Todd (ch.5) – Omniscience and the Open Future

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

Chapter 5 is a relatively short chapter that initially focuses on how to understand divine omniscience in relation to an open future but that is mostly aimed at developing a logic of omniscience that reflects and supports Todd’s rejection of will excluded middle (WEM) in Chapter 3.

I. Open Futurism, Open Theism, and Divine Omniscience

God’s omniscience is standardly understood as implying that God knows all there is to know and knows it perfectly, as thoroughly and securely as possible. One way to put this is to say that God knows all truths (with subjective certainty) and believes no falsehoods. That’s a characterization in terms of what Bertrand Russell called “descriptive” knowledge. Another way to put this is to say that God is fully and immediately acquainted with all of reality. That’s a characterization in terms of what Russell called “acquaintance” knowledge. These two characterizations of omniscience are mutually compatible and a full characterization should, I submit, affirm both.

But can an open futurist who is a theist—i.e., an open theist—affirm God’s omniscience? Todd’s answer is affirmative, and I concur. Indeed, this is a point I’ve been making since at least 2006. The fundamental difference between open theism and “closed” theism concerns the nature of the future, not the nature or scope of God’s knowledge. IF there is a “complete, exhaustively determinate, true story” of the future, then an unqualifiedly omniscient God must know that story, in which case open theism is false and closed theism is true. But IF, as open futurists maintain, there is no such story then it can be no fault of God’s omniscience for Him not to know it. Indeed, IF the full truth about the future is presently incomplete and partly indeterminate—precisely because the story is still being written—then an unqualifiedly omniscient God must know that story, in which case open theism is true and closed theism is false. Either way, both sides can agree that if God is unqualifiedly omniscient, then His knowledge perfectly tracks reality. The disagreement concerns the content of God’s omniscience, not the fact of God’s omniscience. And the disagreement over the content of God’s omniscience is rooted in a disagreement about the nature of the future: Is the future exhaustively determinate/settled? Or is it partly indeterminate/open-ended?

One point Todd makes on p. 109 is that IF there are future contingents, then it is utterly mysterious how there could be a fully determinate story of the future for an omniscient God to know. Where could such a fully determinate story come from? How can it already have been “fully written” if there remain future contingents yet to resolve? There are, to my knowledge, only four positive proposals out there: (1) determinism, (2) eternalism, (3) ersatz eternalism, and (4) Molinism. The first of those is explicitly denies future contingency. The other three are implicitly incompatible with future contingency (as I argue in this YouTube interview). Perhaps the most common response (outside of scholarly circles) is an appeal to mystery—God somehow just “knows” the future as though it were fully determinate even though it objectively isn’t. But that implicitly amounts to a denial of divine omniscience because it has God believing reality to be otherwise than it actually is.

II. Omni-Accuracy, Propositional Attitudes, and Scope Distinctions

Most of the above is my own riff on pp. 108–109 of Todd’s chapter. The bulk of his Ch. 5 is about “the logic of temporal omniscience” (p. 109), which focuses on the relations between divine omniscience, various propositional attitudes God might have, and tense logic. Todd begins by defining what he calls “omni-accuracy”, which he takes to be an entailment of omniscience:

omni-accuracy (OA): p iff God believes p. (p iff Belp)

OA says that for all propositions p, if p, then God believes p, and if God believes p, then p. In other words, there is a perfect correlation between what God believes and what is the case.

Todd considers OA in relation to three different propositional attitudes: belief (Bel), anticipation (Ant), and remembrance (Rem). For God to believe p is for God to believe that p is the case. For God to anticipate p is for God to believe that p will be the case (i.e., for God to believe Fp). For God to remember p is for God to believe that p was the case (i.e., for God to believe Pp).

Given OA and Todd’s understanding of the Ant propositional attitude, we get the following equivalence (cf. p. 110):

omni-accuracy about the future (OAF): Fp iff Bel(Fp) iff Ant(p)

So far so good. Before we can proceed, however, we need to pause and consider an issue that Todd overlooks (at least until Chapter 6).

