect being. Scrutinizing this argument, however, I find it less than convincing. Moreover, and more importantly, I venture a positive account of my own: a non-technical and distinctively metaphysical definition of omnipotence which, if true, sidesteps quite a (...) number of well-known pitfalls. Also, by way of introduction, I review some earlier attempts. (shrink)