Future Contingents and the Logic of Temporal Omniscience*
2019; Wiley; Volume: 55; Issue: 1 Linguagem: Inglês
10.1111/nous.12294
ISSN1468-0068
Autores Tópico(s)Philosophy and Theoretical Science
ResumoAt least since Aristotle's famous 'sea-battle' passages in On Interpretation 9, some substantial minority of philosophers has been attracted to what we might call the doctrine of the open future. This doctrine maintains that future contingent statements—roughly, statements saying of causally undetermined events that they will happen—are not true.1 But, prima facie, such views seem inconsistent with the following intuition: if something has happened, then (looking backwards) it was the case that it would happen. How can it be that, looking forwards, it isn't true that there will be a sea-battle, while also being true that, looking backwards, it was the case that there would be a sea-battle? This tension forms, in large part, what might be called the problem of future contingents. Open-future: Future contingents are not true. Retro-closure: From the fact that something is true, it follows that it was the case that it would be true.3 It is well-known that reflection on the problem of future contingents has in many ways been inspired by importantly parallel issues regarding divine foreknowledge and indeterminism. Arthur Prior, whose work figures centrally in these debates, was explicitly motivated by the problems of foreknowledge and human freedom, drew inspiration from ancient and medieval discussions of this problem, and formulated various positions regarding future contingents (e.g., "Ockhamism", after William of Ockham) with an explicit eye towards how they might resolve it.4 The current paper is, in a sense, a continuation of this Priorean project – one he most rigorously pursues in his 1962 paper, "The Formalities of Omniscience". The combination of Open-future and Retro-closure, though rigorously investigated in temporal logic, has been underexplored in connection with foreknowledge, omniscience, and related issues. Our contention is this: Once we take up this perspective, and ask what accepting both Open-future and Retro-closure predicts about omniscience, we'll see that the view harbours some substantial unnoticed costs. We will argue that a temporal semantics that adopts this conjunction, in fact, rules out the existence of an omniscient being (under certain plausible assumptions)—or, at least, requires that any indeterministic universe lacked an omniscient being at some point in its past. Not only does this prove far too much, we will also argue that the resulting picture, in itself, seems incoherent. Notably, although we will use God as our proxy for certain epistemic ideals, the considerations we adduce here needn't be viewed through the lens of philosophy of religion. When we theorize about an ideal knower, we are theorizing about what an agent ought to believe. Thus, if the conjunction of Open-future and Retro-closure leads to an unacceptable view of ideally rational belief, this casts doubt on that conjunction.5 Our aim in what follows is to more fully unpack the problems raised by omniscience for views that maintain both Open-future and Retro-closure. We will first briefly explain the theoretical and formal underpinnings of the Open-future and Retro-closure theses, and explain how one might maintain both. We call the resulting view Open-closurism.6 Open-closurism accepts the doctrine of the open future: that future contingent statements are not true. Underlying the view is a familiar model of the future. Roughly, that model is this: indeterminism plus no privileged branch. In the context of causal indeterminism, we have various "branches" representing causally possible ways things might go from a given moment, consistently with the past and the laws. Importantly, no one branch is "metaphysically privileged" with regard to the others. Future contingents, however, could only be true if one particular branch was so privileged. Future contingents are therefore not true. It seems clear that tomorrow we will know more about which of the various possible future contingencies facing us at present were realized. For example, if it is sunny, we'll look back and say, "Yesterday it was the case that Berkeley would be sunny now". In terms of the tense-logical operators, P ("one day ago") and F ("one day hence"), the Retro-closure principle amounts to the thesis that every instance of the following schema is true: [ϕ → PFϕ].8 Now, again, some theorists see a tension between Open-future and Retro-closure, and accordingly adopt one in preference to the other. But Open-closurism maintains both by putting forward the following picture. Looking forwards, there is no privileged branch. Accordingly, looking forwards, future contingents, such as "There will be a sea-battle tomorrow" and "There will not be a sea-battle tomorrow", which (letting B stand for "there is a sea-battle") might symbolised as FB and F¬B respectively, are not true. However, looking