Foreknowledge of free actions

I think the following yields a pretty good formulation of the argument for incompatibility of foreknowledge and free will. Start with the principles:

1. If x freely chooses A at t, and p is a truth solely about what happened prior to t, then p does not entail that x freely chose A at t.
2. <God believes at t* that x freely chooses A at t> entails <x freely chooses A at t>.
3. <God believes at t* that x freely chooses A at t> is solely about what happens at t*.
Now note that if I will freely choose A tomorrow, and God has foreknowledge, then God now believes that I freely choose A tomorrow, and <God now believes that I will freely choose A tomorrow> is a truth purely about what happens today that entails that I freely choose A tomorrow, contrary to (1). So if (1)-(3) hold, then God lacks foreknowledge or we don't choose freely.

But here is a criticism of (1) that I don't remember seeing, though it's obvious enough that I expect it's there somewhere. Claim (1) is supposed to capture our intuition about alternate possibilities. But it fails to capture these intuitions. Consider this case. Suppose the laws of nature are necessary, and you simultaneously deterministically cause me to have an irresistible desire to do a Hitler salute and push me into a time machine so that it is nomically necessary that I perform the Hitler salute in the year 3000 BC. Next thing I see, it's the first moment of the year 3000 BC, and I am doing a Hitler salute. Intuitively, here is a violation of alternate possibilities. But (1) does not indicate this. Let p be a complete description of the universe at the time you push me into the time machine. Then p entails that I do a Hitler salute in the year 3000 BC. But p is not a proposition about what happened prior to the year 3000 BC. Hence, (1) does not rule out my freedom, even though it is surely meant to.

Here's a second, less weird case. Simultaneous causation is at least imaginable. Imagine the laws are necessary, and there is some state of the world that deterministically causes me to simultaneously raise my arm in a Hitler salute. Again, (1) does not tell me that the action is unfree, even though the alternate-possibilities intuitions that led to (1) surely do. So (1) does not capture these intuitions.

So what went wrong in (1)? I know two suggestions. The first one is that "prior to t" in (1), which was originally meant to be "objectively temporally prior" should be understood: "temporally prior in x's subjective time." I think this is unsatisfactory. For instance, x's subjective time only runs when x exists. But surely (1) is meant to rule out a necessitating manipulator of a free agent even when the necessitating manipulator acted before x's conception. The second suggestion is that "prior to t" should become: "explanatorily prior to the agent's freely choosing A." This gives the correct result in time travel case. For while your pushing me in the time machine is not temporally prior to my arriving at 3000 BC, it is explanatorily prior. And it gives the right answer in the simultaneous causation case.

But now note that if we replace "prior to t" in (1) with "explanatorily prior to the agent's freely choosing A", then the argument against foreknowledge fails. For the defender of libertarian free will and foreknowledge can simply deny that God's belief that I will freely do something is explanatorily prior to my doing it.

Now, granted, we might try to capture the intuitions by replacing "prior to t" with "temporally prior to t or explanatorily prior to the free action". But that's too messy.

Now note that if I will freely choose A tomorrow, and God has foreknowledge, then God now believes that I freely choose A tomorrow, and is a truth purely about what happens today

A bit off topic, but surely the proposition -God now believes that I will freely choose A tomorrow- is not purely about what happens today. I concede that there isn't a really good analysis of 'about today' available. I further concede that soft fact/hard fact distinction is finally too unclear to be useful in the context. What the non-fatalist needs is just to show that the "power entailment principles" don't do the work they're designed to do, and that's not too hard to show.

On your main point, Lewis discusses this problem (or one very close) in 'The Paradoxes of Time Travel' under 'fatalist's methods', p. 78 ff.

Are you thinking that is also about whatever is about? Or your point special to the case of God.

Necessarily, God believes at t that it will be the case that p only if it is the case that p at t' (for some t' later than t). God's belief entails that a future contingent state of affairs obtains. So it cannot be purely about what happens at t.

I don't think entailment is a good way of checking if a proposition is solely about a time

Alex,

Right. But I didn't say entailment was a good criterion. What I said was this.

Necessarily, God believes at t that it will be the case that p only if it is the case that p at t' (for some t' later than t). God's belief entails that a future contingent state of affairs obtains. So it cannot be purely about what happens at t.

