From three or four problems of omniscience down to one

The three most influential problems of omniscience are:

1. Boethius’ problem of foreknowledge: What is known is necessarily so, and thus if God knows what you will do, you will necessarily do it.

2. Pike’s problem of foreknowledge: If you can act otherwise, you can thereby make it be that either God didn’t exist or that God wasn’t omniscient or that God had believed otherwise than God actually did, and you just can’t do that.

3. The simplicity and knowledge of contingents problem: If the world had been different, God’s beliefs would have been different, which implies that God’s beliefs are accidents of God, contrary to divine simplicity.

Of these, (1) is fully solved by Boethius/Aquinas by distinguishing between necessity of consequence and necessity of consequent. The problem in (1) is just a simple matter of a fallacy of modal scope ambiguity. It’s a non-problem.

I now want to argue that the most widely accepted solution to (3) also solves (2).

This solution, likely already known to Aquinas, is that God’s belief in contingent facts is partly extrinsically constituted by creatures, and all the contingency is on the created side. For instance, God’s belief that there are zebras is grounded in essential facts about God that do not vary between possible worlds and the actual existence of zebras, which only obtains in some possible worlds.

Suppose we apply this solution to (3). Then God’s belief that you will ϕ at t is partly grounded in your ϕing at t and partly in essential facts about God. At this point it is obvious that:

4. If you were not to ϕ at t, God wouldn’t have believed you would ϕ at t.

For the contingent part of the grounds of God’s believing that you would ϕ at t is your actually ϕing at t, so when you take that away, God’s belief goes away. And if instead you ψ at t, your action thereby constitutes the contingent part of the grounds of God’s believing that you would ψ at t, and so:

5. If you were to ψ at t, God would have believe you would ψ at t.

If God’s past belief is partly constituted by our actions, it is no surprise that there is counterfactual dependence between our actions and God’s past belief. In other words, the classical theist who accepts divine simplicity has a way out of Pike’s argument that is motivated completely independently of considerations of time and freedom, namely by embracing counterfactuals like (4) and (5) that Pike considers absurd.

Of course the extrinsic constitution of divine beliefs is somewhat hard to swallow, notwithstanding excellent work by people like W. Matthews Grant to make it more plausible (I myself have swallowed it). But once we do that, problem (2) is gone, and problem (1) was never there as it was based on a fallacy.

There is a fourth problem, a more recondite one, which is about the incompatibility between God’s knowledge of what time is objectively present (assuming the A-theory of time) and divine immutability. Probably the most extensive pressing of this problem is in Richard Gale’s On the Nature and Existence of God. But Aquinas (according to the very plausible interpretation by Miriam Pritschet in an excellent paper I heard yesterday at the ACPA) responds to the fourth problem precisely by using the extrinsic constitution of God’s knowledge of continent facts (indeed this is why I said that the solution to the simplicity problem was likely known to Aquinas). So even that fourth problem reduces to the third—or just doesn’t get off the ground if the B-theory of time is true.

Aquinas on God's knowledge of propositions

Does God know that the sky is blue?

That seems like a silly question. It’s not like we’re asking whether God knows future contingents, or counterfactuals of freedom. That the sky is blue is something that it is utterly unproblematic for God to know.

Except that it is tempting to say that God has no propositional knowledge, and knowing that the sky is blue is knowing a proposition.

It seems that Aquinas answers the question in Summa Theologiae I.14.14: “God knows all the propositions that can be formulated” (that’s in Freddoso’s translation; the older Dominican translation talks of “enunciable things”, but I think that doesn’t affect what I am going to say). It seems that God does have propositional knowledge, albeit not in the divided or successive way that we do.

But what he is up to in I.14.14 is not what it initially sounds like to the analytic philosopher’s ear.

For consider Thomas’s argument in I.14.14 that God knows all formulable propositions:

Since (a) to formulate propositions lies within the power of our intellect, and since (b), as was explained above (a. 9), God knows whatever lies within either His own power or the power of a creature, it must be the case that God knows all the propositions that can be formulated.