backwards, e.g. from the perspective of a current sea-battle, there is, now, a way things went to get us to here; accordingly, in a statement such as "It was the case yesterday that there would be a sea-battle today" (symbolised as PFB) when the past tense operator takes us "back" to a point in the "temporal tree" to evaluate the future tensed statement FB, we do at that point have, in some sense, a privileged branch of evaluation, viz., the one we took to get us to back to that point. In short, when we have a simple formula Fϕ, with ϕ on some but not all branches, then given that there is no privileged branch, the semantic clauses do not deliver a truth. However, when F is embedded under P, the semantic theory (in some sense) tells you: go back – but then return from whence you came, and check whether ϕ. And thus, the picture validates Retro-closure. These clauses specify how the temporal operators "shift" forward and backwards on a given possible history of the world. Truth: ψ is true at a time t iff ψ is satisfied by all histories h that overlap at t, and ψ is false at a time t iff ψ is unsatisfied by all histories h that overlap at t, and ψ is indeterminate otherwise. Both FB and F¬B are not true at t, since some future histories from that time feature a sea-battle and some don't. (Consult left figure.) But from the perspective of a future time t′ at which there is a sea-battle, since B is true, PFB must also be true: If B is true at t′, then every history that overlaps at t′ has a past that has a future that features B, so it follows that PFB is also true at t′. (Consult the right figure.) In general, ϕ will imply PFϕ, in accordance with the intuitions supporting Retro-closure, and yet we still maintain Open-future. This is the elegant Open-closurist package, which promises a resolution to the Aristotelian puzzles surrounding future contingents. A: Does Jones correctly believe that there will be a sea-battle tomorrow? B: It is not true that he does. A: Does Jones incorrectly believe that there will be a sea-battle tomorrow? B: It is not true that he does. A: So, the future is open? B: Precisely. It is indeterminate whether Jones' belief is correct. [… a day passes, and a sea-battle rages] A: Did Jones correctly believe yesterday that there would be a sea-battle today? B: Yes, of course he did. He believed that there would be a sea-battle today – and there is a sea-battle today. The position of the Open-closurist is that B's pattern of response is perfectly coherent, and furthermore, could be perfectly accurate. And now note what seems to be the consequence of the accuracy of B's position: the past would seem to have undergone a sort of change. Crucially, however, it has undergone merely what we might call an extrinsic change – or a so-called "Cambridge change". More particularly, in the dialogue, we have "moved" (over time) from the untruth of "Jones' belief is correct" to the later truth of "Jones' belief was correct." Thus: at a certain point in time, it is not true that Jones' belief has a certain property (the property of being correct). Later, however, Jones' belief did have that property at that time. At this stage, however, it is important to note that the proponent of Open-closure will insist that this sort of "change in the past" is not the sort of radical "change in the past" which clearly seems impossible. For instance, suppose that, on a given day, "Jones is in Los Angeles" is untrue, but then, on the next day, "Jones was in Los Angeles yesterday" is true – or, in another preview of what's to come, consider the move from the initial untruth today of "Jones believes that ϕ" to the later truth of "Jones believed that ϕ yesterday." Intuitively, these sorts of "changes" would require intrinsic changes in the past – and these sorts of changes, the Open-closurist can insist, are the ones that are impossible. (More about these issues shortly.) However, the change at issue in the dialogue above is not a change of this kind. For consider: whether a given belief counts as being correct or incorrect would plainly seem to be a relational property of that belief; whether a belief is correct or incorrect is constituted, roughly, by how that belief is related to the world. Thus, in the dialogue above, when a sea-battle comes to pass, this brings it about that Jones' prior belief was correct (when he held it). However, had a sea-battle failed to come to pass (which was objectively possible), this would have brought it about that Jones' prior belief was incorrect (when he held it). However, it is crucial to observe that in both scenarios, "the past" – in the ordinary sense of "the past" – is exactly the same: the difference is solely that, in one scenario, a past belief comes to have had a certain relational property, and in the other scenario, that belief comes to have had a different (incompatible) relational property. The past, however, remains intrinsically just the same in both scenarios. As we will see, these differences – between