If the truth-conditions for p at t specify contingent states of affairs that obtain (or not) at t' (later than t) then p is not purely about time t. I'm not proposing this as an analysis of what it means for a proposition to 'be about' one time or another. I think it is one case in which a proposition at t is about a states of affairs that occurs at t'. As I said, I don't think there is a good analysis of a proposition 'being about' some time or other.

Is the proposition that it is true at t* that x freely chooses A at t solely about what "happens" at t*? On my view of aboutness, it is: it's solely about a proposition, namely, the proposition that x freely chooses A at t.

But that means God's belief isn't playing a significant role in the argument.

I don't know what you mean by "truth conditions" here. Do you just mean "necessary conditions", or something stronger?

In this case it is a necessary condition of God believing at t that p is true at t' that a contingent state of affairs obtains at t'.

But, let me emphasize that I think the whole "theory of 'aboutness'" approach to this is hopeless.

Alex,

I think something like the following might be suitable. Let's say that true proposition p is purely about time t in w iff. p is true in w - t+. (where t+ is every moment of w after t). In short, if p is true in w and purely about t in w, then p is true under the assumption that w terminates at t.

Is the proposition that it is true at t* that x freely chooses A at t solely about what "happens" at t*? On my view of aboutness, it is: it's solely about a proposition

But the following is a necessary truth.

T. N(it is true at t* that x freely chooses A at t iff. x freely chooses A at t).

If you take possible worlds to individuate propositions, then it turns out that P = x freely chooses A at t is also about a proposition. But P is not about a proposition. Of course you might hold that worlds are not sufficiently fine-grained to individual propositions. Fair enough. In that case, suppose it is true at w that it is true at t* that x freely chooses A at t. Wouldn't that proposition be false at w if t* were the last moment of w? But then how is that proposition purely about what happens at t*?

This is compatible with time terminating at t0, but it is surely not solely about t0.

Are you sure that proposition is not solely about t0? If it isn't, then every proposition is about the future. Since of course for any p, N(Vp)(p iff. p v p at t10). But is every proposition be about the future? Can't be right, I think.

Alex,

I didn't appeal to q. Only to p. Let p range over contingent propositions. I said this (somewhat more articulated below).

N(Vp)(p iff. (p v p-at-t10)).

"I agree that specifying the "aboutness" is going to be hard. But if one can't make sense of "solely about a time", then the foreknowledge-freedom problem can't get off the ground."

I see that the way you formulated the foreknowledge-freedom problem makes explicit reference to the "solely about a time" notion. Do you think that all formulations do this? Or that the best formulations do? Or that any formulation that doesn't is probably vulnerable to an objection that will involve making a distinction involving this notion?

Alex,

I think the explanatory-priority point is a fair one. Let's run with it. I think it doesn't get us off the hook totally, until we understand what the explanatory relations are between God's knowledge and my action.

One might try to say that God's knowledge, like other knowledge, is explanatorily posterior to what it is knowledge of. But since it is foreknowledge, it has to be posterior to something that does not exist yet. Too weird.

Maybe we could try to avoid this by appeal to God's eternity. But I'm not seeing this as a solution: there are certainly no causal influences from time into eternity. At any rate, I don't think so. How is some contingent temporal event supposed to explain some aspect of an eternal, immutable being? (Side question: if we say it can, do we have Cosmo Argument problems?)

The traditional solution is that God's knowledge either is his will or is explained by it; on this view, both God's knowledge and the contingent event are explained by God's will. But then we can just run the argument with God's will put in for God's foreknowledge, with unhappy results for free-will partisans of alternate possibilities.

Alex,

You offered a counterexample to the world-termination criterion. It was what you took to be a proposition that was true, but also 'about' both t0 and, some later time, t1. Here.

The termination criterion is something Richard Gale tries. I think it doesn't work. Consider this proposition:
*Either the sky is blue at t0 or snow is white at t1*
This is compatible with time terminating at t0, but it is surely not solely about t0.

What I was doing was supplying a counterexample to the counterexample. If that proposition is really about t0 and some later time t1, then every proposition is about some later time. This is because every proposition is equivalent to a disjunction that includes a term refering to a later time. It's not hard to show this, since we have N(Vp)(p iff. (p v p-at-t10)). But surely not every proposition is about some later time. But if that's so, then it's not true that disjunctions of the sort you offered are about some later time, t1. This is the counterexample to the counterexample.

