Abstract
In this chapter, I argue that on a natural understanding of both views, indeterminism and branching time are incompatible, contrary to what recent literature on the open future suggests. In the first section, I introduce two notions of truth-determination that importantly differ from the notion of truth-making. In the second section, I use these notions to devise a definition of determinism that captures the central idea that, given the past and present, the future cannot but be a certain way. Indeterminism is then defined in opposition to determinism in the third section. In the fourth section, I argue that the tree-like representation of future possibilities is not suggestive of branching time and that indeterminism is perfectly consistent with assumption of a Thin Red Line, that is, a unique way things will turn out to be, a claim shown to be unthreatened by considerations concerning human freedom. In the fifth section, I argue that taking branching time seriously implies commitment to determinism. In the sixth section, I consider a recent attempt to capture the open future and show that it is naturally seen to draw on a conception of the determinately true as what is determined to be true in the second of the senses introduced in the first section. In the seventh section, I argue that the authors’ suggestion that determinism is nonetheless consistent with admission of a multitude of future possibilities is at best unmotivated and at worst misguided. Section eight summarises the results.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Assuming facts to be tensed has the advantage that we can sensibly talk about facts existing at certain times but not at others, for example, at past times but not at future times. Yet, most of what follows could be recast in terms of tenseless facts that have the relevant times as constituents. However, such reformulations would be unnecessarily cumbersome. For suitable accounts of tensed facts, see Correia and Rosenkranz 2011.
- 2.
As Lewis notes, this at most holds for cases of immediate causation, as we wish to say that c causes e if c causes e′ which in turn causes e. In other words, we take causation to be transitive, while counterfactual dependence is not. The obvious remedy is to define causation in terms of causal chains, that is, chains of pairwise counterfactually dependent events (Lewis 1986: 167). For simplicity’s sake, I will stick to the above formulation. Consequently, ‘cause’ should here be taken to mean ‘immediate cause’. For further provisos, see next footnote.
- 3.
This reasoning relies on ‘□((∼A □→ ∼B) → (B → A))’ which is uncontroversial given only that no world is closer to the actual world than the actual world itself. Note that since ‘→’ is transitive, the existence of causal chains involving intermediate causes will leave the claimed inference from terminal conditions to initial conditions unaffected. See previous footnote.
As Lewis reminds us, there are likely to be cases of causal preemption (and overdetermination) so that c would have caused e if c′ had not occurred. In such cases, we would still want to be able to say that c′ causes e, although there is no counterfactual dependence (Lewis 1986: 171–72). The causalist doctrine mentioned in the text does not exclude such cases, even if they render doubtful that the suggested counterfactual characterisation captures our ordinary concept of causation, for note that causal preemption and overdetermination are relations between particular events. Yet, even if c′ preempts c’s causing e, or c and c′ overdetermine e, so that, either way, it is not the case that e would not have occurred if c′ had not occurred, there may still be a c" such that e would not have occurred without it and an e′ such that it would not have occurred without c′. To skirt any further issues, let ‘(immediate) cause’, as it occurs in the causalist doctrine, henceforth be a technical term understood to imply counterfactual dependence.
- 4.
Often, determinism is identified with the combination of this thought and the causalist doctrine. However, since indeterminists may endorse the latter, it will be more convenient to reserve ‘determinism’ for the former. (As we shall see in section ‘Branching Time and Determinism’ below, if time exhibits forward branching, the ‘one way to go’ from the initial conditions may consist in a unique manifold of continuations spread across distinct time-series just like the crown of a tree.)
Note that I here diverge from Lewis who explicitly denies that determinism should be understood in either of these ways because, for him, the direction of time is to be explained in terms of causation and causation is analysed in terms of counterfactual dependence (see Lewis 1986: 32–38, 167). By contrast, merely to say, as I do, that causation implies counterfactual dependence neither precludes the thought that the past and present might also counterfactually depend upon the future, nor renders that thought incompatible with the idea that time’s arrow can be explained in terms of causal asymmetry.
- 5.
I here take it that, according to determinism, the connection between initial and terminal conditions is law-governed so that, where A states the initial conditions and B states the terminal conditions, if ‘∼B ʿ→ ∼A’ holds in the actual world, it will also hold in all nomologically possible worlds, and consequently that if ‘∼B ʿ→ ∼A’ holds, ‘A → B’ will hold in all nomologically possible worlds (see last but one footnote). If A itself entails the conjunction of the relevant laws as well as the claim that they are laws and nothing else is, ‘A → B’ will furthermore be necessary simpliciter: any metaphysically possible world satisfying A will then be a nomologically possible world. See footnote 8 below for the assumption that A, though made true by present and past facts alone, can nonetheless be understood to entail the relevant laws as well as the claim that they are laws. For the thought that the causalist doctrine need not issue in a corresponding claim of necessitation, see footnote 16.