intrinsic and extrinsic changes in the past – play a crucial role in our arguments to come.11 The medieval discussion regarding the logic of divine foreknowledge is, from a formal point of view, very close to the classical discussion concerning future contingency. If we add the assumption that necessarily, something is true if and only if it is known to God, then it is easy to see how the discussion regarding the logic of divine foreknowledge is, from a formal point of view, essentially the same discussion as the classical discussion concerning future contingency. This was clearly realised by the medieval logicians. (Øhrstrøm and Hasle 2015) Omni-accuracy: ϕ if and only if God believes ϕ We will argue that this principle combined with Open-closurism quickly leads to some undesirable results. Omni-correctness: Tϕ if and only if God believes ϕ These, then, are the two options characterizing (a necessary condition on) divine omniscience that we will explore in connection with Open-closurism.13 With these abbreviations we can also contrast Omni-accuracy and Omni-correctness as follows.15 More naturally: if ϕ, then God anticipates remembering that ϕ. For example: if a sea-battle is ongoing, then God anticipates remembering the sea-battle. The principle captures a natural thought: anything that happens will always be remembered by God. Now, we could, of course, detain ourselves for some time developing the parallels between various principles in tense-logic with their "theological" counterparts; we believe that these parallels deserve a more thorough treatment than that which we propose to give them in this paper. (On this approach, we transform the logic of the tenses into the logic of divine anticipations and remembrances.) But we now have enough on the table to assess the two options, given the assumptions of both Open-future and Retro-closure. More naturally: if ϕ, then God remembers anticipating that ϕ. For example: if there is a sea-battle (ongoing), then God remembers anticipating that sea-battle yesterday. More simply: if there is a sea-battle today, then yesterday God anticipated a sea-battle today. Now, here we have a principle with direct and obvious implications for the traditional picture of divine foreknowledge – and a principle whose implications have been debated for millennia. From the fact that something has happened, does it follow that God has always anticipated it? This is, of course, the traditional, orthodox position on divine foreknowledge, and this implication would certainly be accepted by contemporary proponents of such orthodoxy (e.g., Plantinga 1986) – and it certainly would have been accepted by Ockham. Indeed, the principle arguably encapsulates precisely the spirit of Ockham – and other defenders of the traditional picture of divine foreknowledge. When Augustine complains (in On Free Choice of the Will) that it would be absurd to deny that God has foreknowledge, precisely his complaint is that it would be absurd to maintain that there are things that happen which God hasn't always known (viz., anticipated) would happen. Us: God, do you anticipate a sea-battle tomorrow? God: It is not true that I do. Us: Do you anticipate peace tomorrow? God: It is not true that I do. Us: So, the future is open? God: Precisely. [… a day passes, and a sea-battle rages] Us: God, did you anticipate this sea-battle? God: Yes, of course I did. But surely this is unacceptable. How can this make sense, unless God has fundamentally changed the past? According to the Omni-accuracy principle, the open future licenses God's initial claim that it is not true that he has the anticipation. When God faces the open future—and sees that things could go so that B or so that ¬B—it is not true that FB, so it is not true that God anticipates that B. But likewise, Retro-closure licenses God's maintaining that he had the anticipation all along: Retro-closure plus Omni-accuracy yields that everything has been anticipated by God. There is thus a challenge for the Open-closurist who accepts Omni-accuracy: they must explain how it is that God could have the set of seemingly impossible attitudes exemplified in Dialogue-2. But let's slow down. Recall the issues at the end of Section 1: Open-closurism requires the coherence of extrinsic or "mere Cambridge" changes in the past. As we saw, it requires a "move" (over time) from the untruth of "Jones' belief is correct" to the later truth of "Jones' belief was correct." But we distinguished that sort of "change in the past" with a different sort of change in the past: an intrinsic change in the past – the sort of change in the past that more clearly seems objectionable. And now the problem: the sort of change in the past involved in Dialogue-2 would seem to imply an intrinsic change in the past; we have moved from the initial untruth of "God believes that ϕ" to the later truth of "God believed that ϕ". We do not profess to know the operations of the divine mind. But we do claim that if this move represents those operations, those