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Summary What is modality? The question is hard to make more precise in a theory-neutral way. The different approaches to modality encompassed within this section disagree radically over the sorts of resources that should be invoked when explaining the workings of our modal thought and talk. One widespread approach takes for granted the philosophical perspicuity of possible-worlds semantics, and then seeks to provide a metaphysical interpretation of the semantics. What kind of thing is a possible world? Are worlds linguistic entities, complex properties, fictions, concrete material objects resembling the actual world, or sui generis abstract entities? But other approaches to modality reject the possible-worlds framework, treating modal discourse as descriptive of the essential or dispositional properties of objects, or as expressive of our own inferential dispositions.
Key works A large proportion of the recent literature on the nature of modality responds to  Lewis 1986, which is both a presentation of Lewis' radical thesis of modal realism and a sustained methodological reflection on what is required of a theory of modality. At the other end of the spectrum from Lewis, Sider 2011 defends a conventionalism about modality which treats the distinction between contingent and non-contingent propositions as entirely of our own making. Rosen 1990 piggybacks on modal realism to propose an influential early version of modal fictionalism. Armstrong 1989 defends an alternative style of fictionalism. Relatedly, Blackburn 1993 overlays a non-cognitivist ('quasi-realist') metasemantics on the Lewisian picture.  Thomasson 2007 sets out 'modal normativism', an alternative form of non-cognitivism. Fine 1994 argues that essence cannot be reduced to modality and sketches the program of understanding modality in terms of essence. Vetter 2010 proposes to reduce modality to dispositional properties.
Introductions Sider 2003
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Modal Combinatorialism
  1. J. R. A. (1977). A Theory of Possibility. Review of Metaphysics 31 (2):329-330.
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  2. D. M. Armstrong (2004). Selection From A Combinational Theory of Possibility. In Tim Crane & Katalin Farkas (eds.), Metaphysics: A Guide and Anthology. OUP Oxford
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  3. 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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  4. D. M. Armstrong (1986). The Nature of Possibility. Canadian Journal of Philosophy 16 (4):575 - 594.
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  5. 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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  6. Raymond Bradley (1989). Possibility and Combinatorialism: Wittgenstein Versus Armstrong. Canadian Journal of Philosophy 19 (1):15 - 41.
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  7. 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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  8. Gerard Casey (1988). A Combinatorial Theory of Possibility. Philosophical Studies 32:274-283.
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  9. 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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  10. Tom Stoneham David Efird (2008). What is the Principle of Recombination? Dialectica 62 (4):483-494.
    In this paper, we give a precise characterization of the principle of recombination and argue that it need not be subject to any restrictions.
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  11. 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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  12. Janne Hüpakka, Markku Keinänen & Anssi Korhonen (1999). A Combinatorial Theory of Modality. Australasian Journal of Philosophy 77 (4):483 – 497.
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  13. 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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  14. Jaegwon Kim (1986). Possible Worlds and Armstrong's Combinatorialism. Canadian Journal of Philosophy 16 (4):595 - 612.
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  15. Anssi Korhonen (2008). Armstrong on the Metaphysics of Modality: Two Dilemmas. Acta Philosophica Fennica 84:153.
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  16. David K. Lewis (1992). Armstrong on Combinatorial Possibility. In Papers in Metaphysics and Epistemology. Cambridge Up 196-214.
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  17. Cynthia Macdonald (1991). A Combinatorial Theory of Possibility. Philosophical Books 32 (3):163-164.
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  18. 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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  19. Howard Robinson (1998). Some Problems with the Combinatorial Theory of Possibility. Acta Analytica 21:147-161.
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  20. 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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  21. 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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  22. 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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  23. Brian Skyrms (1981). Tractarian Nominalism. Philosophical Studies 40 (2):199 - 206.
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  24. Holly Gail Thomas (1996). Combinatorialism and Primitive Modality. Philosophical Studies 83 (3):231 - 252.
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  25. 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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  26. 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.
