Abstract
Open future is incompatible with realism about possible worlds. Since realistically conceived (concrete or abstract) possible worlds are maximal in the sense that they contain/represent the full history of a possible spacetime, past and future included, if such a world is actual now, the future is fully settled now, which rules out openness. The kind of metaphysical indeterminacy required for open future is incompatible with the kind of maximality which is built into the concept of possible worlds. The paper discusses various modal realist responses and argues that they provide ersatz openness only, or they lead to incoherence, or they render the resulting theory inadequate as a theory of modality. The paper also considers various accounts of the open future, including rejection of bivalence, supervaluationism, and the ‘thin red line’ view (TRL), and claims that a version of (TRL) can avoid the incompatibility problem, but only at the cost of deflating the notion of openness.
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Notes
(3) makes (OF) deviant even in terms of deviant logic. In three-valued logic, a disjunction of two indeterminates is traditionally either indeterminate (in Łukasiewicz’s and Kleene’s systems) or false (in Bochvar’s system) (cf. Malinowski and Grzegorz 2001).
The supervaluationist analysis of future contingents was originally proposed by Thomason (1970), but he did not suggest an interpretation involving ontic vagueness. (For his own metaphysics, see fn. 6.) Formally, the Barnes–Cameron idea is similar to Arthur Prior’s (1957, p. 100) classic analysis of openness, which denies that “~(It will be the case that P)” and “It will be the case that ~P” are equivalent. This move allows one to say that “It will be the case that P” and “It will be the case that ~P” are both false now.
It is arguable that supervaluationist frameworks are generally incompatible with ontic vagueness (Williamson 2003, p. 701ff).
Although Barnes and Cameron (2009, p. 295f and passim) are adamant that they preserve bivalence, it is arguable that they do so half-heartedly. Premise (iiiΔ) secures excluded middle, but it does not guarantee that if P is not true now, then P is false now (which is customary under bivalence, following from True(P∨~P) and ~True(P)). Indeed, the Barnes–Cameron theory requires that there be propositions that are not (determinately) true nor (determinately) false now. Even if this is ‘bivalence’ in some sense, is it bivalence in the ordinary sense?
Alternatively, one could retain bivalence in (NU/NF) by supposing that propositions about the future do not exist now. But then clause (A) is in trouble. One might fix this by having (A) refer to sentences instead of propositions, but then one needs to explain what it means for a sentence which does not express a proposition to be possibly true.
Similar remarks apply to the ‘shrinking block’ model where alternative future timelines get pruned off as we go along (see Dainton 2001, pp. 72–74; McCall 1976, 1984). The existence and disappearance of such alternative timelines seem perfectly compatible with the idea that our world (i.e. the timeline that prevails) was fated to develop a specific way.
For a helpful overview of the thin red line theory, including its connections to the medieval problem of future contingents, see Øhrstrøm (2009). The theory was originally proposed by McKim and Davis (1976) and by Thomason and Gupta (1980). The phrase “thin red line” was imported into the discussion by Belnap and Green (1994).
MacFarlane (2003, p. 326) argues that (TRL) is by definition a theory of epistemic openness.
Formally, MacFarlane’s theory is very similar to (OF), my own definition of metaphysical openness, so let me stipulate that (OF) goes with a metaphysically robust conception of context-independent truth. Such a conception might be supplied by a states-of-affairs ontology (Armstrong 1997, 2004; see Forrest 2006, p. 149ff for an account of openness along these lines), or by a theory where being true is a primitive property of propositions (Merricks 2007). For a medieval view which has some affinity with (OF), see Hirsch (2006).
If tense is irreducible, (PO) must be modified: P must be a future-tensed proposition (e.g. “C will come up heads n seconds from now”), and (PO) must require that P isn’t determinately true even though its future equivalent (“n seconds have passed and C has come up heads”) is.
Note, however, that Jubien does not endorse modal abstractionism. He rejects possible worlds and opts for ante rem properties that code necessity through entailment relations.
This is generally guaranteed by the second part of clause (i) of (PO).
More precisely, intuition-preserving theories of openness rule out modal abstractionism, but I shall drop this proviso until the penultimate section.
In a different context, Merricks (2007, p. 76) considers a version of abstractionism where worlds only entail physically and metaphysically necessary truths, remaining silent about contingent facts. I take it that such incomplete worlds make abstractionism so heavily impoverished that it is no longer a useful theory of modality.
That abstract worlds must be simples has been argued by Lewis (1986, p. 174ff) and van Inwagen (2001b, p. 234). For the contrary view, see Jubien (1991) (esp. 264ff). The price of overlap is to allow abstract worlds to be structured, which probably leads to admitting nonactual (abstract) individuals and/or uninstantiated properties.
For a succint exposition of this anti-Lewisian point, see Jubien (2009, pp. 59–67).
Notice that Lewis, even though he rails against concrete overlap at length, does not object to this kind of scenario (Lewis 1986, p. 206).
References
Adams, R. M. (1974). Theories of actuality. Noûs, 8, 211–231.
