Todd (ch.7) – Against Open-Closurism

By | October 6, 2022

This is part 8 of my ongoing series on Patrick Todd’s recently published book The Open Future: Why Future Contingents are All False (Oxford, 2021). (Previous installments: 1, 2, 3, 4, 5, 6, 7.)

In Chapter 7 Todd and his coauthor, Brian Rabern, tackle a view that they dub “open-closurism”. It’s the view espoused by Richmond Thomason and, most notably and recently, by John MacFarlane according to which (a) will excluded middle (WEM) is true, (b) bivalence (BV) is false, and (c) retro-closure (RC) is true.

open-closurism (OC) = WEM + RC + bivalence fails for future contingent propositions.

This combination has an interesting consequence: semantic relativism. Because of WEM and the failure of bivalence it follows that prior to the occurrence of a future contingent event (say, rain tomorrow) it is not true that it will rain tomorrow, and it is not true that it will not rain tomorrow. But because of RC it follows that after the occurrence of a future contingent event, it was previously true that it was going to occur. This sets up a seeming contradiction: If we suppose that rain tomorrow is a future contingent and that tomorrow it does rain, then by WEM and non-bivalence it is not true today that it rains tomorrow whereas tomorrow by RC it is true today that it rains tomorrow. Since it can’t both be true and not true today that it rains tomorrow, something has to give. Open-closurists resolve this tension by semantic relativism (SR):

semantic relativism (SR) = Propositional truth values need to be relativized not only to times (i.e., a “context of utterance”), but also to perspectives (i.e., a “context of assessment”).

Combining OC and SR allows one to avoid the apparent contradiction generated by WEM + non-bivalence, on the one hand, and RC, on the other:

  • Let t0 be the present moment (the context of utterance) and p be a future contingent that may or may not obtain at future time t1.
  • Let F(p) be the claim that p will obtain at t1.
  • Suppose that p does obtain at t1.
  • Then, F(p) is neither true nor false at t0 from a future-oriented perspective (a prior context of assessment) but is also true at t0 from a past-oriented perspective (a posterior context of assessment).

This is the model that Todd and Rabern wish to critique in Ch. 7. They say

Our contention is this: Once we take up this perspective, and ask what [OC] … predicts about omniscience, we’ll see that the view … 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 the past. (p. 149)

They add that their critique does not presuppose the existence of God; rather, they use God as a “proxy for certain epistemic ideals” to ascertain whether OC is compatible with an “ideal knower” (p. 149).

I. Clarifying open-closurism

Todd and Rabern explain open-closurism in terms of the tense-logical operators P1 = “one day ago” and F1 = “one day hence”. In these terms RC says that every instance of the schema φ → P1F1φ is true (p. 151). To reconcile RC with WEM + non-bivalence, open-closurists offer the following picture:

Looking forwards, there is no privileged branch. Accordingly, looking forwards, future contingents … are not true. However, looking backwards, … there is, now, a way things went to get us to here; accordingly, … we do at that point have, in some sense, a privileged branch of evaluation, viz., the one we took to get 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. (p. 151)

OC is thus committed to the idea that certain past states can “change” in certain relational respects. Prior to φ’s coming to pass, it was neither true nor false that Fφ, but after φ’s coming to pass it was true that Fφ. The antecedent truth value of Fφ changed from neither-true-nor-false to true in virtue of, and in relation to, φ’s having come to pass (p. 154).

II. The logic of temporal omniscience

In order to develop their omniscience objection against OC, Todd and Rabern revisit the distinctions of Todd’s Ch. 5. I invite readers to review my blog post on that chapter for more detail, but Ch. 7 provides a short recap. The main distinction is between two ways of cashing out the notion of omniscience:

omni-accuracyp iff God believes p. (p iff Belp)

omni-correctness: it is true that p iff God believes that p (i.e., Tp iff Belp)

As in my post on Ch.5, I underline “believes” and other doxastic attitude terms when they are to be read as implying maximal credence. To say that God believes p is to say that God believes p with subjective certainty. In short, there is no doubt in God’s mind concerning p.

