The open future: bivalence, determinism and ontology


In this paper we aim to disentangle the thesis that the future is open from theses that often get associated or even conflated with it. In particular, we argue that the open future thesis is compatible with both the unrestricted principle of bivalence and determinism with respect to the laws of nature. We also argue that whether or not the future (and indeed the past) is open has no consequences as to the existence of (past and) future ontology.

This is a preview of subscription content, access via your institution.


  1. 1.

    See, inter alia, Markosian (1995), Tooley (1997), MacFarlane (2003); Bourne (2004) and Brogaard (2008).

  2. 2.

    See Prior (1967), Honderich (1988), van Inwagen (1989), and Markosian (1995). The fact that there exists an ongoing debate as to whether or not determinism entails the permissibility of ‘pre-punishment’ (as in Smilansky (2007)) shows just how endemic the idea is: if, as we will argue, determinism and the open future are entirely independent, the truth or falsity of determinism is an issue totally orthogonal to the permissibility of pre-punishment, where what matters is whether it was settled that the crime would occur.

  3. 3.

    See Diekemper (2005, 2007).

  4. 4.

    The open future thesis is a metaphysical thesis, and as such we will be making use of a notion of metaphysical indeterminacy: sometimes the world just doesn’t settle things one way or another. For us, this notion of metaphysical indeterminacy, or unsettledness, is primitive; however, that doesn’t mean we can’t say interesting things about it in explication—see Barnes and Williams (ms.) for an attempt to do just this.

  5. 5.

    The notion of indeterminacy that applies to states of the world can be defined in terms of the sentential determinacy operator as follows: Ic iffdf □∀t(Sct → ∃p([¬Dp]t & [¬D¬p]t))—that is, c is an indeterminate state of the world iffdf, necessarily, and for all times t, if c is the state of the world at time t, then there is at least one proposition that is indeterminate at t: i.e. that is neither determinately true at t nor determinately not true at t.

  6. 6.

    Examples include the account of semantic indeterminacy defended by McGee and McLaughlin (1995), and the account of metaphysical indeterminacy defended by Barnes and Williams (ms.).

  7. 7.

    In part due to the growing uneasiness about the consequences of adopting more familiar supervaluationist theories, which retain classical logic but deny bivalence (allowing for ‘truth value gaps’). See e.g. Fara (forthcoming).

  8. 8.

    NB: These examples are paradigm cases of semantic indeterminacy. Williamson (1994, Ch. 5, 2004) has strongly criticized McGee and McLaughlin’s bivalent theory of semantic indeterminacy on the grounds that its central notion (indeterminacy in which interpretation is intended) is primitive rather than semantic, and thus that the theory does not succeed as a semantic theory of indeterminacy (and must collapse into epistemicism). This criticism, regardless of how potent it is against McGee and McLaughlin’s view, is obviously no argument against an analogous model applied to the metaphysical sort of indeterminacy we find in the open future.

  9. 9.

    We are representing the strongest sense of openness here: all futures which are possible given the state of the world up to t are metaphysically open at t. The open future theorist might well want to restrict this, and there are various principled ways she could go about doing so. She might say, e.g., that {Futures} contains only the law-like worlds compatible with how things have been up to t, or that the worlds in {Futures} differ only with respect to the results of the free actions of agents. This would allow her to say that while it’s open that you wear a red shirt tomorrow and open that you wear a green shirt, it’s not open, for example, that tomorrow everything will be fish. The open future theorist doesn’t, however, need to place such restrictions on {Futures} in order to maintain the truth of future-directed conditionals like: ‘if the world continues tomorrow, there will be things other than fish’. We can define a closeness metric for the worlds in {Futures} that can allow for the truth of such plausible future-directed conditionals while allowing for the inclusion of fishy worlds in {Futures}. In that case, ‘if the world continues tomorrow, there will be things other than fish’ could be true and it still be metaphysically open that everything will be a fish tomorrow.

  10. 10.

    For simplicity, we’ll speak of {Futures} getting smaller. Of course, sets don’t undergo change in their members: what’s really going on is that the referent of the term ‘{Futures}’ is changing—at each moment in time it refers to a proper sub-set of the set that it referred to before.

  11. 11.

    We say ‘perhaps’ because nothing we say forces us to say that at the final moment of time {Futures} is a singleton set. That will only be true if the only source of indeterminacy is from the openness of the future; we simply remain silent on whether that’s the case.

  12. 12.

