Abstract
Explanations of the genuine openness of the future often appeal to objective indeterminacy. According to the received view, such indeterminacy is indeterminacy of certain future-tensed state of affairs that presently obtain. We shall call this view the weak indeterminate present, to distinguish it from the view we will defend in this paper, which we dub the strong indeterminate present. According to our view, unsettledness of the future is grounded on the present indeterminacy of some present-tensed state of affairs. In order for an indeterminate present-tensed state of affairs to explain the unsettledness of a future-tensed state of affairs, there has to be a connection between the two. We argue that this connection can only be provided if we look at the internal structure of the relevant state of affairs. Finally, we will suggest that the best background theory to explain the connection are the so-called spontaneous collapse models of quantum mechanics.
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Notes
Notice that the fact that memory has such a normative aspect is compatible with the fact that psychologists are usually interested in the cognitive mechanisms underlying memory regardless of their truthfulness. See (Bernecker and Michaelian 2011).
This may not be a fatal strike to the proposal. After all, one may follow (Łukasiewicz 1967) and argue that if our best account of the openness of the future comes with a confutation of the asymmetry, so much the worst for the latter. In what follows we will put on a side this option, since our focus is over a view of openness that aims to preserve the asymmetry intuition.
Notice that failure of having assigned at a time a determinate truth value does not necessarily entail failure of bivalence. See, e.g.: (McCall 1994; Iacona 2007; Barnes and Cameron 2009). For instance, views that encompasses a thin red line (cf. Øhrstrøm 2009) maintain bivalence within a branching framework. In the rest of the paper, for simplicity’s sake, we will talk about unsettledness as if it implies failure of bivalence.
A claim is the utterance of a sentence in a specific context, and claims usually express propositions. Propositions aim at representing state of affairs, which are what make them true, when they are true. We use the notation “\(< \ldots>\)” for propositions, and the notation “[...]” for states of affairs. We take the notion of being tensed to be applied to sentences, but also, derivatively, to the claims made by using sentences, to the propositions expressed, and to the state of affairs they aim at representing.
Notice that, if you are already committed to accept metaphysical unsettledness, then accepting metaphysical indeterminacy does no harm. The use of the notion of metaphysical indeterminacy just is the best way to spell out a prior commitment towards taking unsettledness in a robust way. ( Barnes and Cameron 2009, p. 304) admit that the acceptance of metaphysical indeterminacy in order to defend the open future might be taken as a cost. However, they correctly rejoin that their proposal “is concerned with someone who has already accepted the open future thesis. She is therefore already committed to making sense of robust, non-representational indeterminacy (indeterminacy in how things are, rather than how they are described). In her case, she is committed to worldly indeterminacy concerning the future.”
The notion of constitution that we use is not innocent and could meet some resistance. Someone believing in irreducibly future-tensed properties may want to have the present constituted by future-tensed state of affairs or facts too. In the literature, Lucretian presentism (cf. Bigelow 1996) is probably the position less sympathetic to our characterisation of constitution. Roughly, according to the Lucretian, present truths about the past are made truth by presently obtaining states of affairs involving the world and past-tensed properties. For instance, that Cesar crossed the Rubicon is made true by the presently obtaining state of affair that the world instantiates (now) being such that Cesar crossed the Rubicon. Given that such past-tensed properties are taken to be primitive and irreducible, it is plausible to maintain that in this view present is constituted (in our intended sense) by past-tensed states of affair. This is, of course, compatible with our claim that the present is not constituted by future-tensed states of affairs. Indeed, the Lucretian usually does not postulate future-tensed primitive properties along with the past-tensed ones, precisely in order to respect the asymmetry intuition (see also Tallant and Ingram 2020). However, a perverse interpretation of Lucretianism, in which also irreducible future-tensed properties are at present instantiated by the world would be a trouble-maker for us. We set aside this worry for the purpose of the paper.
Does this come with failure of bivalence? Again, not necessarily, but we can assume that bivalence fails to keep things simple.