Side topic: OAF and credence. One thing Todd does not consider in Chapter 5 is how varying degrees of credence and chance might factor into God’s propositional attitudes. This arguably doesn’t matter when it comes to the past or present because we normally conceive of those as fully determinate. Since God is essentially omniscient, there is a fully determinate fact of the matter about how the past was that God remembers or believes (with maximal credence) to have been the case. Likewise, there is (arguably) a fully determinate fact of the matter as to how things presently are that God believes (with maximal credence) to be the case. But we don’t tend to think of the future as being fully determinate—or, it’s at least somewhat controversial to think of it that way. As Master Yoda famously says, “always in motion the future is”. If we assume that Yoda is right and that the future is not fully determinate—if what shall happen henceforth is, in some respects, still “up in the air”—then plausibly God can anticipate things that don’t actually happen. If so, then the equivalence that OAF posits between Fp, Bel(Fp), and Ant(p) can break down. Suppose, for example, that there is objectively a 75% chance of rain tomorrow. Intuitively (in accordance with David Lewis’s famous “principal principle”), God should then believe with a credence of 0.75 that there will be rain tomorrow or, alternatively, anticipate rain tomorrow with a credence of 0.75. Now suppose that open futurism is true. It follows that it is not now the case that F(it rains tomorrow). So it seems like we have ~F(it rains tomorrow), Bel(F(it rains tomorrow)), and Ant(it rains tomorrow), in which case OAF fails. To maintain OAF, then, we have to take Bel and Ant to mean believes/anticipates with maximal credence. Under that restrictive stipulation, since God does not believe F(it rains tomorrow) with maximal credence, we don’t get Bel(F(it rains tomorrow)) but rather ~Bel(F(it rains tomorrow)). And since God does not anticipate rain tomorrow with maximal credence we don’t get Ant(it rains tomorrow) but rather ~Ant(it rains tomorrow). By this means we can preserve the OAF equivalence between ~Fp, ~Bel(Fp), and ~Ant(p). We can still say (if we wish) that God anticipates rain tomorrow (with a credence of 0.75), but that use of “anticipates” must be distinguished from Ant. Likewise, we can still say (if we wish) that God believes that it will rain tomorrow (with a credence of 0.75), but that use of “believes” must be distinguished from Bel. To avoid confusion I will underline “anticipate” and “believes” in what follows when they have the maximal credence sense of Ant and Bel.

Now, intuitively, propositional attitudes like Bel, Ant, and Rem allow for a scope distinction with respect to negation. In the case of us fallible, non-omniscient humans, such scope distinctions exist in part because of our ignorance. When p falls into a gap in our knowledge, we can and arguably should be neutral with respect to belief and disbelief, anticipation and disanticipation, remembrance and disremembrance. If I am completely agnostic about something, with no reason think reality leans one way or the other, then I should neither believe nor disbelieve it but rather maintain a posture of doxastic neutrality. When it comes to an essentially omniscient being like God, however, the possibility of such scope distinctions depends not on ignorance, but on whether reality is indeterminate. More specifically, with respect to Ant, it depends on

open futurism (OF): there are future contingents and, for future contingent p, neither Fp nor F~p is true

Given OF and OAF, it follows that there are possible futures that God neither anticipates nor disanticipates, in which case we get a scope distinction between Ant(~p) and ~Ant(p).

Todd insists that whether there is a scope distinction between Ant(~p) and ~Ant(p) is not a semantic matter (p. 111). That is, one cannot straightforwardly infer “God anticipates that ~p” from “God does not anticipate that p“. Considered independently of OAF this is indeed a highly plausible claim. For example, not anticipating that p is compatible with having no thoughts at all about p, so it obviously can’t entail anticipating that ~p. But given OAF the lack of any such entailment is not so obvious. Since for no p can an essentially omniscient being have no thoughts at all about p, it’s not clear how reflection on propositional attitudes like Bel, Ant, and Rem can provide independent support for a scope distinction. The scope distinction between Ant(~p) and ~Ant(p), like that between F(~p) and ~F(p), seemingly stands or falls on whether OF is true.

