¹ Quine, W. V. ‘Two Dogmas of Empiricism’, Philosophical Review (1951) 60: 20–43 CrossRefGoogle Scholar, reprinted in Quine, W. V., From a Logical Point of View (Cambridge, MA: Harvard University Press, 1953): 20–46 Google Scholar.

² Lewis, David, On the Plurality of Worlds (Oxford: Blackwell, 1986)Google Scholar.

³ Supporters of dispositionalist accounts of modality include: Martin, C. B. and Heil, John, ‘The Ontological Turn’, Midwest Studies in Philosophy (1999) 23: 34–60 CrossRefGoogle Scholar; Pruss, A. R., ‘The actual and the possible’, in The Blackwell Guide to Metaphysics, ed. Gale, R. M. (Oxford: Blackwell, 2002): 317–33Google Scholar; Bird, Alexander, Nature's Metaphysics (Oxford: Oxford University Press, 2007)CrossRefGoogle Scholar; Borghini, Andrea and Williams, Neil E., ‘A Dispositional Theory of Possibility’, Dialectica 62 (2008): 21–41 CrossRefGoogle Scholar; Jacobs, Jonathan D., ‘A powers theory of modality: or, how I learned to stop worrying and reject possible worlds’, Philosophical Studies 151 (2010): 227–248 CrossRefGoogle Scholar; Vetter, Barbara, ‘Recent Work: Modality without Possible Worlds’, Analysis Reviews 71 (2011): 742–754 CrossRefGoogle Scholar; Potentiality: From Dispositions to Modality (Oxford: Oxford University Press, 2015)Google Scholar.

⁴ The term ‘hardcore actualism’ is due to Contessa, G., ‘Modal Truthmakers and Two Varieties of Actualism’, Synthese 174 (2010): 341–353 CrossRefGoogle Scholar.

⁵ For a comprehensive discussion of non-hardcore actualism, see Divers, John, Possible Worlds (London: Routledge, 2002)Google Scholar.

⁶ I will primarily draw upon the work of Vetter, op. cit., 2015, alongside Borghini and Williams op. cit. and Jacobs op. cit.

⁷ Lewis, David, Counterfactuals (Oxford: Blackwell, 1973), 85 Google Scholar; op. cit., passim.

⁸ This condition is famously thought to make knowledge of abstract objects problematic. See Benacerraf, Paul, ‘What numbers could not be’, Philosophical Review 74 (1965): 47–73 CrossRefGoogle Scholar; ‘Mathematical Truth’, The Journal of Philosophy 70 (1973): 661–679 CrossRefGoogle Scholar. I will predominantly be concerned with ontological rather than epistemological matters in this paper.

⁹ Given that this paper is primarily a critique of Strong Dispositionalism, I will not examine whether modal realism lives up to the claims which I make for it here. Importantly, if it does not, Strong Dispositionalism's position will be comparatively better. See Divers op. cit.

¹⁰ The term ‘safe and sane’ originates with Lewis (op. cit. 1986, 141, 143, 155) and has been employed in metaphysical discussions of modality since.

¹¹ See Quine op. cit., 31 and ‘On the individuation of attributes’ in Theories and Things (Cambridge, MA: Harvard University Press, 1981): 100–112 Google Scholar; Armstrong, David, Universals and Scientific Realism vol. 1: Nominalism and Realism (Cambridge: Cambridge University Press, 1978): 28–43 Google Scholar for famous counterexamples to this thesis.

¹² For modal realism about metaphysically ‘impossible’ worlds, see Yagisawa, T., ‘Beyond Possible Worlds’, Philosophical Studies 53 (1988): 175–204 CrossRefGoogle Scholar. For difficulties with this view and with unrestricted modal range more generally, see Allen, Sophie R., ‘Curiosity kills the categories: a dilemma about categories and modality’, Metaphysica 16 (2015): 211–30CrossRefGoogle Scholar.

¹³ Fine, Kit (‘Essence and Modality’ Philosophical Perspectives 8 (1994): 1–16 CrossRefGoogle Scholar; Modality and Tense (Oxford: Oxford University Press, 2005)Google Scholar) argues for a slightly different hardcore actualist account of modality, using essences instead of dispositional properties to ground modality. I will not debate the relative merits of Fine's essentialist modality versus dispositionalism here, although further discussion of this point can be found in Barbara Vetter, ‘Essence and Potentiality’ MS academia.edu.

¹⁴ For arguments in favour of a dispositionalist conception of properties see, for example, Shoemaker, Sidney, ‘Causality and Properties’, in van Inwagen, Peter, ed. Time and Cause (Dordrecht: D. Reidel, 1980): 109–35CrossRefGoogle Scholar; Mumford, Stephen, Dispositions (Oxford: Oxford University Press, 1998)Google Scholar; Molnar, George, Powers: a study in metaphysics (Oxford, Oxford University Press, 2003)Google Scholar; Bird, Alexander, Nature's Metaphysics (Oxford, Oxford University Press, 2007)CrossRefGoogle Scholar; Wilson, Alastair, ‘Schaffer on laws of nature’ Philosophical Studies 164 (2013): 653–667 CrossRefGoogle Scholar; and against, see Schaffer, Jonathan, ‘Quiddistic knowledge’ Philosophical Studies 123 (2005): 1–32 CrossRefGoogle Scholar.

