Knowledge of objective modality


The epistemology of modality has focused on metaphysical modality and, more recently, counterfactual conditionals. Knowledge of kinds of modality that are not metaphysical has so far gone largely unexplored. Yet other theoretically interesting kinds of modality, such as nomic, practical, and ‘easy’ possibility, are no less puzzling epistemologically. Could Clinton easily have won the 2016 presidential election—was it an easy possibility? Given that she didn’t in fact win the election, how, if at all, can we know whether she easily could have? This paper investigates the epistemology of the broad category of ‘objective’ modality, of which metaphysical modality is a special, limiting case. It argues that the same cognitive mechanisms that are capable of producing knowledge of metaphysical modality are also capable of producing knowledge of all other objective modalities. This conclusion can be used to explain the roles of counterfactual reasoning and the imagination in the epistemology of objective modality.

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  1. 1.

    See Strohminger and Yli-Vakkuri (2017) for review.

  2. 2.

    Williamson is, of course, far from being the only philosopher to recognize a broad category of non-epistemic modalities that includes metaphysical modality: see, for example, Lange (2009), Hale (2013), Kment (2014) and Vetter (2015). Linguists have recognized a similar—perhaps the same—category of ‘root’, ‘circumstantial’, or ‘dynamic’ modality since the 1970s (Kratzer 1981, 2012; Portner 2009).

  3. 3.

    See Sainsbury (1997), Peacocke (1999: 310–328) and Williamson (2000: 123–130).

  4. 4.

    Are all and only objective modalities properties of propositions? This seems to us more a matter to be decided than discovered. We think of the objective modalities as all and only those that can be characterized by a restricting condition in the sense of Sect. 2. This does not include all properties of propositions, since there are at least as many properties of propositions as there are functions from metaphysically possible words to propositions: such a function σ characterizes the (or a) property P such that a proposition p has P at w iff pσ(w). The alternative notion of an objective modality as a property of propositions is adequately captured by Scott-Montague ‘neighborhood semantics’, in which a modal operator is interpreted by an assignment of a set of sets of worlds, thought of as the set of relevantly necessary propositions, to each world. As we point out in Sect. 2, our own approach is equivalent to a relational (or ‘Kripke’) approach to the semantics of modal logic. Unlike neighborhood semantics, relational semantics cannot interpret a modal operator by an arbitrary property of propositions (see Bull and Segerberg 1984: §21).

  5. 5.

    See Fine (2014) for discussion.

  6. 6.

    See Yli-Vakkuri and Hawthorne (MSa) for discussion.

  7. 7.

    Thanks to Timothy Williamson for this example. See Yli-Vakkuri and Hawthorne (MSb: note 5) for discussion.

  8. 8.

    In doing so, we retread some ground covered by van Fraassen (1977), Humberstone (1981) and Hale and Leech (2017). None of these authors propose the analysis we give. Although there is a certain superficial similarity between our analysis and Hale and Leech’s, there is also an important difference: see note 11.

  9. 9.

    Since we are only concerned with objective modalities in this paper, we will henceforth leave the ‘objective’ implicit.

  10. 10.

    Here we are assuming a coarse-grained conception of propositions (conditions) as sets of worlds, but the inter-translatability of accessibility-relation talk with restricting-condition talk does not require that assumption. As long as, for each set of worlds W, there is a proposition f(W) that is true at exactly the worlds in W, f(W) can play the role of the restricting condition that holds at exactly the worlds in W. And it does seem plausible, even given a view on which propositions have arbitrarily fine-grained structure, that there is a function f that fits this description: f(W) might be, for example, the proposition that at least one of the worlds in W is actualized, where ‘actualized’ is understood in a non-rigid way, so that it is contingent which world is actualized. (Note that we are not assuming that, for each set of worlds W, there is a unique proposition that is true at exactly the worlds in W. That would be implausible on a structured-propositions view. The axiom of choice guarantees the existence of a suitable function f even if there are sets of worlds that exactly verify more than one proposition. Nor are we assuming the consistency of views on which propositions are arbitrarily fine-grained—theories that posit extremely fine-grained propositional structure are inconsistent: see Dorr (2016a) and Goodman (2017). Given an inconsistent view, anything whatsoever is the case.)

