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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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  1. George S. Boolos (2011). The Logic of Provability. Cambridge University Press.
    This book, written by one of the most distinguished of contemporary philosophers of mathematics, is a fully rewritten and updated successor to the author's earlier The Unprovability of Consistency. Its subject is the relation between provability and modal logic, a branch of logic invented by Aristotle but much disparaged by philosophers and virtually ignored by mathematicians. Here it receives its first scientific application since its invention. Modal logic is concerned with the notions of necessity and possibility. What George Boolos does (...)
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  2. Markus Schrenk (2015). Trigger Happy. Ein Kommentar zu Barbara Vetters Potentiality. Zeitschrift für Philosophische Forschung 69 (3):396-402.
    This is a review of Barbara Vetter’s book Potentiality: From Dispositions to Modality. Oxford University Press (2015). The first part of Vetter’s book aims to show that the standard semantic and/or metaphysical interpretation of dispositional predicates and/or dispositions fails and that it ought to be replaced by Vetter’s own potentiality metaphysics. This review critically investigates the consequences this view has. (The review is written in German, an English version is available on request.).
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  3. Jose Tomas Alvarado (2009). A Causal Theory of Modality. Ideas Y Valores 140:173-196.
    This work presents a causal conception of metaphysical modality in which a state of affairs is metaphysically possible if and only if it can be caused (in the past, the present or the future) by current entities. The conception is contrasted with what is called the "combinatorial" conception of modality, in which everything can coexist with anything else. This work explains how the notion of 'causality' should be construed in the causal theory, what difference exists between modalities thus defined from (...)
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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. 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 at the bottom of the world. Logical atomism is, I incline to think, no better than ‘speculative cosmology’ as opposed to ‘analytic ontology’, to use Donald Williams’ terminology. It is, (...)
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  6. John C. Bigelow (1988). Real Possibilities. Philosophical Studies 53 (1):37 - 64.
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  7. Raymond Bradley (1989). Possibility and Combinatorialism: Wittgenstein Versus Armstrong. Canadian Journal of Philosophy 19 (1):15 - 41.
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  8. 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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  9. Keith Campbell (2014). David Malet Armstrong (8 July 1926 – 13 May 2014). Australasian Journal of Philosophy 92 (3):617-618.
  10. Gerard Casey (1988). A Combinatorial Theory of Possibility. Philosophical Studies 32:274-283.
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  11. 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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  12. 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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  13. 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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  14. Janne Hiipakka, Markku Keinänen & Anssi Korhonen (1999). A Combinatorial Theory of Modality. Australasian Journal of Philosophy 77 (4):483 – 497.
    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.
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  15. 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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  16. Jaegwon Kim (1986). Possible Worlds and Armstrong's Combinatorialism. Canadian Journal of Philosophy 16 (4):595 - 612.
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  17. Max Kistler (2004). Le combinatorialisme et le réalisme nomologique sont-ils compatibles? In Jean-Maurice Monnoyer (ed.), La Structure Du Monde. Vrin, Paris 199-221.
    English title: Are combinatorialism and nomological realism compatible?
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  18. Anssi Korhonen (2008). Armstrong on the Metaphysics of Modality: Two Dilemmas. Acta Philosophica Fennica 84:153.
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  19. David K. Lewis (1992). Armstrong on Combinatorial Possibility. In Papers in Metaphysics and Epistemology. Cambridge Up 196-214.
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  20. Roberto Loss (2016). Grounds, Roots and Abysses. Thought: A Journal of Philosophy 5 (1):41-52.
    The aim of this study is to address the “Grounding Grounding Problem,” that is, the question as to what, if anything, grounds facts about grounding. I aim to show that, if a seemingly plausible principle of modal recombination between fundamental facts and the principle customarily called “Entailment” are assumed, it is possible to prove not only that grounding facts featuring fundamental, contingent grounds are derivative but also that either they are partially grounded in the grounds they feature or they are (...)
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  21. Cynthia Macdonald (1991). A Combinatorial Theory of Possibility. Philosophical Books 32 (3):163-164.
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  22. Christopher Menzel, Possible Worlds. Stanford Encyclopedia of Philosophy.
    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).
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  23. 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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  24. Howard Robinson (1998). Some Problems with the Combinatorial Theory of Possibility. Acta Analytica 21:147-161.
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  25. 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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  26. 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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  27. 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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  28. Brian Skyrms (1981). Tractarian Nominalism. Philosophical Studies 40 (2):199 - 206.
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  29. Holly Gail Thomas (1996). Combinatorialism and Primitive Modality. Philosophical Studies 83 (3):231 - 252.
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  30. 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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  31. 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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  32. David Weissman (1991). A Combinatorial Theory of Possibility. Review of Metaphysics 44 (3):614-617.
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  33. 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, 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 (...)
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  34. 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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  35. José L. Zalabardo (2015). Representation and Reality in Wittgenstein's Tractatus. Oxford University Press Uk.
    José L. Zalabardo puts forward a new interpretation of central ideas in Wittgenstein's Tractatus Logico-Philosophicus concerning the structure of reality and our representations of it in thought and language. He presents the picture theory of propositional representation as Wittgenstein's solution to the problems that he had found in Bertrand Russell's theories of judgment. Zalabardo then attributes to Wittgenstein the view that facts and propositions are ultimate indivisible units, not the result of combining their constituents. This is Wittgenstein's solution to the (...)
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Modal Conventionalism
  1. A. Ahmed (2012). Modality: Metaphysics, Logic, and Epistemology, Bob Hale and Aviv Hoffmann (Eds). Mind 121 (483):817-822.
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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. Roberta Ballarin (2004). The Interpretation of Necessity and the Necessity of Interpretation. Journal of Philosophy 101 (12):609 - 638.
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  7. Max Black (1943). The Analysis of a Simple Necessary Statement. Journal of Philosophy 40 (2):39-46.
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  8. 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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  9. Jeffrey Scott Coombs (1990). The Truth and Falsity of Modal Propositions in Renaissance Nominalism. Dissertation, The University of Texas at Austin
    During a short-lived renaissance of medieval Nominalism lasting from approximately 1480 to 1530, many Renaissance Nominalist logicians devoted a great deal of attention to the task of developing an account of the truth and falsity of modal propositions. A modal proposition is any proposition containing one or more occurrences of the four modal terms: possible, necessary, impossible, and contingent. The Nominalist account follows the general procedure outlined in William of Ockham's Summa totius logicae, the goal of which is to translate (...)
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  10. Hans-Johann Glock (2010). Necessity, a Priority and Analyticity: A Wittgensteinian Perspective. In Daniel Whiting (ed.), The Later Wittgenstein on Language. Palgrave Macmillan
  11. 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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  12. José Edgar González Varela (2013). Caution and Necessity. Manuscrito 36 (2):229-261.
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