But now notice an ambiguity in “God knows the proposition that the sky is blue.” In one sense, which I will call “alethic”, this just means God knows that the sky is blue. In another sense, the “objectual”, it means that God knows a certain abstract object, the proposition that the sky is blue. In the objectual sense, God also knows the proposition that the sky is green—God fully knows that proposition, just as he knows other objects, like the person Socrates. But God does not, of course, have the alethic knowledge here—God does not know that the sky is green, because the sky is not green.

If it was the alethic sense that Thomas was after, his argument would be invalid. For in article 9, the discussion clearly concerns objectual knowledge. Exactly the same argument establishes that God knows the proposition that the sky is green as that he knows the proposition that the sky is blue. Furthermore, the Biblical quote Thomas gives in support of his view is “The Lord knows the thoughts of men” (Psalm 93:11). But the Lord doesn’t know all of them to be true, doesn’t know all of them alethically, because not all of the thoughts of humans are true.

Furthermore, if it was alethic knowledge that Aquinas were after, it would be inaccurate to say God knows all propositions. For only “half” of the propositions can be known alethically—the true ones!

All that said, I think we can still bootstrap from the objectual to the alethic knowledge. God’s knowledge of objects is perfect (Aquinas relies on this perfection multiple times in Question 14) and hence complete. If God knows something, God also knows all of its properties, intrinsic and relational. Thus, if God knows a proposition objectually, and that proposition has a truth value, God knows that truth value. In particular, if that proposition is true, God knows that it is true. And that seems to suffice for counting as knowing the proposition alethically.

So, it looks like Aquinas is committed to God objectually knowing both the propositions that the sky is green and that the sky is blue, and also knowing that the former is false and the latter is true—which seems to be enough for God to count as knowing that the sky is blue. (Though I could see this last point getting questioned.)

Freedom: a problem for presentism and growing block

A number of people have told me that they have the intuition that a four-dimensional picture of reality like that in the B-theory undercuts free will.

I want to suggest that there is one way in which it is a presentist picture of temporal reality that undercuts free will. (A similar argument applies to growing block, but curiously enough not to shrinking block.)

Assume that open future views are false: there are always determinate facts about contingent future events. (If your reason for thinking that four-dimensional theories undercut free will is because you are an open futurist, then you won’t be impressed by what I say.) Suppose it is a fact that tomorrow morning I will have oatmeal for breakfast. On presentism, this fact can only be grounded in what is present, since on presentism, what is present is all there is. Maybe it’s grounded in the present existence of a future-tensed fact or maybe it’s grounded in my having a future-tensed property of being such that I will eat oatmeal in nine hours. But in any case, things right now are already such as to ground and guarantee that I will have oatmeal for breakfast. Moreover, this was already true five minutes ago—five minutes ago, things were also already such as to ground and guarantee that I will have oatmeal for breakfast tomorrow. This sure feels like it should undercut free will! It seems pretty intuitive that freedom isn’t compatible with there existing grounds that guarantee the action prior to the choice.

On the other hand, on a four-dimensional view while it is a fact that I will eat oatmeal for breakfast tomorrow, the grounds of this fact are not located in the present—and were never located in the past. Rather, the grounds of this fact are where they should be—at tomorrow morning. How things are on the present slice of reality, or on past slices, does not determine (assuming indeterminism) what I will have for breakfast tomorrow. That’s left for tomorrow.

The neatest way out for the presentist is to deny with Merricks that contingent truths about the future and past have any grounds. But that’s also costly.

After writing the above, I came across this related paper by Hunt. No time to revise right now to see what similarities or differences there are.

The good of success is not at the time of success

It’s good for one to succeed, at least if the thing one succeeds in is good. And the good of succeeding at a good task is something over and beyond the good of the task’s good end, since the good end might be good for someone other than the agent, while the good of success is good for the agent.

Here’s a question I’ve wondered about, and now I think I’ve come to a fairly settled view. When does success contribute to one’s well-being? The obvious answer is: when the success happens! But the obvious answer is wrong for multiple reasons, and so we should embrace what seems the main alternative, namely that success is good for us when we are striving for the end.