    This article argues that there is a great divide between semantics and metaphysics. Much of what is called metaphysics today is still stuck in the linguistic turn. This is illustrated by showing how Fraser MacBride misunderstands David Armstrong's theory of modality.
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  27. David Weissman (1991). A Combinatorial Theory of Possibility. Review of Metaphysics 44 (3):614-617.
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  28. Jessica M. Wilson (2015). Hume's Dictum and Metaphysical Modality: Lewis's Combinatorialism. In Barry Loewer & Jonathan Schaffer (eds.), The Blackwell Companion to David Lewis. Blackwell 138-158.
    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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  29. Jessica M. Wilson (2010). What is Hume's Dictum, and Why Believe It? Philosophy and Phenomenological Research 80 (3):595 - 637.
    Hume's Dictum (HD) says, roughly and typically, that there are no metaphysically necessary connections between distinct, intrinsically typed, entities. HD plays an influential role in metaphysical debate, both in constructing theories and in assessing them. One should ask of such an influential thesis: why believe it? Proponents do not accept Hume's arguments for his dictum, nor do they provide their own; however, some have suggested either that HD is analytic or that it is synthetic a priori (that is: motivated by (...)
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  30. Jose L. Zalabardo (forthcoming). Representation and Reality in Wittgenstein's Tractatus. Oxford University Press.
    The book puts forward an interpretation of some central ideas of Wittgenstein’s Tractatus Logico-Philosophicus concerning the structure of reality and our representations of it in thought and language. It presents the origins of Wittgenstein’s picture theory of propositional representation in Russell’s theories of judgment, arguing that the picture theory is Wittgenstein’s solution to some problems that he found in Russell’s position. It defends the view that, for Wittgenstein, facts in general, and the facts that play the role of propositions in (...)
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Modal Conventionalism
  1. Arif Ahmed (2012). Modality. [REVIEW] Mind 121 (483):877-822.
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  2. Jamin Asay (2013). Truthmaking for Modal Skeptics. Thought: A Journal of Philosophy 2 (4):303-312.
    Standard truthmaker theory has generally assumed a realist account of de re modality and essences. But there are reasons to be skeptical about such a view, and for considering antirealist alternatives. Can truthmaker theory survive in the face of such skepticism? I argue that it can, but that only certain antirealist perspectives on de re modality are acceptable for truthmaker theory. In particular, either a quasi-realist or conventionalist account of de re modality is needed to provide the best account of (...)
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  3. A. J. Ayer, C. H. Whiteley & M. Black (1936). Truth by Convention : A Symposium. Analysis 4 (2-3):17-32.
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  4. Jody Azzouni (1990). Truth and Convention. Pacific Philosophical Quarterly 71 (2):81-102.
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  5. Tom Baldwin (2002). The Inaugural Address: Kantian Modality: Tom Baldwin. Aristotelian Society Supplementary Volume 76 (1):1–24.
    Kant's claim that modality is a 'category' provides an approach to modality to be contrasted with Lewis's reductive analysis. Lewis's position is unsatisfactory, since it depends on an inherently modal conception of a world. This suggests that modality is 'primitive'; and the Kantian position is a prima facie plausible position of this kind, which is filled out by considering the relationship between modality and inference. This provides a context for comparing the Kantian position with Wright's non-cognitivist 'conventionalism'. Wright's position is (...)
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  6. Ross P. Cameron (2010). The Grounds of Necessity. Philosophy Compass 5 (4):348-358.
    Some truths are necessary, others could have been false. Why? What is the source of the distinction between the necessary and the contingent? What's so special about the necessary truths that account for their necessity? In this article, we look at some of the most promising accounts of the grounds of necessity: David Lewis' reduction of necessity to truth at all possible worlds; Kit Fine's reduction of necessity to essence; and accounts of necessity that take the distinction between the necessary (...)