In addition to belief that p (Belp), Todd and Rabern also introduce the attitudes of anticipation that p (Antp) and remembrance that p (Remp). With these three doxastic operators in hand, they contrast omni-accuracy and omni-correctness as follows (p. 156):

omni-accuracy omni-correctness
φ ↔ Belφ Tφ ↔ Belφ
Fφ ↔ Antφ TFφ ↔ Antφ
Pφ ↔ Remφ TPφ ↔ Remφ

In these terms, retro-closure (φ → PFφ) can be represented as follows:

omni-accuracy omni-correctness
φ ↔ Ant(Remφ) Tφ ↔ Ant(Remφ)

For most theists, the distinction between omni-accuracy and omni-correctness doesn’t matter, because most of us think that God believes p iff p is true (omni-correctness) and also that p is true iff p, which together with omni-correctness entails omni-accuracy. But, as was argued in Ch. 5, non-bivalentists have a reason to prefer omni-correctness over omni-accuracy, because the latter leads to a bizarre indeterminacy in God’s mind about what He Himself believes. Todd and Rabern press similar objections against OC: the tension between non-bivalent open-futurism and retro-closure may be suppressed by semantic relativism but it reasserts itself again in full force in the context of non-relativistic concepts like omniscience that require a unified, total perspective.

III. Open-closurism can’t make sense of omniscience

If the open-closurist endorses omni-accuracy, then it would seem that before the occurrence of future contingent event (say, a sea battle), God neither anticipates the event (sea battle) nor its complement (no sea battle) and yet after the event God’s prior attitude changes so that He always did anticipate things playing out however they did. This change in attitudes seems like an intrinsic change in the past, something that nearly everyone thinks impossible (pp. 157–158). (Why think such intrinsic changes are impossible? Because if they were possible, then something that actually happened could later become such that it never happened. The only way to make sense of that and avoid contradiction is to make a deeply controversial appeal to hypertime.)

Todd and Rabern consider (and reject) a possible reply: “[P]erhaps we can … say that the coming to pass of a sea-battle retroactively constitutes the (prior) state of God’s mind as having been the anticipation of a sea-battle” (p. 159). They don’t put it this way, but the suggested reply amounts to an endorsement of content externalism with respect to God’s anticipations. This has recently become a fashionable idea in Thomistic circles through the work of W. Matthews Grant, but the whole idea seems incredibly implausible to me. Indeed, I contend that it’s an implicit denial of divine omniscience, for it means that with respect to future contingents not even God can know the contents of His own thoughts until external conditions clarify those thoughts for Him. Whatever plausibility content externalism may have for finite knowers like us, I don’t see any way to reconcile it with an essentially perfect knower like God.

What if the open-closurist endorses omni-correctness instead of omni-accuracy? On the one hand, he can avoid the conclusion that God’s antecedent state of mind was either (a) intrinsically indeterminate and thus requiring an intrinsic change in the past when it becomes retroactively determinate, or (b) extrinsically determinate but unknowable by God until the determining event comes about. On the other hand, he falls into another problem, for now it seems that God Himself will have to admit to His own antecedent ignorance. Todd and Rabern illustrate this with a couple imagined dialogues on pp. 161–162 and p. 171. I’ve blended and modified the dialogues to make the point more succinctly:

US: Do you anticipate a sea-battle tomorrow?
GOD: No, I don’t, because 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 and in that sense you are omniscient?
GOD: Correct.
[… a day passes, and a sea-battle now rages]
US: God, did you anticipate this sea-battle yesterday?
GOD: No, I didn’t anticipate this sea-battle yesterday.
US: But by retro-closure it was true yesterday that this sea-battle was going to occur today, correct?
GOD: Yes, correct.
US: But then there was a truth yesterday that escaped your gaze, namely, that there was going to be a sea-battle today.
GOD: That follows.
US: And did you know yesterday that either there will be a sea-battle today or there will not be a sea-battle today?
GOD: Yes, that follows from WEM.
US: So you knew yesterday that your present self would regard your past self as not omniscient! How then can you have regarded yourself as omniscient yesterday?