    The terminology should be familiar from ersatz theories of modality—there are many abstract representations of how reality could be, but only one (the one which matches the way the concrete actual world in fact is) is actualized.

  13. 13.

    In what follows we make use of the apparatus for thinking about indeterminacy developed in Barnes (ms. a).

  14. 14.

    Supervaluational accounts of the open future are quite common—see Thomason (1970) for the basic version. The supervaluationist model outlined here is somewhat non-standard, though, (as we shall note later) in a way that helps to avoid various problems with the basic supervaluational framework.

  15. 15.

    This is a departure from the traditional supervaluationist apparatus, in which no single precisification is privileged. The model here is thus more formally analogous to the so-called ‘non-standard’ supervaluationism of, e.g., McGee and McLaughlin (1995) (where there is a single intended interpretation, but indeterminacy in which interpretation is the intended one). This departure from standard supervaluationism allows for the endorsement of bivalence, as well as for a disquotational treatment of truth. For further elaboration see Barnes (ms. a) and Barnes and Williams (ms.).

  16. 16.

    Citing the many counter-intuitive results that non-bivalent precisificational theories lead to. See Fara (forthcoming, 2004).

  17. 17.

    MacFarlane speaks in terms of the assertions being true or false; we’ll leave his words unaltered, but when we come to discuss the intuitions we’ll speak in terms of the truth-value of the proposition expressed by the utterances.

  18. 18.

    MacFarlane (2003, p. 321).

  19. 19.


  20. 20.

    Ibid, p. 322.

  21. 21.

    We grant that ‘p and it is indeterminate that p’ sounds a bit strange. But we have a diagnosis of why it sounds strange: it’s that it can never be determinately true. And we need not commit to the assertability of ‘p and it is indeterminate that p’. Our claim is just that ‘p and it is indeterminate that p’ is perfectly consistent and that ‘it was the case that (p and it is indeterminate that p)’ can be determinately true (and assertable). For discussion of the consistency of ‘p and it is indeterminate that p’ see Barnes and Williams (ms.) and Greenough (2008).

  22. 22.

    The terminology itself suggests (falsely) an incompatibility—it’s somewhat natural to think that determinism about the future entails determinacy about the future. But really these are just two separate concepts, and any connection would need to be argued for.

  23. 23.

    You might not agree with this. But the hardest case for us is if this assumption is true (as well as it being used in this argument that determinism entails the closed future it will also be used in a potential objection to us in Sect. 3.3 below), and so we will show that we can make our case even if it is true. In fact, we feel some pull to this claim. For us, what is determinately true is what is true at every precisification, where these precisifications are certain ersatz worlds: namely, those ersatz worlds that don’t determinately misrepresent the way the actual world is. Whether or not necessity entails determinacy depends on whether the precisifications are all possible worlds or whether impossible worlds may number amongst the precisifications. If the former then, since a necessary truth is true at every possible world it is also true at every precisification, and hence is also a determinate truth. If the latter then there might be an impossible world that is nevertheless a precisification, in which case there will be some necessary truth that is false at it, and hence not determinately true. We are attracted to the idea that every precisification is a possible world because it then falls out of the semantics that the law of excluded middle and bivalence are determinately true, whereas if there can be impossible precisifications the semantics might allow that they are both determinately true but it won’t guarantee it.

    Note that the constraint is just that what is metaphysically necessary is determinately true, and that this is compatible with the claim that it can be indeterminate whether or not a proposition in fact is metaphysically necessary. We are silent on whether there are any of the latter cases. If there are, though, it will require a rejection of S4. For on our account, which eschews a third-value or gappy treatment of indeterminacy, indeterminacy with respect to p is compatible both with the truth and the falsity of p. (See Barnes and Williams ms.) So it being indeterminate whether or not a proposition is necessary should be compatible with it being necessary. But if p’s being necessary entails it being necessary necessarily (as in S4) then, given the assumption that necessity entails determinacy and the transitivity of entailment, p’s being necessary entails p’s being determinately necessary, in which case it being indeterminate whether p is necessary entails that p is not necessary, and so indeterminacy as to whether a proposition is necessary is not compatible with it being necessary after all. Reductio. This shouldn’t be thought to be a problem though; semantic considerations like this are exactly the kind of reasons that one should appeal to when deciding whether or not to accept such and such a modal system.

  24. 24.

    For formulations of regularity theory see, inter alia, Lewis (1994) and Loewer (1997).

  25. 25.

    See especially Armstrong (1983) for details.

  26. 26.