¹⁵ Bird op. cit. holds a restricted version of this view. See note 16.

¹⁶ The instantiation here is tenseless: a property exists if and only if it has been, is, or will be, instantiated in space-time.

¹⁷ There is room for the Platonists to disagree about which uninstantiated powers exist. For instance, one might restrict the range of powers to those which could be instantiated alongside those which actually are and resist alien universal powers which could never be instantiated by actual individuals. (One might do this to account for the fact that certain determinate quantities of a determinable, such as mass, are not actually instantiated.) However, in the context of grounding modality, one might prefer a wider range of powers in order to ground a wider range of possibilities and thus include alien powers among the universal powers which exist. Since I will concentrate upon the Aristotelian conception, I will not examine these options here.

¹⁸ For a notable exception, see Smith, Quentin, ‘Absolute Simultaneity and the Infinity of Time’, in Poidevin, Robin Le, ed., Questions of Time and Tense (Oxford: Oxford University Press, 1998): 135–183 Google Scholar.

¹⁹ While Plato accepted the existence of causal relations between abstract forms, it is not popular among contemporary philosophers. See for instance Phaedo, 96a, 97c-d.

²⁰ For instance, the Resemblance Nominalism in Gonzalo Rodriguez-Pereyra's Resemblance Nominalism (Oxford: Oxford University Press, 2002)Google Scholar or Resemblance Class Trope Nominalism, as discussed in Ehring, Douglas, Tropes: Properties, Objects and Mental Causation (Oxford: Oxford University Press, 2011)CrossRefGoogle Scholar.

²¹ The formal versions are due to Yates, David, ‘Dispositionalism and the Modal Operators’, Philosophy and Phenomenological Research 91 (2015): 414 CrossRefGoogle Scholar. Since NEC and POSS are interdefinable, we need only one of them. I have chosen a version of dispositionalism which quantifies over powers and not over the individuals which have them (pace Vetter, 2015 op. cit.), since this allows the theory to account for a wider range of possibilities from the outset. For instance, it is more plausible to think that the possibility that this paper was written in German rather than in English is determined by powers instantiated by its author (me) and my environment and history, rather than by powers which the paper itself instantiates.

²² Goodman, Nelson, Fact, Fiction and Forecast (Cambridge, MA: Harvard University Press, 1954)Google Scholar; Prior, Elizabeth, Dispositions (Aberdeen: Aberdeen University Press, 1985)Google Scholar; Lewis, David, ‘Finkish Dispositions’, The Philosophical Quarterly 47 (1997): 143–158 CrossRefGoogle Scholar; Mellor, D. H., ‘The Semantics and Ontology of Dispositions’, Mind 109 (2000): 757–780 CrossRefGoogle Scholar.

²³ Individuation by manifestations alone is preferred by Strong Dispositionalists about modality. See Borghini and Williams op. cit., 24, 27 and Vetter op. cit., 2015, 35 and ch. 3 passim. For simplicity, I will not discuss Borghini and Williams’ distinction between dispositions and dispositional properties since nothing in my argument depends upon this.

²⁴ I will not rely upon establishing this point. Not only would one have to argue that we do indeed have first person experience of instantiating dispositions as agents, one would also have to affirm that this conception generalises to properties which are not a matter of our direct subjective experience. See Mumford, Stephen and Anjum, Rani Lill, Getting Causes from Powers (Oxford: Oxford University Press, 2011), 176 CrossRefGoogle Scholar.

²⁵ Quine, W. V., ‘On what there is’, Review of Metaphysics 5 (1948): 21–38 Google Scholar, reprinted in Quine, W. V., From a Logical Point of View (Cambridge, MA: Harvard University Press, 1953): 1–19 Google Scholar; ‘Ontological Relativity’, in Ontological Relativity and Other Essays (New York: Columbia University Press, 1969): 28–68 Google Scholar.

²⁶ Kripke, Saul, Naming and Necessity, (Cambridge, MA: Harvard University Press, 1980): 45, note 13Google Scholar.

²⁷ Mumford, Stephen, Laws in Nature (London: Routledge, 2004)CrossRefGoogle Scholar; Bird, op. cit.; Wilson, op. cit.

²⁸ I shall, for the purposes of this paper, assume that the dispositionalist can at least do this. However, for an argument against the view that dispositional properties produce their manifestations as a matter of necessity, see Mumford and Anjum, op. cit., 8.2. which might undermine the project to employ powers to ground modality. Their conclusion is challenged in Vetter op. cit. 2015, 92–3; Marmadoro, Anna, ‘Dispositional Modality vis-à-vis Conditional Necessity’ Philosophical Investigations 39 (2015): 205–14CrossRefGoogle Scholar.

²⁹ For instance, see Borghini and Williams, op. cit. 35–40; Wilson op. cit.; Vetter, op. cit. 2015, 267–273.