Todd and Rabern consider a possible reply: Retro-closure entails that if B [= a sea-battle occurs] then PFB [a sea-battle was going to occur], but it doesn’t entail that PTFB, i.e., that it was true that a sea-battle was going to occur. The problem with this reply, they point out, is that the distinction it makes between PFB and PTFB implies that it wasn’t antecedently true because it wasn’t antecedently determined, and “one can accept this view only at the expense of giving up on the fundamental intuitions that motivate Retro-closure in the first place” (p. 165). The main point here is that RC is supposed to be true regardless of whether the events in question are determined since, according to RC, the mere occurrence of an event is supposed to entail that it was antecedently going to occur. But if it can only be antecedently true that an event is going to occur if it is antecedently determined, then the event’s mere occurrence does not entail that it was true that the event is going to occur and so (it would seem) does not entail that the event was going to occur, contrary to RC. In other words, the distinction between PFB and PTFB seems wholly artificial: How can a sea-battle be going to occur without it being true that a sea-battle is going to occur? In the absence of some plausible way of shoring up that distinction, it undermines RC and with it, open-closurism.

IV. Metaphysically loaded semantics and an open theistic comparison

No semantics should, all by itself, entail substantive metaphysical conclusions that are tangential to the concerns of semantics proper. As Todd and Rabern put it, “Just as it is not for the semanticist to say whether the future is causally open, it is likewise not for the semanticist to say whether the universe contains or ever did contain an omniscient being” (p. 167). The latter point might perhaps be contested by some defenders of the ontological argument, but the salient point remains: the semantics of the future-tense shouldn’t have these kinds of metaphysical implications. And yet, if Todd and Rabern’s arguments are correct, then the relativistic semantics of open-closurism seems to entail that there is no omniscient being unless the future is wholly determined. So the semantics is metaphysically loaded in a way that no semantics should be. So it’s a bad semantics.

I agree with the preceding paragraph. The central problem of open-closurism is that its commitment to semantic relativism rules out the possibility of a non-relativistic perspective on reality, such as an omniscient God would presumably have to have. It’s fine to say that truth is relative to times, worlds, reality, etc., so long as none of those are understood in a way that precludes an all-encompassing total perspective, a “God’s eye” view of things, or truth simpliciter. But the moment you say that truth as such is relative to some partial or limited perspective á la MacFarlane’s “context of assessment” you run into problems, not only with omniscience, but with self-reference, e.g., is the claim that truth is relative to a context of assessment only true from certain contexts of assessment? Is so, then it’s self-defeating. If not, then we seem to have recovered an absolute conception of truth in relation to which the tension between RC and WEM + non-bivalence reemerges. Hence, open-closurism doesn’t solve anything.

Todd and Rabern further explore the problematic metaphysical implications of open-closurism by comparing it with a certain version of open theism, one that might initially seem to be allied with open-closurism’s implicit denial of omniscience. This type of open theism affirms that there is a complete, true story of the future—a unique actual future—but says that the parts of that story that concern future contingencies are simply unknowable, even for God. Both views, in effect, deny omniscience. Both agree that it is impossible for an otherwise perfect knower like God to anticipate future contingent outcomes. But they offer different grounds for this impossibility (p. 169). The open theists in question are semantic Ockhamists, and there is no pressure from such a semantics against the possibility of an omniscient being. They deny omniscience instead for broadly metaphysical reasons, on the grounds that “no one has or could have any … mystical insight” into the contingent future (p. 170). Open-closurists, in contrast, implicitly deny omniscience precisely for semantic reasons, thereby flouting the metaphysical neutrality that semantics should have (for issues like that).

V. Rejecting retro-closure

Todd and Rabern agree with MacFarlane that the idea of an open-ended future and the idea of retro-closure both have intuitive appeal, but they argue as we have seen that the conjunction of those two ideas is not tenable: “if Open-future is true, then Retro-closure is not” (p. 172). In the Appendix to Ch. 7 (pp. 173–180), Todd undertakes to explain how open-futurists “might credibly deny Retro-closure” (p. 173).

I’m not going to cover this section in detail, mainly because it doesn’t add much to the discussion of Ch. 6, which I’ve already blogged on. The short of it is this: Instead of agreeing with RC that if a sea-battle occurs then F<A sea battle occurs> was previously true, the open-futurist can say that F<A sea battle occurs> was not previously true—on account of the fact that it was then an open-question whether a sea-battle would occur—but that <A sea battle occurs> subsequently became true. Todd articulates an open-futurist account of what it means for a prediction to become true in some detail on p. 176. In the last few pages of the Appendix, Todd then applies his account of becoming true to rebut various arguments that have been offered for retro-closure. Provided some such account of becoming true is coherent, it follows that RC is false because it is a non sequiturPace RC, it simply does not follow from the occurrence of an event that it was previously true that the event was going to occur.

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