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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.

David Armstrong sets out his metaphysical system in a set of concise and lively chapters each dealing with one aspect of the world.

In this paper I argue against Armstrong’s recent truthmaking account of possibility. I show that the truthmaking account presupposes modality in a number of different ways, and consequently that it is incapable of underwriting a genuine reduction of modality. I also argue that Armstrong’s account faces serious difficulties irrespective of the question of reduction; in particular, I argue that his Entailment and Possibility Principles are both false.

This major new work by David Armstrong is a contribution to recent philosophical discussions about possible worlds. Taking Wittgenstein's Tractatus as his point of departure, Armstrong argues that non-actual possibilities and possible worlds are recombinations of actually existing elements and as such are useful fictions. Included is an extended criticism of the alternative possible worlds approach championed by the American philosopher David Lewis.

For almost fifty years, David Armstrong has made major contributions in analytic philosophy. The aim of this volume is to collect papers that situate, discuss and critically assess Armstrong’s contributions. The book is organized in three parts. In Section I: Analytical Metaphysics and Its Methodology, certain basic principles of analytic metaphysics advocated by Armstrong (such as truthmaker maximalism and the Doctrine of Ontological Free Lunch) and their consequences are critically examined. The articles of Section II: Laws of Nature, Dispositions, and Modality, study the constraints Armstrong’s naturalism sets to his ontology of modality, laws and dispositions. Finally, the articles of Section III: Mind and Epistemology, study and critically evaluate Armstrong’s contributions in epistemology, the philosophy of perception and color. The collection is meant for all philosophers and scholars interested in these central topics of analytic philosophy.

David Armstrong has argued that the properties of a thing are parts of it and predications are necessary. This article criticises this view and presents and alternative.

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.

Part I will deal with the central system of metaphysics that Armstrong developed between 1978 and 1997. This will concern, in turn, the major topics of universals, laws, modality, facts or states of affairs, and dispositions. It will be demonstrated how Armstrong’s distinct contributions to these separate problems came together in a unified and systematic account such that he could be judged as holding a single, very appealing, metaphysical theory.

We argue that Armstrong's Combinatorialism allows for the possibility of nothing by giving a Combinatorial account of the empty world and show that such an account is consistent with the ontological and conceptual aims of the theory. We then suggest that the Combinatorialist should allow for this possibility given some methodological considerations. Consequently, rather than being 'spoils for the victor', as Armstrong maintains, deciding whether there might have been nothing helps to determine which metaphysics of modality is to be preferred.