III. WEM, Bivalence, and the Indeterministic Lottery

There are, however, two different ways in which OF can be true. One retains bivalence and the other denies it. Let’s call these OFB and OFN, respectively:

open futurism + bivalence (OFB): there are future contingents and, for future contingent p, Fp and F~p are both false

open futurism + non-bivalence (OFN): there are future contingents and, for future contingent p, Fp and F~p are both neither true nor false

The main reason why one might deny bivalence for future contingents is because one thinks that OF and will excluded middle (WEM) are both true. WEM says that for all p, either Fp or F~p. Given WEM and bivalence it follows that either Fp is true and F~p is false, or else Fp is false and F~p is true. Both results conflict with OF. So the only way to affirm WEM and be an open futurist is to deny bivalence. One has to say, with OFN, that future contingents are neither true nor false.

Todd doesn’t make the bivalence connection clear in Ch. 5. He spends about four pages (pp. 114–117) talking about open futurist proponents of “scopelessness/Will Excluded Middle” without providing any context for why anyone might hold that position. In any case, Todd thinks he can leverage OFA to bring some pressure to bear on non-bivalentist open futurists (OFN).

Suppose there is an indeterministic lottery with three tickets, T1, T2, and T3, each with an equal chance of winning. Let p1, p2, and p3 stand for “T1 wins”, “T2 wins”, and “T3 wins”, respectively. And suppose, further, that there is zero chance of the lottery not being completed—one ticket, and only one ticket, is going to win. In this scenario F(p1 ∨ p2 ∨ p3) is obviously true, for it is guaranteed that one of those tickets wins. Likewise, given OAF, Ant(p1 ∨ p2 ∨ p3) is also true. God anticipates that one of those tickets wins the lottery. But is it true of any individual ticket (say, T1) that it will win, or that God anticipates it winning?

The bivalentist open futurist (OFB) will answer no to those questions on the grounds that, since the lottery is indeterministic there is no determinate fact of the matter as to which ticket will win and, given bivalence, if there’s no determinate fact that T1 will win, then it is simply false that T1 will win and thus false that God anticipates T1 winning.

In contrast, the Ockhamist (who rejects OF and thinks there is a unique, determinate future) must answer yes. For if there is and always has been a determinate fact of the matter as to which ticket wins the lottery, then an omniscient God would know and anticipate that fact.

But what about the non-bivalentist open futurist (OFN)? Here things get a bit dicey. Given OFN it is not true that T1 will win, and it’s not false either. It’s simply indeterminate. By WEM and OAF it follows that it’s also indeterminate whether God anticipates T1’s winning. Consequently, the proponent of OFN can’t give a clear yes or no answer. Indeterminacy in the future has become indeterminacy in God’s mind. Todd thinks this highly implausible. It does not, he says, have “the ring of truth” (p. 114).

Let me spell out the problem a bit more. Given WEM and F(p1 ∨ p2 ∨ p3) we can derive Fp1 ∨ Fp2 ∨ Fp3. Given that and OAF, we can derive Bel(Fp1) ∨ Bel(Fp2) ∨ Bel(Fp3) and Ant(p1) ∨ Ant(p2) ∨ Ant(p3). Given the indeterministic lottery scenario and OFN, it follows that Fp1 ∨ Fp2 ∨ Fp3, Bel(Fp1) ∨ Bel(Fp2) ∨ Bel(Fp3), and Ant(p1) ∨ Ant(p2) ∨ Ant(p3) are all determinately true even though the disjuncts are all indeterminate (i.e., neither true nor false). So it is determinately the case that God believes (with maximal credence!) of some particular ticket that it will win, but it is indeterminate as to which ticket that is. But that just sounds wrong. It seems to imply that when it comes to future contingents not even God can know what He Himself believes. That’s seriously weird.