  11. 11.

    Hale and Leech (2017: §6.3) propose an analysis of what they call ‘alethic’ modality that is superficially similar to but importantly different from (□R), which they illustrate with the case of nomic or (as they call it) ‘physical’ modality, as follows.


    It is physically necessary that p = defq(π(q) ∧ □(qp)).

    Here ‘π’ is to be read as ‘it is a law of physics that…’ (Hale and Leech 2017: 13). This, however, is not an adequate analysis because it does not give the restricted modality being analyzed a normal modal logic: it validates neither necessitation (p → □Rp, where p is valid) nor the K axiom (□R(pq) → (□Rp → □Rq)). Hale and Leech try to solve this problem in a footnote (note 23). We don’t think their solution works, but we’ll save our criticisms of it for another occasion (Yli-Vakkuri plans to defend his own higher-order analysis elsewhere).

  12. 12.

    This doesn’t exactly get the logical form right, for several reasons, the least subtle one being that set theory isn’t logic. If we want □∃!qR(q) to come out as a logical truth, we’ll have to resort to higher-order modal logic. The full higher-order analysis is beyond the scope of this paper.

  13. 13.

    With whatever restrictions to necessitation are mandated by the presence of the actuality operator @ and other indexicals in the language. By (□R), necessitation for □R inherits these restrictions from necessitation for □.

  14. 14.

    Of course it does not follow that every possible deduction extends knowledge. Knowledge-extending deductions must be ‘competent’ [see Williamson (2000: 117) and Hawthorne (2004: 34−35)].

  15. 15.

    There may be exceptions. Consider a case in which one comes to know a highly non-trivial mathematical fact p by deducing it from some known axioms. We certainly don’t want to claim that it is possible to come to know p simply by doing whatever one actually did to come to know the axioms and then judging that p on that basis. Thanks to Catharine Diehl for discussion here.

  16. 16.

    See Williamson (2007: 156), Lange (2009: 64) and Berto et al. (2017) for recent examples.

  17. 17.

    Lange (2009: 64) endorses Possibility* for what he calls ‘genuine’ modalities. Genuine modalities are objective in the sense of this paper, but not vice versa (207−208, n. 5). According to Williamson (forthcoming), Possibility* is ‘plausible for a wide range of restricted kinds of objective possibility’.

  18. 18.

    See Dorr (2016b) for discussion.

  19. 19.

    Here we cannot, of course, simply think of the laws as what the law books explicitly dictate: what the law books explicitly dictate may be inconsistent, and therefore impossible to obey. The laws, rather, must be thought of as (in the typical case) a possible proposition determined by the explicit contents of legal texts and various features of the surrounding context, such as court decisions and perhaps the intentions of legislators.

  20. 20.

    In common uses of ‘legally possible’ (one can find many examples by searching Google News for ‘legally possible’ together with ‘Trump’) the restricting condition is not that some relevant laws are obeyed. A typical restriction seems to concern particular people obeying laws with respect to particular actions and also to require that certain practical conditions obtain.

  21. 21.

    See the discussion of ‘real-world validity’ in Davies and Humberstone (1980) and Kaplan (1989: XVIII and 539: n. 65) on ‘actually’. The 4-to-5 and 5-to-6 inferences also require the validity of the Barcan formulas for propositional quantifiers, which, in contrast with the first-order Barcan formulas, have tended not to be controversial. (In the recent debate on ‘necessitism’ sparked by Stalnaker (2012) and Williamson (2013), the validity of the propositionally quantified Barcan formulas has also been called into question (see Fritz 2016), but in the present dialectical context we take their validity to be sufficiently uncontroversial to assume without further commentary).

  22. 22.