The two roles are analogous to the double indexing for evaluation of tensed propositions in the relativistic semantics of MacFarlane (2003) (the idea is already in Thomasson (1970).). Roughly, “at t” corresponds to the time of utterance, and “as of t” to the time of assessment. However, the notion used in the existing literature are entirely semantic in nature: they are specification of the evaluation of propositions. The notion that we make use of here have an explicit metaphysic import: they are specification of the obtainment of states of affairs. Note that the semantic notion of truth is used only in the characterization of the primitive notion expressed by “at t”, and the notion of entailment in (as of t) is a relation between two states of affair.
Note that the definition of WIP is B-theoretically acceptable. Although it does contain the predicate “present”, nothing in what we say here forces us to read it in a metaphysically substantive way. It can be read simply as an indexical expression. The same will go for SIP.
As a reviewer has pointed out, it is not clear at all that our own proposal is more parsimonious. We agree that the issue is open. However, the reason we discard this option is that it fails to comply with the requirement to be neutral with respect to various metaphysics of time. A reason that is entirely internal to the dialectics of the paper: we are setting on a side this option because it does not concerns versions of WIP that we are considering here. We are not denying that a “metaphysically loaded” version of WIP may turn out to be the best account overall. (Incidentally, as we will see, our own proposal is neutral at least with respect to the A-theory vs. B-theory debate.)
Of course, one could also react by concluding that the future is not open after all, and that its indeterminacy has no metaphysical source, being just a matter of ignorance. One of the two authors of the paper is indeed very sympathetic to this conclusion, and see the present paper as an exploration of an alternative.
This is the “glutty” version of indeterminacy. Wilson allows also for a “gappy” version in which no determinate of that determinable is instantiated. Since we believe there are good reasons, coming from quantum mechanics, for preferring the “glutty” approach (see Calosi and Wilson 2018), this will be our only focus in this paper.
This characterization may remind of Kim (1993) theory of events. However, note that here times are not constituent of state of affairs/facts. Rather, state of affairs obtain at times. In other terms, we are dealing here with tensed state of affairs.
Note that SIP-Openness is perfectly compatible with a form of B-theory. And indeed it is formulated in a tenseless language. It is true that SIP (as much as WIP) contains the predicate “present”, but as already noted, nothing hinges on reading it in a metaphysically robust sense.
This can be easily generalized. Take a system s and one of its observables O, with distinct eigenstates \(|\psi \rangle \) and \(|\phi \rangle \). Any linear combination \(|\omega \rangle \) = a \(|\psi \rangle \) + b\(|\phi \rangle \) is a superposition. The resulting quantum state \(|\omega \rangle =\) a \(|\psi \rangle +\) b\(|\phi \rangle \), obtaining at a certain time t, is then to be interpreted as [s, O, \(\psi \)O/\(\phi \)O].
Two anonymous reviewers of this journal protest that conditionalising on the possibility that the Tails Problem could be solved is not correct in this context, and that we should rather conditionalise on some specific solution. We believe that the source of the misunderstanding here relates to what exactly the Tails Problem is, and to what it is supposed to show. It is an overall assumption of any realistic collapse theory like GRW that measurement outcomes are definite—the pointer is always either up or down. To better see this, take for instance ( Maudlin 1995) well-known trilemma regarding the measurement problem. According to Maudlin, we can solve the problem by dropping (at least one) of the following three tenets of standard QM: (a) completeness, (b) unitary evolution, (c) definiteness of outcomes. Now, collapse theories drop (b), thus maintaining the determinacy of outcomes (contrary to Everettian-type of interpretation, which drops it). This means that in any such theory we do have determinate SOAs basically by assumption. The tails problem do not relate to the fact that outcomes are not determinate, but rather relates to how it could happen that this is the case, given that the dynamical evolution never evolves into eigenstates. We do not mean to underestimate this latter problem; if it cannot to be solved (as recently argued, for instance, in McQueen (2015)) then GRW would have to be abandoned. But the point is that the reason why it would is precisely that it cannot explain the definiteness of outcomes, which again is an assumption of these models. This arguably shows that no matter how we solve the Tails Problem (if we can solve it), the resulting ontology given by theories like GRW would be one where there exist determinate SOAs. As one of the reviewer points out, Peter Lewis’ Vague Link (Lewis 2016) might be an important exception to the above line of reasoning. In effect, Lewis explicitly allows for indeterminacy in GRW also at the level of the post-collapse ontology. We grant that such a solution to the tails problem would be problematic for our view. However, we shall notice that it is not so clear whether, even adopting Lewis’ Vague Link, a view close to ours could not be defended. Perhaps, for instance, it could be argued that the post-collapse states being sufficiently determinate—possessing the relevant determinate instantiated with a sufficiently high degree—is enough not merely from a pragmatic point of view, but at a metaphysical level as well. We take it to be an interesting issue whether such an extension of the model could be construed, but have to leave the details to another occasion. We thank both reviewers for inviting us to be clear regarding our take on this issue.