- 6.
I here ignore statements affected by semantic indecision, presupposition failure, and comparable linguistic or pragmatic shortcomings. I will also ignore the intuitionists’ view according to which there is a gap between affirming that no statement is such that neither it nor its negation is true at t and affirming (2). There is no evident reason why there shouldn’t be an intuitionistically acceptable version of determinism that foregoes commitment to (2) but affirms its double negation instead. Accordingly, any indeterminist view that takes issue with (2) will here be conceived of as taking issue with its double negation, too.
- 7.
See previous footnote.
- 8.
It might be thought that determinism, as defined, is after all incoherent because it will have to postulate laws which connect the past and present with the future and, as such, are partly determined1 to be true by what will be the case in the future. If so, what will be the case in the future cannot be said to be determined2 to be true, that is, determined1 to be true by present and past facts alone (cf. Barnes and Cameron 2009: 300). However, rather than confuting the present characterisation of determinism, this consideration suggests that determinists had better reject the Humean regularity-based conception of laws and instead conceive of laws as facts relating (potentially uninstantiated) properties or relations. There are independent reasons for construing laws in these terms (cf. Dretske 1977; see Maudlin 2007 for a primitivist alternative to Dretske’s account). Plausibly, if laws are construed as facts relating properties and relations, the existence of such facts metaphysically entails that they are laws.
- 9.
The proof assumes that for any time t, there are times earlier than t. Accordingly, if time has a beginning, the conclusion cannot be proved for all times. But then, under that same assumption, there is no reason to think that determinism involves the idea that, for all times t, including the first time, what is true at t is predetermined by what was the case before t.
- 10.
On the intuitionists’ view, less is needed, viz. merely the necessitation of ‘No statement is such that neither it nor its negation is true at t’. However, as already indicated in footnote 6, once intuitionism comes into view, there is no evident reason why determinism must be construed as involving (2) rather than this (intuitionistically) weaker tenet. The present considerations would mutatis mutandis carry over to this (intuitionistically) weakened version of determinism.
- 11.
Federico Luzzi suggested to me that the present issue might be resolved by conceiving of determinists and indeterminists as having a disagreement about what the determinists’ metaphysical tenets are: while the indeterminists regard (3) as a conceptual truth and take the determinists’ controversial thesis to be (2), the determinists themselves may rather regard (2) as a conceptual truth and take their controversial thesis to be (3). determinists would not then be pictured as treating their central metaphysical tenet as necessary. On this way of construing the debate, however, not only would each party charge the respective other with conceptual error; the conception of truth as supertruth would furthermore involve a bias in favour of indeterminism, given only that it is implausible to think that determinism is true only if necessary. There would thus seem to be no neutral ground from which to argue, as is familiar from the debate concerning logical revisionism. As long as alternative construals are available that do not have this consequence, abandoning the idea of a neutral standpoint would seem to be undesirable already for methodological reasons.
- 12.
Even if we replaced clause (iii) in the definition of truth-determination2 by ‘qÎΣ(δ(q) < 0)’, thereby sidestepping the difficulty mentioned towards the end of the previous section, and understood determinism’s tenet (3) accordingly, it would still, thanks to clause (ii) of that definition, hold that determinism requires necessary links between the present truth of present-tensed statements and the past truth of future-tensed statements, which unnecessitated (2) cannot deliver. In any case, though, after the envisaged redefinition of truth-determination2 and of determinism’s tenet (3), the conception of truth as supertruth would imply that (2) is not the only metaphysically controversial tenet the determinist accepts: if ‘0 days from the present, p’ is true at t0, then, insofar as both (1) and (3) hold, ‘n days from the present, p’ will have to be true at t-n, for some positive n. But what holds on all possible continuations of both what is past at t0 and what is present at t0 may not hold on all possible continuations of both what is past at t-n and what is present at t-n. Accordingly, if truth-determination2 and determinism’s tenet (3) were redefined in the way suggested, supervaluationist indeterminism would no longer be a position of the kind we are here considering, that is, a position that accepts (1) and (3) but rejects (2). Thanks to Graham Priest for pressing me to elaborate on this point.
- 13.
There are fairly obvious problems with ‘alwaysing’ a view such as this. But even if it cannot be part of such a view that it is available at each time and so available at earlier times, this does not alter the fact that, at each time, some view of this kind is available (albeit one which is no longer available at later times, if any).