Before getting to the positive arguments for why the good of success doesn’t apply to us at the time of success, let me say something about one consideration in favor of that view. Obviously, we often celebrate when success happens. However, notice that we also often celebrate when success becomes inevitable. Let’s now move to the positive arguments.

First, success at good tasks would still be good for one even if there were no afterlife. But some important projects have posthumous success—and such success is clearly a part of one’s well-being. And it seems implausible to respond that posthumous success only contributes to our well-being because as a matter of fact we do have an afterlife. Note, too, that in order to locate the good of success at the time of success, we would not just need an afterlife, but an afterlife that begins right at death. For instance, views on which we cease to exist at death and then come back into existence later at the resurrection of the dead (as corruptionist Christians hold) won’t solve the problem, because the success may happen during the gap time. I believe in an afterlife that begins right at death, but it doesn’t seem like I should have to in order to account for the good of success. Furthermore, note that to use the afterlife to save posthumous success, we need a correlation between the timeline the dead are in and the timeline the living are in, and even for those of us who believe in an afterlife right at death, this is unclear.

Second, suppose your project is ensure that some disease does not return before the year 2200. When is your success? Only in 2200. But suppose your project is even more grandiose: the future is infinite and you strive to ensure that the disease never returns. When is your success? Well, “after all of time”. But there is no time after all of time. So although it may be true that you are successful, that success does not happen at any given time. At any given time, there is infinite project-time to go. So if you get the good of success at the time of success, you never get the good of success here. Even an afterlife won’t help here.

Third, consider Special Relativity. You work in mission control on earth to make sure that astronauts on Mars accomplish some task. You are part of the team, but the last part of the team’s work is theirs. But since light can take up to 22 minutes (depending on orbital positions) to travel between Earth and Mars, the question of at what exact you-time the astronauts accomplished their task depends on the reference frame, with a range of variation in the possible answers of up to 22 minutes. But whether you are happy at some moment should not depend on the reference frame. (You might say that it depends on what your reference frame is. But there is no unambiguous such thing as “your” reference frame in general, say if you are shaking your head so your brain is moving in one direction and the rest of your body in another.)

Here is an interesting corollary of the view: the future is not open (by open, I mean the thesis that there are no facts about how future contingents will go). For if the future is open, often it is only at the time of success that there will be a fact about success, so there won’t be a fact of your having been better off for the success when you were striving earlier for the success. That said, the open-futurist cannot accept the third argument, and is likely to be somewhat dubious of the second.

More on A-theory and divine timelessness

Argument One:

1. If from x’s point of view there is an objective fact about what time it presently is, then x is in time.

2. If x knows an objective fact about something, then from x’s point of view there is an objective fact about it.

3. If the A-theory of time is true, then there is an objective fact about what time it presently is.

4. God knows all objective facts.

5. So, if the A-theory of time is true, then God knows an objective fact about what time it presently is. (3 and 4)

6. So, if the A-theory of time is true, from God’s point of view there is an objective fact about time it presently is. (2 and 5)

7. So, if the A-theory of time is true, God is in time. (1 and 6)

Note that no claim is made that if the A-theory of time is true, God changes.

Argument Two:

1. God is actual.

2. Everything actual is in the actual world.

3. If the A-theory of time is true, the actual world is a temporally-centered world (one where there is a fact as to what time is present).

4. Anything that is in a temporally-centered world is in time.

5. So, if the A-theory of time is true, God is in time.

Many will dispute 3, but if we think of worlds as ways for everything to be, then I think it is hard to dispute 3.

I wonder if a classical theist who is an A-theorist might be able to respond that, yes, God is in time but God is not a temporal being. Compare that by doctrine of omnipresence, God is in space, but God is not a spatial being. Still, I think there is a difference. For as the above arguments show, the claim that God is in time is more limiting than the claim that God is spatially omnipresent—it is a claim that God is at the one objectively present point of time (he was and will be at others, of course).