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  7. Hans-Johann Glock (2010). Necessity, a Priority and Analyticity: A Wittgensteinian Perspective. In Daniel Whiting (ed.), The Later Wittgenstein on Language. Palgrave Macmillan
  8. Hans-Johann Glock (2003). The Linguistic Doctrine Revisited. Grazer Philosophische Studien 66 (1):143-170.
    At present, there is an almost universal consensus that the linguistic doctrine of logical necessity is grotesque. This paper explores avenues for rehabilitating a limited version of the doctrine, according to which the special status of analytic statements like 'All vixens are female' is to be explained by reference to language. Far from being grotesque, this appeal to language has a respectable philosophical pedigree and chimes with common sense, as Quine came to realize. The problem lies in developing it in (...)
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  9. José Edgar González Varela (2013). Caution and Necessity. Manuscrito 36 (2):229-261.
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  10. Bob Hale & Aviv Hoffmann (eds.) (2010). Modality: Metaphysics, Logic, and Epistemology. Oxford University Press.
    The philosophy of modality investigates necessity and possibility, and related notions--are they objective features of mind-independent reality? If so, are they irreducible, or can modal facts be explained in other terms? This volume presents new work on modality by established leaders in the field and by up-and-coming philosophers. Between them, the papers address fundamental questions concerning realism and anti-realism about modality, the nature and basis of facts about what is possible and what is necessary, the nature of modal knowledge, modal (...)
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  11. Peter W. Hanks (2008). A Dilemma About Necessity. Erkenntnis 68 (1):129 - 148.
    The problem of the source of necessity is the problem of explaining what makes necessary truths necessarily true. Simon Blackburn has presented a dilemma intended to show that any reductive, realist account of the source of necessity is bound to fail. Although Blackburn's dilemma faces serious problems, reflection on the form of explanations of necessities reveals that a revised dilemma succeeds in defeating any reductive account of the source of necessity. The lesson is that necessity is metaphysically primitive and irreducible.
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  12. Mark Heller (2008). The Donkey Problem. Philosophical Studies 140 (1):83 - 101.
    The Donkey Problem (as I am calling it) concerns the relationship between more and less fundamental ontologies. I will claim that the moral to draw from the Donkey Problem is that the less fundamental objects are merely conventional. This conventionalism has consequences for the 3D/4D debate. Four-dimensionalism is motivated by a desire to avoid coinciding objects, but once we accept that the non-fundamental ontology is conventional there is no longer any reason to reject coincidence. I therefore encourage 4Dists to become (...)
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  13. Richard V. Mason (1990). Explaining Necessity. Metaphilosophy 21 (4):382-390.
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  14. Sean McIntosh, Escaping Regress: Conventionalism and Hale.
    Conventionalism about logical necessity has, since Quine, been criticised for falling into a vicious regress. The conventionalist model involves a base class of directly stipulated necessary truths, and all other logical necessities are taken to follow from this base. The essentialist model described by Hale is constructed in a broadly similar fashion: there is a class of those necessities which hold directly in virtue of the natures of things , and other necessities are from this class derivative. Hale expresses a (...)
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  15. Toby Meadows, Modality Without Metaphysics: A Metalinguistic Approach to Possibility.
    An account of modality is produced which takes as its foundation the idea that modal concepts are parasitic upon our background theoretical commitments. This position is distinguished from the majority of philosophies of modality, which are either primitivist or reductionist. It is in this sense that our account is less burdened by metaphysics. The primary purpose of the document is to demonstrate that our approach is a coherent one. It supports this claim in three stages. First, we identify the historical (...)
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  16. G. E. Moore (1900). Necessity. Mind 9 (35):289-304.
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  17. A. J. R. (1977). A Theory of Possibility. [REVIEW] Review of Metaphysics 31 (2):329-330.
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  18. Alex D. Reid (1975). Natural Necessity. Philosophy 50 (192):221 - 229.
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  19. D. G. Ritchie (1893). The Conception of Necessity as Applied to Nature and to Man. Proceedings of the Aristotelian Society 2 (3):19 - 35.
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  20. Richard Rorty (1976). Necessity and Realism: Milton Fisk's Nature and Necessity. Noûs 10 (3):345-353.
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