Armstrong’s combinatorial theory of possibility faces the obvious difficulty that not all universals are compatible. In this paper I develop three objections against Armstrong’s attempt to account for property incompatibilities. First, Armstrong’s account cannot handle incompatibilities holding among properties that are either simple, or that are complex but stand to one another in the relation of overlap rather than in the part/ whole relation. Secondly, at the heart of Armstrong’s account lies a notion of structural universals which, building on an (...) objection by David Lewis, is shown to be incoherent. I consider and reject two alternative ways of construing the composition of structural universals in an attempt to meet Lewis’ objection. An important consequence of this is that all putative structural properties are in fact simple. Finally, I argue that the quasi-mereological account presupposes modality in a way that undermines the reductionist aim of the combinatorialist theory of which it is a central part. I conclude that Armstrong’ quasi-mereological account of property incompatibility fails. Without that account, however, Armstrong’s combinatorial theory either fails to get off the ground, or else must give up its goal of reducing the notion of possibility to something non-modal. (shrink)

This paper explores the prospects of a combinatorial account of modality. We argue against David M. Armstrong’s version of combinatorialism, which seeks to do without modal primitives, on the grounds, among other things, that Armstrong’s basic ontological categories are themselves subject to non-contingent constraints on recombination. We outline an alternative version, which acknowledges the necessity of modal primitives, at the level of ontology, and not just of our concepts.

The core idea of David Armstrong’s combinatorial theory of possibility is attractive. Rearrangement is the key to modality; possible worlds result from scrambling bits and pieces of other possible worlds. Yet I encounter great difficulty when trying to formulate the theory rigorously, and my best attempts are vulnerable to counterexamples. The Leibnizian biconditionals relate possibility and necessity to possible world and true in.

Nomic realists have traditionally put laws to work within a theory of natural modality, in order to provide a metaphysical source for causal necessitation, counterfactuals, and dispositions. However, laws are well-suited to perform other work as well. Necessitation is a widespread phenomenon and includes cases of categorial, conceptual, grounding, mathematical and normative necessitation. A permissive theory of universals allows us to extend nomic realism into these other domains. With a particular focus on grounding necessitation, it is argued that the sorts (...) of reasons for positing laws in the natural causal domain also apply in other domains. Laws might well be the source of all first-order modality. (shrink)

Many are reluctant to accept primitive modality into their fundamental picture of the world. The worry often traces to this thought: we shouldn't adopt any more primitive - that is, unexplained - notions than we need in order to explain all the features of the world, and primitive modal notions are not needed. I examine one prominent rival to modal primitivism, combinatorialism, and show that in order to account for all the modal features of the world the combinatorialist must adopt (...) two additional primitive notions. My own modal primitivist view takes as primitive the notion of incompatibility between properties or relations. I show how the non-modal notions that the combinatorialist must adopt as primitive may be analyzed using my notion. The upshot is that with respect to the number of primitive notions, my modal primitivist theory comes out ahead. (shrink)