Armstrong, D. M. (1997). A world of states of affairs. Cambridge: Cambridge UP.
Armstrong, D. M. (2004). Truth and truthmakers. Cambridge: Cambridge University Press.
Barnes, E., & Cameron, R. (2009). The open future: Bivalence, determinism and ontology. Philosophical Studies, 146, 291–309.
Belnap, N. (1992). Branching space-time. Synthese, 92, 385–434.
Belnap, N., & Green, M. (1994). Indeterminism and the thin red line. Philosophical Perspectives, 8, 365–388.
Bricker, P. (2001). Island universes and the analysis of modality. In G. Preyer & F. Siebelt (Eds.), Reality and Humean supervenience (pp. 27–55). Lanham, MD: Rowman & Littlefield.
Dainton, B. (2001). Time and space. London: Acumen.
Forbes, G. (1996). Logic, logical form, and the open future. Philosophical Perspectives, 10, 73–92.
Forrest, P. (2006). General facts, physical necessity, and the metaphysics of time. In D. W. Zimmerman (Ed.), Oxford studies in metaphysics (Vol. 2, pp. 137–152). Oxford: Oxford University Press.
Helm, P. (1988). Eternal God. Oxford: Clarendon Press.
Hirsch, E. (2006). Rashi’s view of the open future: indeterminateness and bivalence. In D. W. Zimmerman (Ed.), Oxford studies in metaphysics (Vol. 2, pp. 111–135). Oxford: Oxford University Press.
Jubien, M. (1991). Could this be magic? The Philosophical Review, 100(2), 249–267.
Jubien, M. (2009). Possibility. Oxford: Clarendon Press.
Lewis, D. (1979). Counterfactual dependence and time’s arrow. Noûs, 13(4), 455–476.
Lewis, D. (1986). On the plurality of worlds. Oxford: Blackwell.
Lewis, D. (1994). Humean supervenience debugged. Mind, 103(412), 473–490.
Loewer, B. (2004). David Lewis’s Humean theory of objective chance. Philosophy of Science, 71, 1115–1125.
MacFarlane, J. (2003). Future contingents and relative truth. The Philosophical Quarterly, 212, 321–336.
Malinowski, G. (2001). Many-valued logics. In L. Goble (Ed.), The Blackwell guide to philosophical logic (pp. 309–335). Oxford: Blackwell.
McCall, S. (1976). Objective time flow. Philosophy of Science, 43, 337–362.
McCall, S. (1984). A dynamic model of temporal becoming. Analysis, 44, 172–176.
McKim, V. R., & Davis, C. C. (1976). Temporal modalities and the future. Notre Dame Journal of Formal Logic, 17(2), 233–238.
Merricks, T. (2007). Truth and ontology. Oxford: Clarendon Press.
Øhrstrøm, P. (2009). In defence of the thin red line. Humana.Mente, 8, 17–32.
Plantinga, A. (1974). The nature of necessity. Oxford: Clarendon Press.
Prior, A. (1957). Time and modality. Oxford: Clarendon Press.
Prior, A. (1967). Past, present and future. Oxford: Clarendon Press.
Sider, T. (2011). Writing the book of the world. Oxford: Clarendon Press.
Stalnaker, R. C. (1979). Possible worlds. In M. J. Loux (Ed.), The possible and the actual (pp. 225–234). Ithaca, NY: Cornell University Press.
Teller, P. (2001). Against overlap and endurance. In G. Preyer & F. Siebelt (Eds.), Reality and Humean supervenience (pp. 105–121). Lanham, MD: Rowman & Littlefield.
Thomason, R. H. (1970). Indeterminist time and truth-value gaps. Theoria, 36, 264–281.
Thomason, R. H., & Gupta, A. (1980). A theory of conditionals in the context of branching time. The Philosophical Review, 89(1), 65–90.
van Inwagen, P. (2001a). Indexicality and actuality. In his Ontology, Identity, and Modality (pp. 165–185) Cambridge: Cambridge University Press.
van Inwagen, P. (2001b). Two concepts of possible worlds. In his Ontology, Identity, and Modality (pp. 206–242) Cambridge: Cambridge University Press.
Williamson, T. (2003). Vagueness in reality. In M. J. Loux & D. W. Zimmerman (Eds.), The Oxford handbook of metaphysics (pp. 690–715). Oxford: Oxford University Press.
Zagzebski, L. T. (1991). The dilemma of freedom and foreknowledge. Oxford: Oxford University Press.
Zagzebski, L. T. (2002). Recent work on divine foreknowledge and free will. In R. Kane (Ed.), The Oxford handbook of free will (pp. 45–64). Oxford: Oxford University Press.
Acknowledgments
I’d like to thank Howard Robinson, Mike Griffin, and the reviewer who made me reconsider the thin red line theory.
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Kodaj, D. Open future and modal anti-realism. Philos Stud 168, 417–438 (2014). https://doi.org/10.1007/s11098-013-0137-3
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DOI: https://doi.org/10.1007/s11098-013-0137-3