A reviewer of this journal raises a very interesting worry. It is a feature of GRW that whenever a certain particle undergoes a collapse, its wave function is immediately, once again, spread across space. This entails that to every evolution from indeterminacy to determinacy (to every collapse) there corresponds a somewhat symmetric evolution from determinacy to indeterminacy (the spreading of the wave function). Thus, the reviewer contends, one could well imagine a model similar to ours (by carefully rewriting the (i)-(iv) clauses) and argue that on GRW the past is open and the future fixed. Of course, this would be an unwelcome consequence. Notice, however, that for such an Open Past thesis to be true we would need an explanatory claim similar to our SIP-Openness, on which determinacy in the present explains indeterminacy in the past. We take it to be quite natural to reject that such a claim is a good explanation. Furthermore, the above worry seems to rest on the idea that GRW does not prefer one direction over the other. However, it is important to remind that in GRW the fundamental laws of dynamical evolution are temporally asymmetric—contrary to what happens with almost every other interpretation of QM. As a matter of fact, it has been even suggested that on GRW we can explain the temporal asymmetry of thermodynamics, along with the arrow of time given by direction of entropy (see Albert 1992). Therefore, in GRW the indeterminacy-to-determinacy evolution is in fact priviledged.
As a reviewer of this journal has pointed out, since collapses are extremely unlikely to occur for individual systems, it could be argued that clause (\({\mathrm{iv}_{\mathrm{s}}^{*}}\)) is not always met—as of t*, for the individual system that does not collapse, there is no determinate state of affairs that obtains. Although this is correct, we do not take it as an objection to the model. As a matter of fact the universe we live in is made of a large number of highly entangled particles. This means that for the vast majority of particles collapses are way more likely to occur than not. One could push this point further, and imagine a case of a perfectly isolated electron in an otherwise highly entangled universe. However, even in this case, it seems natural to assume that in such a universe the model will apply, given that it applies to a vast portion of the particles and in any case to the universe as a whole (that is considered as a system). In a way, we would imagine these entangled particles to drag forward passage of time for the isolated particle too. The reviewer acknowledges that this is correct, but then wonders whether this would entail that evidence for the open future depends on the existence of a large number of entangled particles. Our reply to this further worry is that it does, but rather than take this feature as a weakness of the model, we actually believe it is one of its main strengths. Suppose we take a universe populated by very few particles which never interacts one to another; would the future be open to them? We have to bite the bullet here, and agree that according to our model the future would not be open in that universe. However, we take our model to be motivated by a certain empirical theory which happens to be true in a universe with a large number of entangled particles, namely the actual universe. Although we understand that not everyone will be happy with such a reply, we nonetheless stress that the above objection is not a fatal one, but only shows one of the conceptual features of the model. For this reason we thank once again the reviewer for inviting us to clarify this issue.
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Acknowledgements
We would like to thank Craig Callender, Peter Lewis, Jessica Wilson, and especially Claudio Calosi, and Jonathan Tallant for useful comments on previous versions of this manuscript. We also thank the audiences of the V and VI International Association for Philosophy of Time Annual Meeting in Seoul and Boulder (CO) for comments and suggestions. Finally, we would like to thank all the members of the Centre for Philosophy of Time in Milan and the Centre for Time in Sydney for useful discussions on a previous draft of the paper.
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Cristian Mariani acknowledges the generous support of the French National Research Agency, under the program Investissements d’avenir (ANR-15-IDEX-02). Giuliano Torrengo acknowledges the generous support of the Spanish Ministry of Science and Innovation (PID2019-108762GB-I00).
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Mariani, C., Torrengo, G. The indeterminate present and the open future. Synthese 199, 3923–3944 (2021). https://doi.org/10.1007/s11229-020-02963-y
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DOI: https://doi.org/10.1007/s11229-020-02963-y