    The realist about laws might object that laws are meant to ‘govern’ what happens, and hence that letting what laws obtain get settled by what happens gets things the wrong way round. It’s not overly clear how the law-governing conception is meant to be understood, however. If what it is for laws to ‘govern’ the future is simply: for any world w, for all times t and t* such that t* is later than t, the laws at w settle at t (given the way w is at t) what happens at t*, then the law-governing conception is perfectly compatible with what we’ve said, and thus perfectly compatible with the open future. If, however, the metaphor of ‘governing’ is cashed out in some stronger way, such that the determinacy of the future falls out of it, then obviously the open future isn’t compatible with the existence of deterministic governing laws. However, it’s not clear (due to exactly the kinds of reasons we’ve been pressing) that such a stronger understanding of the ‘governing’ metaphor is warranted; it certainly no longer seems like an empirical scientific claim that such laws obtain, and so we maintain our claim that the open future theorist shouldn’t be worried about the possibility that empirical science will conflict with her view.

  27. 27.

    This might be considered a tension for the person who wants to restrict the worlds in {Futures}—how can you make a principled selection of which worlds can be included in {Futures} without reference to laws? The tension here is only a surface one, however. It’s plausible that the person who wants to restrict {Futures} needs to make reference to laws (or law-like relations, regularities, etc.)—but she doesn’t need to make reference to specific laws. So, e.g., she can stipulate that determinately all the worlds in {Futures} are law-like while still maintaining that there’s no particular law-like way which all the worlds in {Futures} determinately are.

  28. 28.

    See, inter alia, Shoemaker (1980) and Bird (2004).

  29. 29.

    Objection: That would be to accept an open present—but the open future thesis is only interesting if the future is open in some way that is in contrast to how the present is. In accepting indeterminacy in the present your theorist isn’t seeing anything distinctive about the future being unsettled: she just sees unsettledness everywhere.

    Reply: The difference between the present and the future is the extent of the unsettledness. To make the open future thesis consistent with strong determinism we need only say that some claim about how things presently are is currently unsettled. That’s consistent with plenty—indeed, most—of the contingent claims concerning how things presently are being currently settled; whereas the open future theorist may (see fn. 9) hold that no contingent claim about how things will be is currently settled, or that no contingent claim concerning how free agents will act is currently settled. Either way, the future is filled with unsettledness, whereas the present is settled in many, perhaps most, respects. That’s exactly as it should be: one shouldn’t be discounted as an open future theorist just by believing in some present unsettledness.

  30. 30.

    See, e.g., Barnes (ms. a) and Barnes and Williams (ms.).

  31. 31.

    Markosian (1995).

  32. 32.

    Though we don’t. For a survey of arguments against ontic indeterminacy, together with the reasons why they are unconvincing, see Barnes (ms. b).

  33. 33.

    And besides, the first example—appealing to regularity theory—is neutral on these concerns, and thus the main point endorsed in this section—that determinism does not rule out the open future—stands regardless of worries about metaphysical indeterminacy.

  34. 34.

    Diekemper (2005, 2007).

  35. 35.

    Again: we make no commitment to the claim that at the last moment, everything is determinate. Our commitment is only that prior to this moment, some things are not determinate.

  36. 36.

    You might be worried about the claim that the domain of the unrestricted quantifier can be indeterminate, as a result of Sider’s argument (Sider 2001, pp. 128–129) that the unrestricted quantifier doesn’t admit of multiple precisifications. But remember that the view in question is that it is metaphysically indeterminate what the domain of the unrestricted quantifier is. Sider’s argument simply does not have such a view as its target: he is quite explicit (p. 129) that his argument is directed against only those who share his assumption of the linguistic theory of vagueness. For discussion of Sider’s argument and metaphysical indeterminacy in what there (unrestrictedly) is, see Woodward (ms.).

  37. 37.

    For discussion see the symposium on ‘Defining Presentism’ between Thomas Crisp and Peter Ludlow in Zimmerman (2004, pp. 15–46) .

  38. 38.

    See Cameron (ms.); cf. Bigelow (1996).


  1. Armstrong, D. M. (1983). What is a law of nature? Cambridge: CUP.

    Google Scholar 

  2. Barnes, E. (ms. a). Ontic vagueness: A guide for the perplexed.

  3. Barnes, E. (ms. b). What’s so bad about ontic vagueness.

  4. Barnes, E., & Williams. (ms.). A theory of metaphysical indeterminacy.

  5. Bigelow, J. (1996). Presentism and properties. Nous, Vol. 30, Supplement: Philosophical Perspectives 10, Metaphysics, pp. 35–52.