- 14.
Belnap et al. identify the doctrine of the open future with ‘the view that in spite of indeterminism one neither needs nor can use a Thin Red Line’, where the latter is meant to refer to a TRL1 (Belnap et al. 2001: 136). But then why isn’t this suggestive of a decapitated trunk rather than a branching tree? The answer presumably is that only a branching tree can represent future possibilities. But this, as argued, is not suggestive of branching time and neither rules out, nor makes it superfluous to think, that there is a TRL1.
- 15.
See footnote 20 for further discussion. MacFarlane seeks to discredit assumption of a TRL1 by suggesting that it rests on the confused idea that we move through time as a car moves along a road (MacFarlane 2008: 85–86). I fail to see any such connection.
- 16.
To accept this claim may not be unproblematical, though. Let A be the initial conditions and B be the terminal conditions; then, according to the causalist doctrine, ‘∼A ʿ→ ∼B’ holds. Now if ‘∼A ʿ→ ∼B’ holds in all nomologically possible worlds, so will ‘B → A’. If B entails the natural laws as well as the claim that they are laws and nothing else is – call the combination of these claims ‘N’ – then ‘B → A’ will be not only nomologically necessary but necessary simpliciter: every metaphysically possible world satisfying N will be a nomologically possible world. On this kind of view, true statements about the past (initial) conditions will indeed be determined1 to be true in virtue of the present (terminal) conditions and so be determined3 to be true. However, it is hard to see how ‘B → A’ may be necessary without ‘A & N → B’ being necessary, unless some of the laws in N are asymmetric. Yet, science would only seem to provide us with symmetric laws (Hoefer 2010: §2.3), while indeterminists reject that ‘A & N → B’ is necessary (see footnote 5). If, in the light of this, indeterminists forego commitment to the claim that ‘∼A □ → ∼B’ is nomologically necessary, they will lose any basis for claiming that the past is fixed in the sense suggested.
- 17.
Epiphenomena are phenomena that lack causal powers. Yet, it is one thing to say of a given phenomenon that it lacks causal powers and another to say that it contingently fails to exercise any of its causal powers. Accordingly, it might now be suggested that the idea that the past’s present description is determined3 to be presently true is already undermined by humdrum cases in which an event’s causing another is preempted by a third. However, that a given event does not cause another but could have done so if things had been slightly different does not yet imply that that event causes nothing at all, and the idea that a given event is absolutely causally inert, even if only for contingent reasons, strikes me as just as hard to believe as epiphenomenalism (see footnote 3).
- 18.
In other words, the problem of temporary intrinsics, that already arises for linear time, does not get any worse once time is taken to branch in the way suggested.
- 19.
Note that this is not a claim about ordinary language but about the language of metaphysical theory. See footnote 23 (and also footnote 6).
- 20.
If we merely have to sit and wait until history decides the matter, it becomes entirely unclear why the context of utterance fails to fix a unique value for the history parameter: even if nothing that has come to be the case up to the moment of utterance, including the utterance itself, determines2 what comes to pass thereafter (Belnap et al. 2001: 151), the contention that amongst the equally possible future courses of events there is a unique such course of events that will unfold after that moment is enough to vindicate the claim that the identity of that moment uniquely fixes that course of events. (Belnap et al. themselves profess that if the history parameter ‘can be fixed by the context, then we automatically do let the context fix it for stand-alone sentences’ (Belnap et al. 2001: 148).) Of course, Belnap et al. deny that amongst the equally possible future courses of events, there is a unique such course of events that will unfold after that moment, even if they affirm that it will be the case that a unique such course of events unfolds. But, contrary to what they suggest, such denial is not sanctioned by indeterminism which is after all consistent with genuinely future-tensed statements being determined1 to be presently true courtesy of what will happen, as long as what will happen will do so contingently. If time will tell whether there is a sea battle tomorrow, then an utterance of ‘One day hence, there will be a sea battle’ may presently have a definite truth-value that it has only courtesy of what time will tell. If waiting until tomorrow will be enough for it to be settled whether there will be a sea battle tomorrow, ‘One day hence, there will be a sea battle’ may be presently true solely in virtue of there going to be a sea battle after one’s having waited 24 hours. Similarly, the present assignment of a particular value to the history parameter may be correct courtesy of all that will happen after the moment of utterance, even if nothing that is present or past at the moment of utterance grounds that assignment. A moment of utterance can thus fix a unique future without determining it, just as a shadow can fix a unique object without determining it (see Rosenkranz 2012).
