Abstract
The thin red line is the view that time branches towards the future, but future contingent has already in the present a determinate truth-value. On the face of it, such a view avoids determinism and fatalism, while also representing the fact that there is a future which is ‘special’ because it is the one that will be the case. However, many have objected to the tenability of the thin red line theory by arguing that either it collapses on linear time or it compels us to endorse thick metaphysical theses about the future. In this chapter, we argue against such attacks and show that TRL’s metaphysical grounds are solid.
Keywords
- Branching time theory
- Thin red line
- Metaphysics of the thin red line
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Notes
- 1.
Hence, strong fatalism implies physical determinism, while the latter does not imply the former, thus being compatible with the world having been otherwise, assuming that the initial condition of the world could have been otherwise. Also, strong fatalism is intended as opposed to weak fatalism, according to which whatever I will do now will not affect what will be the case. Weak fatalism, instead, does not imply, nor is implied, by physical determinism.
- 2.
MacFarlane (2003): 325.
- 3.
Belnap and Green (1994): 367.
- 4.
- 5.
Belnap et al. (2001): 140. The other postulates are non-triviality (the structure is not empty), partial order and historical connection (for every distinct t1 and t2, there is a t3 such that t1 > t3 and t2 > t3). In order to keep the discussion under more familiar terms, our characterization of branching time theory differs in some minor respects from the one offered in Belnap et al. (2001) and Thomason (1970, 1984).
- 6.
Of course, in a relativistic setting, the division of space-time into moments is always relative to a system of coordinates. We will not consider here the further complications due to special and general relativity (for a formulation of BTT in a relativistic space-time, see Belnap 1992).
- 7.
Alternatively, we can define simultaneity between events in terms of identity of moments: two events are simultaneous if and only if they belong to the same moment. Here, neither we are interested in providing a detailed formalization of our account nor we deem necessary to discuss what notions should be taken as primitive, since nothing of what we claim depends on these tasks.
- 8.
We are not forced to have a metric on ‘>’ to define cross-simultaneity; we only need a relation of same temporal distance from a moment. Of course, within a temporal metric, such a relation is trivially defined.
- 9.
Note that we are not postulating isomorphism between histories and then define instants on such grounds. Our definition of instant holds even if there is not a complete order of instants.
- 10.
The reader should be alerted that what we call same-branchness most often goes by same-historiness. An analogous remark applies for determinate/indeterminate at a branch and necessary/possible at a branch, which would usually be called determinate/indeterminate with respect to a history and necessary/possible with respect to a history. We prefer the term ‘branch’ as we find it theoretically more neutral. In particular, and as we shall clarify later, the totality of the branches of a tree may not (and in most cases do not) represent the totality of the metaphysical possibilities at a time. Yet we find that speaking of the totality of histories may, although only implicitly, suggest the misguided reading.
- 11.
The postulate of historical connection (for every distinct t1 and t2, there is a t3 such that t3 < t1 and t3 < t2) in Belnap et al. (2001) makes each moment trivially same-wordly with any other. This is a difference between their formulation and ours. Indeed, as it will be clear below, we aim at characterizing the structure also with respect to metaphysically possible alternative situations and not just with respect to our world.
- 12.
McCall (1984). The idea that indeterminist causality can be exploited to ground the ‘arrow’ of time, that is, not simply a temporal asymmetry between the two directions of the temporal relation but also a preferred direction as the direction of time dates back to Reichenbach (1956); see also Horwich (1987).
- 13.
Prior (1967). In what follows, we will speak as if future moments are real, as usually branching theorists do. If topological connection requires sameness of ontological status and there is at least one real moment on a tree (for instance, the present), then this follows (see note 20). However, what is relevant here is that (i) branching time is compatible with the thesis that future moments are ontologically on a par with the present and the past and (ii) branching time vindicates the intuition of openness not through an ontological difference between the past and the future (even granting there is any). Besides, we will often speak in terms of the present, along with past and future moments. These locutions – ‘present’, ‘past’ and ‘future’ – have to be taken informally, since nothing of what we claim hinges on endorsing some dynamic or tense-realist view.
- 14.
- 15.
See, for example, Lewis (1986): 89.
- 16.
One may even add a relation of accessibility among world-tree structures, but we shall not delve into this detail here as it is not relevant to the present discussion.
- 17.
We will not take into account Belnap and Green alternative view, according to which the thin red line is not simply a history, but rather a function from moments to histories (intuitively, the thin red line of each moment). They introduce this alternative only to discuss a rather technical point but then show that the same problems hold for both versions (for a criticism of Belnap and Green’s argument against TRL based on such technical point, see Øhrstrøm 2009). See Belnap and Green (1994): 379–381 and an even more articulated version in Belnap et al. (2001): 162–8.
- 18.
For a formal characterization of the ‘auxiliary’ parameters, see Belnap et al. (2001): 147. As for the terminology, we rely on Belnap et al. (2001) for ‘closed by independence’ (what is dubbed ‘closed by constancy’ in Belnap and Green 1994) and on Belnap and Green (1994) for ‘closed by context’ (what is dubbed ‘closed by initialization’ in Belnap et al. 2001).
- 19.
- 20.
It should be clear that Belnap and Green’s objection is not concerned with TRL’s capacity to propose a solution for the assertion problem. Indeed, they are quite clear on TRL solving the problem, they just object to the solution. ‘The […] far more prevalent response to the assertion problem is to hold that future-tensed sentences are closed by context. On this view, future-tensed sentences make reference to a particular history supplied by the context of use – The Thin Red Line. […W]e argue at length against this tempting evasion of the assertion problem.’ (Belnap and Green 1994: 378.)
- 21.