operations imply an intrinsic change in the past. We have brought out how Open-closurism together with Omni-accuracy predicts the pattern of response in Dialogue-2, and we have thereby defended (1). In this paper, we simply assume the truth of (3).16 That leaves (2). Might the Open-closurist insist that, on closer inspection, the "move" at issue in Dialogue-2 implies no more of an intrinsic change in the past than the "move" at issue in Dialogue-1? Unsettled Mind: For some ϕ, ¬T(Ant ϕ), and ¬T(¬Ant ϕ). That is, given that it is indeterminate whether there will be a sea-battle, it is also indeterminate whether God anticipates a sea-battle.17 But if it is indeterminate whether God anticipates a sea-battle, then perhaps we can say the following: God's mind is either in a state of sea-battle-anticipation or it's in a state of non-anticipation, but it is metaphysically indeterminate which. And if we can say that, then perhaps we can also say that the coming to pass of a sea-battle retro-actively constitutes the (prior) state of God's mind as having been the anticipation of a sea-battle. Prior to the sea-battle, no one (not even God!) can tell determinately whether the relevant mental state is the anticipation of a sea-battle (because it is not determinately such an anticipation). But once the sea-battle transpires, God's mental state had been (all along) the anticipation of a sea-battle. Thus, in an important sense, what we do now partially constitutes which mental state God had been in – the belief-state that we would battle, or instead the belief-state that we would not battle. Thus, the changes at issue concerning God's mental state would be mere extrinsic changes on analogy with the sorts of changes already acknowledged to be required for the Open-closurist's treatment of future contingents. And if this is so, premise (2) is false. This, then, is the picture that the proponent of Open-closurism and Omni-accuracy must defend. Such a picture is, of course, mysterious – but we think it's even worse than that. Consider the nature of the "indeterminacy" of God's belief-states that this approach must posit. God's beliefs concerning future contingents are indeterminate in the sense that what belief state God is in constitutively depends on what eventuates in the future – that is, constitutively depends on whether or not a sea-battle eventuates. However, very plausibly, whether God currently counts as believing that there will be a sea-battle tomorrow doesn't await the unfolding of time. Nevertheless, this is what the view under consideration must be insisting: Whether God counts as having a certain present anticipation constitutively depends on what the future has not yet settled.18 This sort of indeterminacy, which we will call "future history indeterminacy", can be defined as follows: Definition 1.ϕ is future history indeterminate at t iff there are some possible histories overlapping at t according to which ϕ and some possible histories overlapping at t according to which ¬ϕ. (And ϕ is future history determinate otherwise.)19 Intuitively, however, whether someone counts as believing that an event will happen is not indeterminate, in this sense. That is, belief and anticipation would seem to be future-history determinate affairs: whether a person has or lacks a given belief at t does not depend, in this sense, on what happens in the future relative to t.20 Notice that, in this respect, belief differs importantly from correct belief. As we brought out in Dialogue-1, whether one counts as correctly believing that an event will take place is, at least in part, a matter of (is constitutively dependent on) whether in fact it will take place. Contrary to the current suggestion, however, whether one counts as believing that an event will take place is not constitutively dependent on whether it will take place. And so this way of denying premise (2) seems untenable. Us: Do you anticipate a sea-battle next year? God: It is not true that I do. Us: What would be rational for you to do, if you did anticipate a sea-battle next year? God: I would employ 1000 workers from Tyre to take those stones in the quarry to construct a wall around the city. Us: And peace? God: I would employ 1000 workers from Sidon to take those same stones and instead construct a temple in the center of the city. Us: Are you currently doing either of those things? God: It is not true that I am, nor true that I am not. [… a year passes, and a sea-battle rages] Us: Did you anticipate a sea-battle a year ago? God: Yes, I did. Us: Then why didn't you employ those 1000 workers from Tyre to construct a wall around the city? The rampaging army will be here soon! God: What? Behold: there indeed have been workers from Tyre building such a wall with those stones over the past year; haven't you noticed the influx of Tyronians? Fear not: the wall is in good stead (and this is why there is no temple in the center of the city). After all: I anticipated this sea-battle. Us [dumbstruck]: Oh my