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Summary This category covers a variety of approaches to modality, characterized by their including a principle of recombination whereby there is a possibility for each way of combining some elements.
Key works Skyrms 1981 develops a combinatorialism inspired by Wittgenstein's Tractatus. A principle of recombination is at the heart of Lewisian modal realism (Lewis 1986). Armstrong 1989 sets out a fictionalist combinatorialism with distinctive commitments, among them that there are no alien universals (i.e. universals not instantiated at the actual world).
Introductions Wilson forthcoming
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  1. D. M. Armstrong (1989). A Combinatorial Theory of Possibility. Cambridge University Press.
    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.
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  2. D. M. Armstrong (1986). The Nature of Possibility. Canadian Journal of Philosophy 16 (4):575 - 594.
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  3. David Armstrong, Combinatorialism Revisited.
    The object of this paper is to argue once again for the combinatorial account of possibility defended in earlier work (Armstrong, 1989, 1997). But there I failed fully to realise the dialectical advantages that accrue once one begins by assuming the hypothesis of logical atomism, the hypothesis that postulates simple particulars and simple universals (properties and relations) at the bottom of the world. Logical atomism is, I incline to think, no better than ‘speculative cosmology’ as opposed to ‘analytic ontology’, to (...)
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  4. Raymond Bradley (1989). Possibility and Combinatorialism: Wittgenstein Versus Armstrong. Canadian Journal of Philosophy 19 (1):15 - 41.
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  5. Ross P. Cameron (2008). Recombination and Intrinsicality. Ratio 21 (1):1–12.
    In this paper I argue that warrant for Lewis' principle of recombination presupposes warrant for a combinatorial analysis of intrinsicality, which in turn presupposes warrant for the principle of recombination. This, I claim, leads to a vicious circularity: warrant for neither doctrine can get off the ground.
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  6. Nicola Ciprotti (2006). A Puzzle About Restricted Recombination in Modal Realism. In Paolo Valore (ed.), Topics on General and Formal Ontology. Polimetrica. 281.
    This paper addresses a specific issue inherent to David Lewis’s conception of possible worlds, namely whether or not they are liable to being limited in size. The paper purports to show that, if a certain argument against unlimited worlds’ size is valid, then the way of countering it by means of positing an upper limit to size (as Lewis himself and John Divers have suggested) leads to a troublesome distortion of some modal phenomena, such as de re ascriptions of properties. (...)
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  7. David Efird & Tom Stoneham (2006). Combinatorialism and the Possibility of Nothing. Australasian Journal of Philosophy 84 (2):269 – 280.
    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.
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  8. Janne Hüpakka, Markku Keinänen & Anssi Korhonen (1999). A Combinatorial Theory of Modality. Australasian Journal of Philosophy 77 (4):483 – 497.
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  9. Javier Kalhat (2011). Is There A Quasi-Mereological Account of Property Incompatibility? Acta Analytica 26 (2):115-133.
    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 (...)
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  10. Jaegwon Kim (1986). Possible Worlds and Armstrong's Combinatorialism. Canadian Journal of Philosophy 16 (4):595 - 612.
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  11. Thomas Mormann (1997). Topological Aspects of Combinatorial Possibility. Logic and Logical Philosophy 5:75 - 92.
    The aim of this paper is to show that topology has a bearing on<br><br>combinatorial theories of possibility. The approach developed in this article is “mapping account” considering combinatorial worlds as mappings from individuals to properties. Topological structures are used to define constraints on the mappings thereby characterizing the “really possible” combinations. The mapping approach avoids the well-known incompatibility problems. Moreover, it is compatible with atomistic as well as with non-atomistic ontologies.It helps to elucidate the positions of logical atomism and monism (...)
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  12. Susan Schneider (2001). Alien Individuals, Alien Universals, and Armstrong's Combinatorial Theory of Possibility. Southern Journal of Philosophy 39 (4):575-593.
    Armstrong's combinatorialism, in his own words, is the following project: "My central metaphysical hypothesis is that all there is is the world of space and time. It is this world which is to supply the actual elements for the totality of combinations. So what is proposed is a Naturalistic form of a combinatorial theory."2 Armstrong calls his central hypothesis "Naturalism." He intends his well−known theory of universals to satisfy this thesis. He now attempts to give a naturalistic theory of modality.
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  13. Theodore Sider (2009). Williamson's Many Necessary Existents. Analysis 69 (2):250-258.
    This note is to show that a well-known point about David Lewis’s (1986) modal realism applies to Timothy Williamson’s (1998; 2002) theory of necessary existents as well.1 Each theory, together with certain “recombination” principles, generates individuals too numerous to form a set. The simplest version of the argument comes from Daniel Nolan (1996).2 Assume the following recombination principle: for each cardinal number, ν, it’s possible that there exist ν nonsets. Then given Lewis’s modal realism it follows that there can be (...)
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  14. Theodore Sider (2005). Another Look at Armstrong's Combinatorialism. Noûs 39 (4):679–695.
    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.
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  15. Brian Skyrms (1981). Tractarian Nominalism. Philosophical Studies 40 (2):199 - 206.
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  16. Holly Gail Thomas (1996). Combinatorialism and Primitive Modality. Philosophical Studies 83 (3):231 - 252.
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  17. Holly Gail Thomas (1995). The Principle of Recombination and the Principle of Distinctness: A Puzzle for Armstrong's Theory of Modality. Australasian Journal of Philosophy 73 (3):444 – 457.
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  18. Daniel von Wachter (2004). The Ontological Turn Misunderstood: How to Misunderstand David Armstrong's Theory of Possibility. Metaphysica 5 (2):105-114, http://epub.ub.uni-muen.
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  19. Jessica M. Wilson (forthcoming). Hume's Dictum and Metaphysical Modality: Lewis's Combinatorialism. In Barry Loewer & Jonathan Schaffer (eds.), The Blackwell Companion to David Lewis. Blackwell.
    Many contemporary philosophers accept Hume's Dictum (HD), according to which there are no metaphysically necessary connections between distinct, intrinsically typed entities. Tacit in Lewis's work is a potential motivation for HD, according to which one should accept HD as presupposed by the best account of the range of metaphysical possibilities---namely, a combinatorial account, applied to spatiotemporal fundamentalia. Here I elucidate and assess this Ludovician motivation for HD. After refining HD and surveying its key, recurrent role in Lewis’s work, I present (...)
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