Here we face another problem: the one cashing out a metric to establish whether a class of alternative futures are at the same distance from the present; we shall leave this on a side.
- 22.
And, in this opinion, we diverge from Belnap and Green, who argue that TRL ‘has troubles with actuality’ because it supposes ‘that there is one from among the histories flowing out of m [the present moment] that is the actual history’ (Belnap and Green 1994: 381). We believe that Belnap and Green’s understanding of TRL, here, rests on a mistake; there is no reason to maintain that the thin red line is singled out by the property of being actual.
- 23.
In particular, if there is at least an actual event in a world with a branching structure, then every event in that world is actual and thus every branch. This can be easily demonstrated. (I) Assume there is at least an actual event (intuitively, all present events, including the present instant, are actual). (II) Any same-world event of an actual event is actual. (III) All events (and, hence, moments) on the red line are same-worldly with past and present events (and moments) and with any event (and moment) on any other branch. (IV) Thus, if the events (and moments) in the red line are actual, so are events (and moments) on any other branch. Note that (III) follows from the definition of same-worldliness and (I) and (II) are very plausible constraints on actuality. Thus, the red line branch is as actual as any other branch, independently on how we construe actuality, insofar as (I) and (II) are satisfied.
- 24.
- 25.
The main limitation is that we will not have general propositions about events, but this will not affect our point but in one minor respect.
- 26.
For an alternative definition of truth at a branch (history), cfr. Thomason (1984).
- 27.
Given that we have assumed that no distinct branches share any of their events.
- 28.
The definition suffers from a problem with counterfactual evaluation, as pointed out in Belnap and Green (1994): 380. We shall not deal with this matter here. However, the ontology of possible worlds sketched in the next section below could be put at use to provide a semantic machinery apt to solve the problem.
- 29.
It is noteworthy that the analysis does not depend on whether one adopts a tensed or a tenseless language. Indeed, ‘e1 will be on the same branch than e2’, when evaluated at t, is still F for TRL and Ind for BTT.
- 30.
Even Belnap et al. (2001) clearly distinguish between the metaphysical picture and the semantic treatment of tensed sentences based on such picture.
- 31.
We call such worlds ‘quasi-standard’ as they are defined in terms of their constituting events and the temporal relations between them, which of course is not the way they are defined in a textbook possible-worlds semantics.
- 32.
The notion of necessity with respect to a tree-world is defined formally; what does it boil down to on a more substantial level depends of course on how we construe the alternatives on the branches. If they are nomologic alternatives, then necessity with respect to a tree-world is physical necessity. An alternative is construing the branches as the metaphysical alternatives at a time t. We will thus have a notion of temporal necessity (parasitic on that of metaphysically possible at a time t) distinct both to physical necessity and necessity simpliciter.
- 33.
- 34.
The distinction that Von Wright (1984) makes between truth and determinate truth (see also Iacona this volume) corresponds to our distinction between being determined with respect to a tree and being necessary (i.e. determinate) with respect to a tree. According to Von Wright, a future-tensed proposition can be true without being determinately true, that is, it can be true at the present time without being true in every future alternative. This holds also in our picture.
- 35.
An exception is McCall (1984).
- 36.
Even if we accept a multiverse, in each single world one effect follows. See Lockwood (2005).
- 37.
See the paper by Iacona (this volume): ‘Perhaps there is nothing in the structure of the world that determines a single possibility to be actual, yet this does not prevent that possibility from being actual’ (p. 41).
References
Belnap, N. 1992. Branching space-time. Synthese 92: 385–434.
Belnap, N., and M. Green. 1994. Indeterminism and the Thin Red Line. Philosophical Perspectives 8: 365–388.
Belnap, N.D., et al. 2001. Facing the future. Agents and choices in our indeterministic world. Oxford: Oxford University Press.
Burgess, J. 1978. The unreal future. Theoria 44: 157–174.
Horwich, P. 1987. Asymmetries in time. Cambridge: MIT Press.
Iacona, A. 2012. Timeless truth. This volume. In Around the tree, ed. Fabrice Correia and Andrea Iacona, 29–46. Dordrecht: Springer.
Lewis, D.K. 1986. On the plurality of worlds. Oxford: Blackwell.
Lockwood, M. 2005. The Labyrinth of time. Introducing the Universe. Oxford: Oxford University Press.
MacFarlane, J. 2003. Future contingents and relative truth. Philosophical Quarterly 53: 321–336.
MacFarlane, J. 2008. Truth in the garden of forking paths. In Relative truth, ed. M. Kölbel and M. Garcia Carpintero. Oxford: Oxford University Press.
McArthur, R. 1974. Factuality and modality in the future tense. Nous 8: 283–288.
McCall, S. 1984. A dynamic model of temporal becoming. Analysis 44(4): 172–6.
Miller, K. 2005. Time travel and the open future. Disputatio I n 19: 197–206.
Miller, K. 2008. Backwards causation, time, and the open future. Metaphysica 9: 173–191.
Øhrstrøm, P. 2009. In defence of the Thin Red Line: A case for Ockhamism. Models of Time: Humana.mente 8: 17–32.
Prior, A. 1967. Past, present and future. Oxford: Clarendon.
Reichenbach, H. 1956. The direction of time. Dover: University of California Press.
Thomason, R. 1970. Indeterminist time and truth-value gaps. Theoria 36: 264–281.
Thomason, R. 1984. Combinations of tense and modality. In Handbook of philosophical logic, vol. II. Dordrecht: Reidel.
Von Wright, G.H. 1984. Determinism and future truth. In Truth, knowledge and modality, 1–13. Oxford: Blackwell.
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Borghini, A., Torrengo, G. (2013). The Metaphysics of the Thin Red Line. 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_7
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