     Contemporary defenses include Yablo (1993), Chalmers (2002), Gregory (2004), Williamson (2007: ch. 5) and Hill (2014).

  23. 23.

    Less roughly, p□→ q is true at a world w iff either (1) p is not true at any world in Sw or (2) p is true at some world v in Sw such that the material conditional pq is true at every world that is at least as close to w as v (Lewis 1973: 49). Because Lewis is not concerned with indexicality, there is no explicit context parameter in his semantics, but the point of the assignment of spheres of similarity to worlds is to represent a restriction supplied by context.

  24. 24.

    Let r be the false but possible proposition that no violations of the (actual) penal code occur, and let p be any truth-functional tautology. Suppose that □→ is restricted to worlds in which r is true. Then p and p□→ r are true but r is false.

  25. 25.

    If that proposition is true; otherwise it is restricted to the empty set.


  1. Berto, F., French, R., Priest, G., & Ripley, D. (2017). Williamson on counterpossibles. Journal of Philosophical Logic.

    Google Scholar 

  2. Bull, R., & Segerberg, K. (1984). Basic modal logic. In D. Gabbay & F. Guenthner (Eds.), Handbook of philosophical logic (Vol. II, pp. 1–88). Dordrecht: D. Reidel.

    Google Scholar 

  3. Byrne, A. (2007). Possibility and imagination. Philosophical Perspectives, 21, 125–144.

    Article  Google Scholar 

  4. Chalmers, D. J. (2002). Does conceivability entail possibility? In T. S. Gendler & J. Hawthorne (Eds.), Conceivability and possibility (pp. 145–200). Oxford: Clarendon Press.

    Google Scholar 

  5. Davies, M., & Humberstone, L. (1980). Two notions of necessity. Philosophical Studies, 38, 1–30.

    Article  Google Scholar 

  6. Dorr, C. (2016a). To be F is to be G. Philosophical Perspectives, 30, 39–134.

    Article  Google Scholar 

  7. Dorr, C. (2016b). Against counterfactual miracles. Philosophical Review, 125, 241–286.

    Article  Google Scholar 

  8. Fine, K. (2014). Permission and possible worlds. Dialectica, 68, 317–336.

    Article  Google Scholar 

  9. Fritz, P. (2016). Propositional contingentism. The Review of Symbolic Logic, 9, 123–142.

    Article  Google Scholar 

  10. Goodman, J. (2017). Reality is not structured. Analysis, 77, 43–53.

    Google Scholar 

  11. Gregory, D. (2004). Imagining possibilities. Philosophy and Phenomenological Research, 69, 327–348.

    Article  Google Scholar 

  12. Hale, B. (2013). Necessary beings: An essay on ontology, modality, and the relations between them. Oxford: Oxford University Press.

    Google Scholar 

  13. Hale, B., & Leech, J. (2017). Relative necessity formulated. Journal of Philosophical Logic, 46, 1–26.

    Article  Google Scholar 

  14. Hawthorne, J. (2004). Knowledge and lotteries. Oxford: Oxford University Press.

    Google Scholar 

  15. Hill, C. S. (2014). Conceivability and possibility. In Meaning, mind, and knowledge (pp. 273–296). Oxford: Oxford University Press.

  16. Humberstone, I. L. (1981). Relative necessity revisited. Reports on Mathematical Logic, 13, 33–42.

    Google Scholar 

  17. Kaplan, D. (1989). Demonstratives. In J. Almog et al. (Eds.), Themes from Kaplan (pp. 481–563). Oxford: Oxford University Press (Completed and circulated in mimeograph in the published form in 1977).

  18. Kment, B. (2014). Modality and explanatory reasoning. Oxford: Oxford University Press.

    Google Scholar 

  19. Kratzer, A. (1981). The notional category of modality. In H.-J. Eikmeyer & H. Rieser (Eds.), Words, worlds, and contexts (pp. 38–74). Berlin: de Gruyter.