- 21.
Note that branching time alone does not entail that ‘TtC’ holds, even if ‘Tt(A & B & C)’ is consistent, since as far as that conception goes, A and B may respectively state laws and initial conditions that do not actually hold at t.
- 22.
If a statement s is true at t iff it is determined2 to be true at t, then it follows both that if s is true at t, s is determined1 to be true at t, and that if s is determined1 to be true at t, s is determined2 to be true at t. Since the converse conditionals are uncontroversial, (1) and (3) follow.
- 23.
Supervaluationists treat future contingents of the form ‘At the time n days from the present, p’ as being neither true nor false and so deny (2). They do so ultimately because they aim to account for the fact that ordinary speakers tend to treat ‘At the time n days from the present, ∼p’ as the negation of ‘At the time n days from the present, p’. However, we are not here concerned with salvaging ordinary language, spoken by potentially uninformed speakers, but with the true description of what temporal reality is like, assuming that we know what it is like. See footnote 19 (and also footnote 6).
- 24.
On any view that implies that there is no future at all, the second assumption will only be acceptable provided that {Future} may be said to include a way the world might be in which there is no future way at all for it to be. However, Barnes and Cameron (2009) make no explicit provision for this.
- 25.
Barnes and Cameron themselves take metaphysical determinacy and indeterminacy to be primitive notions and so presumably deny that we can look beyond (6) and (7) to get a clearer view of what they involve. But, as we shall see in due course, with the conceptual tools introduced in the first section being at our disposal, such pessimism is quite unwarranted.
- 26.
The reasoning relies on the inference from ‘∼(n days from the present, p)’ to ‘n days from the present, ∼p’, but nothing in Barnes and Cameron’s paper suggests that they deny the soundness of this inference.
References
Barnes, E. 2010. Ontic vagueness: A guide for the perplexed. Noûs 44(4): 601–627.
Barnes, E., and R. Cameron. 2009. The open future: Bivalence, determinism and ontology. Philosophical Studies 146: 291–309.
Belnap, N., M. Perloff, and M. Xu. 2001. Facing the future. Oxford: Oxford University Press.
Cameron, R. 2009. Truthmaking for presentists, unpublished manuscript.
Correia, F., and S. Rosenkranz. 2011. As time goes by. Paderborn: Mentis.
Diekemper, J. 2007. B-Theory, fixity, and fatalism. Noûs 41: 429–52.
Dretske, F. 1977. Laws of nature. Philosophy of Science 44: 248–68.
Dummett, M. 2004. Truth and the past. New York: Columbia University Press.
Frege, G. 1892: Über Sinn und Bedeutung. In Gottlob Frege: Funktion, Begriff, Bedeutung, ed. G. Patzig, 40–65. Göttingen: Vandenhoeck und Ruprecht, 1986.
Greenough, P. 2008. Indeterminate truth. Midwest Studies in Philosophy 32: 213–41.
Hoefer, C. 2010. Causal determinism. Stanford encyclopedia of philosophy. http://plato.stanford.edu/entries/determinism-causal/
Lewis, D. 1986. Philosophical papers, vol. 2. Oxford: Oxford University Press.
MacFarlane, J. 2008. Truth in the garden of forking paths. In Relative truth, ed. M. García-Carpintero and M. Kölbel, 81–102. Oxford: Oxford University Press.
Maudlin, T. 2007. The metaphysics within physics. Oxford: Oxford University Press.
Prior, A.N. 1967. Past, present and future. Oxford: Clarendon.
Prior, A.N. 2003. Papers on time and tense. Oxford: Oxford University Press.
Rosenkranz, S. 2012. In Defence of Ockhamism. Philosophia 40: 617–31.
Sorensen, R. 2001. Vagueness and contradiction. Oxford: Oxford University Press.
Thomason, R. 1970. Indeterminist time and truth-value gaps. Theoria 3: 264–81.
Urquhart, A. 1986. Many-valued logic. In Handbook of philosophical logic, Alternatives to classical logic, vol. III, ed. D. Gabbay and F. Guenther, 71–116. Dordrecht: Kluwer.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Rosenkranz, S. (2013). Determinism, the Open Future and Branching Time. In: Correia, F., Iacona, A. (eds) Around the Tree. Synthese Library, vol 361. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5167-5_3
Download citation
DOI: https://doi.org/10.1007/978-94-007-5167-5_3
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-5166-8
Online ISBN: 978-94-007-5167-5
eBook Packages: Humanities, Social Sciences and LawPhilosophy and Religion (R0)