  6. Bird, A. (2004). Strong necessitarianism: The nomological identity of possible worlds. Ratio, 17, 256–276. doi:10.1111/j.0034-0006.2004.00253.x.

    Article  Google Scholar 

  7. Bourne, C. (2004). Future contingents, non-contradiction, and the law of excluded middle. Analysis, 64, 122–128. doi:10.1111/j.1467-8284.2004.00471.x.

    Article  Google Scholar 

  8. Brogaard, B. (2008). Sea battle semantics. The Philosophical Quarterly, 58(231), 326–335.

    Article  Google Scholar 

  9. Cameron, R. (ms.). Truthmaking for presentists.

  10. Diekemper, J. (2005). Presentism and ontological symmetry. Australasian Journal of Philosophy, 83(2), 223–240. doi:10.1080/00048400500111097.

    Article  Google Scholar 

  11. Diekemper, J. (2007). B-theory, fixity, and fatalism. Noûs, 41(3), 429–452.

    Google Scholar 

  12. Fara, D. G. (2004). Gap principles, penumbral consequence, and infinitely higher-order vagueness. In J. C. Beall (Ed.), Liars and heaps: New Essays on the semantics of paradox (pp. 195–221). Oxford: Oxford University Press. Published under the name “Delia Graff”.

  13. Fara, D. G. (forthcoming). Scope confusions and unsatisfiable disjuncts: Two problems for supervaluationism. In R. Dietz & S. Moruzzi (Eds.), Heaps and clouds. Oxford: OUP.

  14. Greenough, P. (2008). Indeterminate truth. In P. French (Ed.), Truth and its deformities, Midwest studies in philosophy (forthcoming).

  15. Honderich, T. (1988). A theory of determinism. Oxford: OUP.

    Google Scholar 

  16. Lewis, D. (1994). Humean supervenience debugged. Mind, 103, 473–490. doi:10.1093/mind/103.412.473.

  17. Loewer, B. (1997). Humean supervenience. Philosophical Topics, 24, 101–126.

    Google Scholar 

  18. MacFarlane, J. (2003). Future contingents and relative truth. The Philosophical Quarterly, 53, 321–336. doi:10.1111/1467-9213.00315.

    Article  Google Scholar 

  19. Markosian, N. (1995). The open past. Philosophical Studies, 79, 95–105. doi:10.1007/BF00989786.

  20. McGee, V., & McLaughlin, B. (1995). Distinctions without a difference. The Southern Journal of Philosophy, 33(Supplement), 204–251.

    Google Scholar 

  21. Prior, A. N. (1967). Past, present, and future. Oxford: Oxford University Press.

    Google Scholar 

  22. Shoemaker, S. (1980). Causality and properties. In P. van Inwagen (Ed.), Time and cause (pp. 109–135). Dordrecht: D. Reidel.

    Google Scholar 

  23. Sider, T. (2001). Four-dimensionalism. Oxford: Oxford University Press.

    Google Scholar 

  24. Smilansky, S. (2007). Determinism and pre-punishment. Analysis, 67, 347–349. doi:10.1111/j.1467-8284.2007.00706.x.

  25. Thomason, R. (1970). Indeterminist time and truth-value gaps. Theoria, 3, 264–281.

    Google Scholar 

  26. Tooley, M. (1997). Time, tense, and causation. Oxford: Oxford University Press.

    Google Scholar 

  27. van Inwagen, P. (1989): When is the will free? Philosophical Perspectives, 3, 399–422.

    Google Scholar 

  28. Williamson, T. (1994). Vagueness. London: Routledge.

    Google Scholar 

  29. Williamson, T. (2004). Reply to McGee and McLaughlin. Linguistics and Philosophy, 27, 113–122. doi:10.1023/B:LING.0000010847.78827.d0.

  30. Woodward, R. (ms.). Metaphysical indeterminacy and vague existence.

  31. Zimmerman, D. (Ed.). (2004). Oxford studies in metaphysics (Vol. 1). Oxford: Oxford University Press.

    Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Ross Cameron.

Additional information

Thanks to Kris McDaniel, Helen Steward, Jason Turner and Robbie Williams for helpful discussion.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Barnes, E., Cameron, R. The open future: bivalence, determinism and ontology. Philos Stud 146, 291 (2009).

Download citation


  • Open future
  • Metaphysical indeterminacy
  • Logical fatalism
  • Determinism
  • Growing block