Abstract
In this chapter we critically discuss the objection that since truths require grounds, the Growing Block Theory must take bivalence to fail for future contingents, while it proves at odds with the best account of such a failure. We challenge the version of the grounding requirement driving this objection, devise a better formulation, and show that the theory can retain bivalence and accommodate an interesting form of indeterminism. After rehearsing the objection in Sect. 7.1, in Sect. 7.2 we review different ways to articulate the grounding requirement, conclude that it should suffice that, for any tensed truth, sometimes there be grounds for it, and show how this requirement can be met by contingent truths about the future. In Sect. 7.3 we explicate a conception of the asymmetry between the open future and the fixed past, consistent with bivalence and available to the Growing Block Theory but none of its rivals.
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Notes
- 1.
- 2.
Metaphysics, 1051b6–8; the translation follows Ross et al. (1908).
- 3.
Dummett argues that ‘a proposition about what I am going to do is true in virtue of my later action’ and, more generally, that ‘[i]t is what is going to happen in the future that renders our statements about the future true, when they are true. This platitude is embodied in the truth-value links’ (Dummett 2004: 81, 83). Dummett concludes that a view like Broad’s , according to which there is now nothing that is only ever going to happen in the future, is bound to deny that statements about the future are true (Dummett 2004: 74, 80). Contrary to what Dummett claims, however, the truth-value links merely yield that a statement about the future such as ‘It will be the case that Mars is being colonized’ is presently true just if it will be the case that ‘Mars is being colonized’ is true. It is only against the backdrop of Dummett’s further contention that ‘a proposition can be true only if there is something in virtue of which it is true’ (Dummett 2004: 74), that we can reason from this to the conclusion that if ‘It will be the case that Mars is being colonized’ is presently true, there is now something in virtue of which ‘Mars is being colonized’ will be true, i.e. a merely future happening. The present suggestion is to replace Dummett’s contention by the claim that a proposition is true at t only if sometimes there is something in virtue of which it is true at t. Note also that, contrary to what Dummett (2004: 80) suggests, the proponent of GBT need not treat the truth-conditions of statements about the past in any substantially different way – irrespective of the fact that, according to GBT, past things still exist (cf. also Broad 1938: 316) .
- 4.
Later Broad clearly distinguished between the future’s being predetermined by past and present facts and its being ‘predeterminate’ in the sense that statements about the future have a definite truth-value (Broad 1937: 204, 206). But since he would seem to have abandoned his 1923 view by that time, he never readdressed the question of why, in the light of this distinction, GBT should be taken to be committed to denying that future contingents are ever true.
- 5.
The same applies to the problem of truth-grounding for certain negative statements, such as e.g. negative existentials, that we have conveniently glossed over by simply assuming that, in general, if F¬φ is presently true, sometimes in the future, its past truth will be grounded in whatever then grounds ¬φ.
- 6.
Bivalence may, of course, be said to fail for other reasons, e.g. vagueness.
- 7.
The formulation of (IND) allows that certain ways the world could have turned out to be were more probable than others given the way the world was up to an earlier time, and so that the laws of nature are probabilistic; and surely, any non-zero probability at least requires nomological possibility.
- 8.
Barnes and Cameron (2009) have even argued that a thesis like (IND) is not necessary for the open future , contrary to what we suggest here. Their reason for this claim is that it may, in some sense of ‘metaphysically indeterminate’, be metaphysically indeterminate what the world is like up to now, so that even fully deterministic laws will only take us from the present indeterminate world state to a later indeterminate world state: if there is any indeterminacy in the present world state, this indeterminacy simply ‘may bleed over’ into the subsequent world state. However, the authors’ reasoning seems flawed because the sense in which the present state of the world might be indeterminate – say, the sense in which it is indeterminate which, if any, cell has survived fission – is not the sense in which the future is said to be indeterminate by being open: by the authors’ own lights, the future is open in a sense in which the present and past are not (see Rosenkranz 2013: 69, for discussion).
- 9.
McTaggart (1927: §337) rightly observed that this would commit proponents of GBT to the truth of statements about the future – something at odds with what Broad takes himself to be committed to (Broad 1923: 73). As we have argued above, however, Broad (1923) is mistaken when he contends that proponents of GBT must treat statements about the future as being neither true nor false: even future contingents can be regarded as bivalent, and some as true, quite consistently with GBT (cf. also Broad 1937: 206).
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Correia, F., Rosenkranz, S. (2018). Bivalence, Future Contingents and the Open Future. In: Nothing To Come. Synthese Library, vol 395. Springer, Cham. https://doi.org/10.1007/978-3-319-78704-6_7
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