    Google Scholar 

  20. Kratzer, A. (2012). Modals and conditionals. Oxford: Oxford University Press.

    Google Scholar 

  21. Lange, M. (2009). Laws and lawmakers: Science, metaphysics, and the laws of nature. New York: Oxford University Press.

    Google Scholar 

  22. Lewis, D. (1973). Counterfactuals. Oxford: Blackwell.

    Google Scholar 

  23. Lewis, D. (1979). Counterfactual dependence and time’s arrow. Noûs, 13, 455–476.

    Article  Google Scholar 

  24. Peacocke, C. (1999). Being known. Oxford: Clarendon Press.

    Google Scholar 

  25. Portner, P. (2009). Modality. Oxford: Oxford University Press.

    Google Scholar 

  26. Sainsbury, M. (1997). Easy possibilities. Philosophy and Phenomenological Research, 57, 907–919.

    Article  Google Scholar 

  27. Stalnaker, R. (2012). Mere possibilities. Oxford: Oxford University Press.

    Google Scholar 

  28. Strohminger, M., & Yli-Vakkuri, J. (2017). The epistemology of modality. Analysis, 77, 825–838.

    Article  Google Scholar 

  29. van Fraassen, B. (1977). The only necessity is verbal necessity. Journal of Philosophy, 74, 71–85.

    Article  Google Scholar 

  30. Vetter, B. (2015). Potentiality: From dispositions to modality. Oxford: Oxford University Press.

    Google Scholar 

  31. Williamson, T. (2000). Knowledge and its limits. Oxford: Oxford University Press.

    Google Scholar 

  32. Williamson, T. (2007). The philosophy of philosophy. Oxford: Blackwell.

    Google Scholar 

  33. Williamson, T. (2016). Knowing by imagining. In A. Kind & P. Kung (Eds.), Knowledge through imagination (pp. 113–123). Oxford: Oxford University Press.

    Google Scholar 

  34. Williamson, T. (2017a). Modal science. In Yli-Vakkuri & McCullagh 2017 (pp. 1–40).

  35. Williamson, T. (2017b). Reply to Sider. In Yli-Vakkuri & McCullagh 2017 (pp. 247–256).

  36. Williamson, T. (forthcoming). The counterfactual-based approach to modal epistemology. In O. Bueno & S. Shalkowski (Eds.), The Routledge handbook of modality. London: Routledge.

  37. Yablo, S. (1993). Is conceivability a guide to possibility? Philosophy and Phenomenological Research, 53, 1–42.

    Article  Google Scholar 

  38. Yli-Vakkuri, J., & Hawthorne, J. (MS a). Modal epistemology (Unpublished manuscript).

  39. Yli-Vakkuri, J., & Hawthorne, J. (MS b). The necessity of mathematics (Unpublished manuscript).

  40. Yli-Vakkuri, J., & McCullagh, M. (Eds.). (2017). Williamson on modality. London: Routledge.

    Google Scholar 

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This paper started out as Margot Strohminger’s project. Juhani Yli-Vakkuri was recruited as a coauthor in the final stages of preparation for publication. Credit (and blame!) should be assigned accordingly. We would like thank Timothy Williamson for detailed comments on early drafts of this paper, as well as Johannes Brandl, Jessica Brown, Catharine Diehl, Peter Fritz, Christopher Gauker, Sören Häggqvist, John Hawthorne, Hannes Leitgeb, Julien Murzi, Christian Nimtz, Barbara Vetter, and audiences at the Munich Center for Mathematical Philosophy (MCMP) at the Ludwig Maximilian University of Munich, the Free University of Berlin, the University of Antwerp, the University of Edinburgh, the University of Salzburg, and Bielefeld University for helpful comments and discussions. This research was supported by the Alexander von Humboldt Foundation.

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Correspondence to Margot Strohminger.

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Strohminger, M., Yli-Vakkuri, J. Knowledge of objective modality. Philos Stud 176, 1155–1175 (2019).

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  • Epistemology of modality
  • Modality
  • Metaphysical necessity
  • Conceivability and possibility
  • Counterfactuals
  • Imagination