³⁰ I will use these terms interchangeably.

³¹ op. cit. 30–1. As Vetter notes, there is some confusion in Borghini and Williams’ text about the numbering and direction of the ordering (op. cit. 2015, 135, note 25). Since the question of where to start ordering is largely arbitrary, I will simply aim for consistency in what I say, rather than attempting to determine what Borghini and Williams intend to say.

³² Borghini and Williams, op. cit. 24 and 27.

³³ Yates argues that axiom (K) ⊢ □ (p ⊃ q) ⊃ (□p ⊃ □q) fails for the same reason as (T). I will not consider this problem separately since it can be rectified by the best response I suggest to preserve (T) which is to insist that all truthmaking properties are dispositional. op. cit. 2015, 414–5.

³⁴ David Yates urges the strong dispositionalist to admit defeat at this point, on the basis of examples such as (iv)–(vi), and proposes an account he calls ‘Weak Dispositionalism’ which amends POSS and NEC to:

$${\rm POSS } \; \left( {{\rm Weak}} \right)\!\!:\; \diamondsuit \;{\rm p} \equiv \{ {\rm p } \vee \;\exists {\rm \varphi }›[{\rm p}]({\rm \varphi })\} $$

$${\rm NEC } \; \left( {{\rm Weak}} \right)\!\!:\; \squ \;{\rm p} \equiv \{ {\rm p }\;\& \; \neg \exists \;{\rm \varphi }›[\neg {\rm p}]({\rm \varphi })\}. $$

Since my concern is the defence of Strong Dispositionalism, I will not explore this proposal here, although Yates’ mixed account potentially requires different truth-makers for some contingent truths and the possibilities associated with them. Thus his view would be susceptible to criticisms of the mixed truthmaker solution in the present paragraph. Yates, op. cit. 419.

³⁵ Hüttemann, Andreas, ‘A disposition-based process-theory of causation’ in Mumford, Stephen and Tugby, Matthew, eds. Metaphysics of Science (Oxford: Oxford University Press, 2013): 101–122 Google Scholar.

³⁶ Schroer, Robert, ‘Can a single property be both dispositional and categorical? The “Partial Consideration Strategy” partially considered’, Metaphysica 14 (2013): 63–77 CrossRefGoogle Scholar.

³⁷ A reply given in a paper by Vetter on 26^th November 2014, University of Oxford.

³⁸ However, this kind of broadly physicalist view of mathematical ontology is rare. See Mill, J. S., A System of Logic, Book II (London: Longmans, Green and Company, 1843)Google Scholar: Chapters 5 and 6.

³⁹ Vetter, op. cit. 2015, 212.

⁴⁰ Salmon, Nathan, ‘The Logic of What Might Have Been’ Philosophical Review 98 (1989): 3–34 CrossRefGoogle Scholar.

⁴¹ Shoemaker, op. cit. For further discussion about the options for individuation, see Allen, S. R., A Critical Introduction to Properties (London: Bloomsbury, 2016)Google Scholar, Ch. 5.

⁴² op. cit. 2015, 86–92.

⁴³ Vetter (ibid.) agrees that further explanation is required, but only hints at the correct analysis. Hence much of my discussion will proceed from first principles.

⁴⁴ There is disagreement over whether fundamental potentialities are instantiated to a maximal degree. Vetter, following Bird, suggests that they are; while Cartwright disagrees. In fact, explaining the degree to which higher level potentialities are possessed might be made easier if they were not. Ibid., 86; Bird, op. cit.; Cartwright, Nancy, Nature's Capacities and their Measurement (Oxford: Oxford University Press, 1989)Google Scholar. It is difficult to resolve this dispute until we have a better idea of what a potentiality's being possessed to a degree involves.

⁴⁵ Op. cit. 2015, 43.

⁴⁶ This reading seems to be close to Mumford and Anjum's conception of powers having intensity. They also call the intensity of a power its ‘degree’. op. cit. 2011, 24–26.

⁴⁷ One might protest at this example on the basis of statistical thermodynamics: there is a minimal but non-negligible chance that the Golden Gate Bridge will melt, so it is incorrect to say that it will never melt on an ordinary California summer day. However, this minimal likelihood will also be true of the granite bridge and so the required contrast will not be captured except perhaps by consideration of counterfactual situations. If we consider actual bridges, there have been no cases of melting (at least none of which I am aware). Thus this analysis of degrees of potentialities would not be an actualist one.

⁴⁸ Vetter, op. cit. 2015, 71–74 appeals to worlds ‘as a heuristic device’ but the problem with the heuristic use of worlds or counterfactual conditionals is that it never permits an explanation of what a potentiality's being had to a degree is (only what it would be were there possible worlds, for instance).

⁴⁹ Imre Lakatos, ‘Science and Pseudoscience’, in G. Vesey, ed., Philosophy in the Open (London: Open University Press).

⁵⁰ I am grateful to the audience at the 2016 conference of the Vienna Forum for Analytic Philosophy (WFAP), especially to Graham Priest, and to Alastair Wilder for comments on this paper.