To avoid this consequence, while continuing to affirm OFN and WEM, we have to drop OFA and OA. That is, we must “deny that F and Ant are intersubstitutable” and “deny that God believes p iff p” (p. 115). If we do that, then we also need a different conception of omniscience. Todd suggests

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

Further, in order to prevent OC from collapsing back into OA, we also have to affirm “the non-equivalence of p and it is true that p” (p. 115), which may seem like a significant theoretical cost. I have argued elsewhere that we should in fact deny that equivalence when it’s understood as a logical necessity. Tp iff p may still be a metaphysical necessity, however, even if it can’t be established by mere reflection on truth and propositions.

The upshot of omni-correctness is that God only believes what is true, and so doesn’t believe or anticipate anything that is neither true nor false. Todd concedes that this is a defensible position (p. 116). One can consistently affirm OFN and be a non-bivalentist open-futurist. Nevertheless, Todd prefers (as I do) a bivalentist version of open futurism (OFB). Here’s his summary argument (p. 117):

1. It is not true that there will be a sea-battle tomorrow and not true that there will be no sea-battle tomorrow. (Premise: the open future)
2. If p is not true, then it is false that God believes that p. So,
3. It is false that God believes that there will be a sea-battle tomorrow, and false that God believes that there will be no sea-battle tomorrow. [From 1 and 2]
4. God believes p iff p. (Premise: omni-accuracy)
5. If (p iff q), then if p is false, q is false. So,
6. It is false that there will be a sea-battle tomorrow and false that there will be no sea-battle tomorrow. [From 3, 4, and 5]

This argument looks to be logically valid. Because we are considering which version of open futurism (OFB or OFN) to affirm, premise (1) can be taken for granted. Premise (5) looks like a conceptual truism. (3) and (6) are logical consequences of the other premises. So that leaves (2) and (4). If we accept both (2) and (4), then we get bivalentist open futurism (OFB) (Todd’s position, and mine). So the non-bivalentist has to deny either (2) or (4). As argued above, if we affirm (4) and deny (2), then we get a really weird sort of indeterminism in God’s mind: It can be that, for some future contingent p, God believes Fp (with maximal credence!) even though Fp is neither true nor false. If that seems too weird, then the only other option for the non-bivalentist is to affirm (2) and deny (4). This amounts to denying omni-accuracy in favor of omni-correctness. To the extent, then, that (4) is more plausible than its denial, we have a reason for preferring OFB to OFN. (4) (i.e., OA) certainly seems plausible, but then again so does omni-correctness (OC). Most theists would, I think, be inclined to accept both OA and OC on the grounds that God believes p iff p is true, and p is true iff p. So the mere fact that OFN (arguably) requires us to choose between OA and OC is a strike against OFN and in favor of OFB.

IV. Concluding Thoughts

I think it would have helped had Todd made explicit the connection between Bel, Ant, and maximal credence more clear. That would have headed off a commonsense objection against OA, namely, that God (like us) can believe things (with less than maximal credence) that might not come about. It might also have afforded him a segue into the “credence problem” discussed in Chapter 6.

I also think his discussion of non-bivalentist (or WEM-affirming) open futurism could have been better motivated. In this chapter the topic seemingly drops into the discussion out of the blue. Yes, the idea does occur as an objection in Chapter 3 (pp. 72ff.), but that’s more than a full chapter removed, and I doubt most readers will readily connect the dots.

Finally, the distinction between omni-accuracy (OA) and omni-correctness (OC) is certainly an interesting one. Both seem like initially plausible ways to cash out omniscience. Indeed, anyone who accepts Tp iff p (as a metaphysical if not a conceptual truth) will think that OA and OC are, at the very least, extensionally equivalent. But if we countenance denying bivalence for future contingents (or denying that Tp iff p), then we have to allow that OA and OC might diverge. Todd has done us a service in drawing out this distinction. My only qualm about the distinction is terminological: the labels for the two positions (OA and OC) don’t convey the nature of the distinction. Indeed, the labels “omni-accuracy” and “omni-correctness” seem on the face of it to be essentially synonymous and are therefore easily confused with one another. For that reason, I would have preferred it if Todd had used more perspicuous language. I suggest “alethic omniscience” in place of “omni-correctness” and maybe “doxastic omniscience” in place of “omni-accuracy”.