God, look at the wall! God: What? Behold: there indeed have been 1000 Sidonians in the city using those stones to build a temple in the center of the city (that is, after all, why there is no wall around the city). Worry not: the temple is in good stead. After all: I anticipated precisely this peace. And it is fundamentally unclear how one and the same set of circumstances could resolve itself into the correctness of both of these speeches: if we get war, then God will be able to make the first speech, and if we get peace, God will be able to make the second. This seems unacceptable – if not simply impossible. The reason these situations strike us as impossible is that affairs such as an agent's current actions or utterances or the current physical locations of stones are future-history determinate affairs. But if such affairs are linked to God's indeterminate anticipations, then they would also have to be indeterminate—but they aren't. Needless to say, these dialogues raise a great many questions, not all of which we address. We simply note the following: it is unclear how they could have adequate answers. Omni-correctness: Tϕ if and only if God believes ϕ Us: Do you anticipate a sea-battle tomorrow? God: No. Us: Why not? God: Well, it isn't true that there will be a sea-battle tomorrow. The future is open. Us: So there are no truths that escape your gaze? God: Correct. Us: And in that sense you are omniscient? God: Correct. […. a day passes, and a sea-battle rages] Us: God, did you anticipate the sea-battle? God: Well… no. I didn't anticipate the sea-battle. Us: But a sea-battle was going to occur! [PFB] God: Granted. Us: So something was going to happen that you didn't anticipate would happen. [P(FB ∧ ¬Ant B)] God: Granted. Us: But isn't that just to say that you weren't omniscient after all? God: …. Now, as a first approximation, the problem is that we seem to have shown that God was not omniscient. After all, God seems to be admitting former ignorance. If there are events that were indeed always going to happen that God didn't anticipate would happen, then in what sense was God omniscient? Given the principle of Omni-correctness and the Open-closurist model, the following statement is true at the sea-battle: P(FB ∧ ¬Ant B). Thus, some instances of the schema P(ϕ ∧ ¬Bel ϕ) are true. Normally, one would take a true instance of that schema to be a statement to the effect that God was ignorant: Something was the case that God didn't believe was the case! Now in response to this complaint, one might maintain that God is not and was not genuinely "ignorant", since one is ignorant only if there is a truth about which that one is ignorant. However, according to the view under discussion, there was no truth of which God was ignorant. At the time of the sea-battle, there was always going to be a sea-battle, but it wasn't always true that there would be a sea-battle. That is, since B is true, then PFB is also true, but PTFB isn't. So while it is right that the sea-battle was going to happen and God didn't anticipate it – P(FB ∧ ¬Ant B) – there is nevertheless no truth that escaped his gaze, since it wasn't true that there would be a sea-battle – ¬PTFB.23 We think that one can accept this view only at the expense of giving up on the fundamental intuitions that motivate Retro-closure in the first place. Very plausibly, if one is moved by the backward-looking intuition that, given that a sea-battle has occurred, it was always going to occur, it seems that one should likewise be moved by the intuition that given that a sea-battle has occurred, it was always true – which is not to say determined! – that it was going to occur. However, by treating truth as, in effect, synonymous with determined, the view under consideration makes it impossible to express the intuition that, though it was true that the sea-battle would occur, it wasn't determined that it would occur. This is, however, an intuition we should be able to express – and this is precisely the intuition that motivates Retro-closure. According to supervaluationism, then, my utterance was not true. By [the definition of T above], the sentence I uttered was neither true nor false at the context in which I uttered it. But surely that is the wrong verdict. I said that it would be sunny today, and look—it is sunny! How could it be, then, that what I said was not true? To see how strange the supervaluationist's verdict is, suppose that the Director of the Bureau of Quantum Weather Prediction now offers me an irrefutable proof that, at the time of my utterance yesterday, it was still an open possibility that it would not be sunny today. Would such a proof compel me to withdraw my assertion? Hardly. If I had asserted that it was settled that it would be sunny today, I would have to stand corrected. But I did not assert that. I just said that it would be sunny—and it is. My prediction was true, as we can demonstrate simply by looking outside. (MacFarlane 2008: 89–90) Retro-closure: For all ϕ, ϕ → PT*Fϕ Open-future: For some ϕ, (¬T*Fϕ ∧ ¬T*F¬ϕ) But validating the latter would seem to invalidate the former—the forward-looking intuition seems to require a robust notion of truth which quantifies over histories, whereas the backward-looking intuition seems to require a more-or-less transparent notion of truth.24 MacFarlane insists that we should "split the difference" by introducing a definition of truth with "double time references"—the time of utterance and the time of assessment (MacFarlane 2003: 331; cf. Dummett 1973: 394–395).25 Various technicalities can be employed at this point to vindicate both principles. But this is not our primary concern. Our point, instead, is this: insofar as the Open-closurist view has a notion of truth that vindicates the (updated) Retro-closure principle, they will have to accept the conclusion that God was genuinely ignorant. Something was true (in the relevant sense) that God didn't believe: P(T*FB ∧ ¬Ant B). This is a conclusion MacFarlane must simply accept (on the assumption that MacFarlane does not wish to accept the first option, Omni-accuracy). In other words: MacFarlane is right about the supervaluationist. But we are right about MacFarlane. On his picture, God was ignorant. The question now becomes: is this result defensible? More particularly, is it (1) defensible that a theory of temporal semantics alone could rule out the former existence of an omniscient being in an indeterministic universe? And (2) is it plausible that, given the open future, we can nevertheless fairly charge God with having been ignorant – as Open-closurism suggests? It is these questions we take up in the remainder of the paper. A proper account of the semantics of future contingents can vindicate ordinary thought and talk about the future in a way that is compatible with branching. […] we assume neither that physical law is deterministic nor that it is not. That is a question for physics. Semantics, conceived as a theory of linguistic meaning, should not presuppose any particular answer to this question. The project is not to give a semantics for future-directed talk that assumes indeterminism, but rather to give one that does not assume determinism. (MacFarlane 2014: 202–204) Nor, we think, should a semantics for future-directed talk make presuppositions about the existence or non-existence of an omniscient being. This is a question for the metaphysician, or perhaps the philosopher of religion, or perhaps even the person in the pew – but at any rate it is not a question for the semanticist qua semanticist. In general, one could argue that a semantic theory—a theory concerned with the logic and compositional structure of the language—ought not settle certain substantive non-semantic questions. Although we find it very attractive, we can't hope to offer a defence of this general semantic neutrality principle here.26 But the appeal to neutrality we are making is much narrower in scope: A correct semantic theory for temporal language must be compatible with the existence of an omniscient agent in a (deterministic or indeterministic) universe. It is worth observing that the main alternative views concerning the semantics for future-contingents don't fail to be neutral in this way. Clearly, the Peircean can maintain the claim that, yesterday, there existed an omniscient God; the Peircean, in virtue of denying Retro-closure, will simply contend that, though yesterday God did not anticipate today's sea-battle, this doesn't show that yesterday God was ignorant – for, according to the Peircean, yesterday it wasn't true that there would be a sea-battle today. Similarly, the Ockhamist can plainly maintain that there exists and did exist an omniscient being (witness, for instance, Ockham). At any rate, if there is no Ockhamist God (no being that knows or did know the Ockhamist facts, as it were), this is certainly not the fault of the Ockhamist semantics. But the Open-closurist semanticist – in virtue of being such a semanticist – cannot maintain the claim (in the relevant context) that, yesterday, there existed an omniscient being. In this, the Open-closurists stand alone – and problematically so. To flesh out this complaint, it is useful to compare the Open-closurist view with a view that might initially be seen as a partner in crime – that is, with a nearby view that also denies that there was an omniscient being, but does so on roughly metaphysical rather than semantic grounds. In particular, consider the picture endorsed by certain so-called "open theists" such as Swinburne, Hasker, and van Inwagen.27 Like Open-closurists, such theists accept the thesis that past indeterminism implies that God was ignorant.28 According to this version of open theism, that is, it was true that certain events were going to happen which God had not anticipated would happen. However, the central argument these philosophers make at this stage is that it was impossible, even for a perfect knower, to anticipat
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