Alex,

Ad 1. I meant “explanatorily posterior.” But I see your point about the symmetry between past and future in this respect, given either presentism or eternalism. So let me recast my objection.

Ordinary knowledge is your (2.ii) posterior to free action. We get it by inference or perception. God does not need to infer anything, I take it, so he gets his knowledge by some analogue of perception. And this is a common way people think of an eternal God: up there somehow observing the entire time-space continuum at once.

With ordinary perception, I have some explanatory story to tell about how perceptual knowledge occurs. Basically, it’s a causal story. That won’t work for God, but is there some alternative explanatory story? I at least see an objection to any possible story. How can a God who knows what he is doing in creation have knowledge about that creation that is explained by creation rather than by his choices and the space of possibilities? Roughly:

1. God creates the world intentionally and freely.
2. God knows what he is doing in creating the world. For all acts of creation A he could perform, there is a possible world w, where w consists of a maximally coherent set of propositions p, such that God knows, “If I perform A, then p.” Some of these p’s are about free creaturely actions. So any p that is true is either intended or foreseen by God.
3. God’s knowledge of the form “If I perform A, then p” is not explained by free creaturely actions. It is either necessary or middle knowledge.
4. God’s knowledge of the form “I perform A” is not explained by free creaturely actions. It is entirely a function of his free will.
5. If God knows the propositions in 3 and 4, he knows p, and this knowledge is not explained by free creaturely actions. This goes for any proposition, including those about free creaturely actions.

I have had some form of this objection for a long time, and it bothers me that more smart people don’t have the same objection. I suspect I am missing something. Am I? (More optimistically, if Trent is right, the fact that I cannot frame a convincing argument for this intuition, but keep having it, is evidence that my intuition is correct! :-) )

Ad 2. I would plump for either (i) or (iii), depending on how we think of God’s will and his knowledge of his actions being related. Surely there could be a non-Molinist (iii), I would think Calvin would be an example. God’s will causes (and explains) effects in the world, and it also explains his knowledge of those effects (God knows what he is doing). God’s will is then the explanation for both his knowledge and the creaturely events, but the knowledge and the events are not directly related.

Why would God's knowledge of everything that would result from his creating have to be explanatorily prior to his deciding what to create? (I take this to be behind your step 3.)

I’m not exactly sure what you’re asking. Is it “why are you so sure God doesn’t just create something and then figure out what will happen”? Because then God doesn’t know what he’s doing in creating. It’s a shot in the dark. And that seems incompatible with divine providence and goodness.

Or is it “why are you so sure that God’s knowledge of the form ‘If I perform A, then p’ is not explained by the fact that p”? Because lots of these p’s are never actualized, and nothing can be an explanans that isn't true. One might reply that these conditionals are only true about the actual world, so that all the p’s are actualized. (a) I doubt it. (b) There is an explanatory circle: God’s creative choice explains the reality of the world; the reality of the world explains God’s knowledge; God’s knowledge informs and helps explain God’s creative choice. (c) Once again I am left with a picture of a God who doesn’t really know what he’s doing in creating, at least compared to alternatives. How does this God know that the world he’s creating is a decent place, if he never considers what else he might have made? And why wouldn’t he consider what else he might have made?

In any case, it does seem to me to be a difficult problem how a creaturely action could explain a divine mental state….the problem is just a special case of the problem of how God can have contingent mental states. … My solution is to take the truthmaker of such states to include a created component.

I’ve never thought about this in detail, but…if simplicity entails qualitative identity across possible worlds, then it’s a hard problem. You could go Leibnizian…there’s only one possible world!

I grant 2. But I deny that 3 follows from 2

That's fine with me, Alex. I deny it, too. But now you're begging the question with the assertion that, in your particular example, which is just an instance of p v q-at-t1, the disjunction is about t1. What's exceptional about your example? You might reply that your proposition is contingent. But I've been stipulating contingency all along, too.

I guess it just seems obvious that when I say "Yesterday or the day before yesterday I went to the store", I am not saying something only about yesterday and I am not saying something only about the day before yesterday.

Then why don't you say the same thing for every contingent proposition p v p-at-t10? Why does it stop seeming obvious?

It is pretty plausible that (p or p-at-t10) is about t10. Yes. But it does not follow that p is about t10.

We've been here before. The only way to affirm what you do just above and reject my argument given further above is to deny that logically equivalent sentences express the same proposition. Maybe that's you're view, since we know that p and (p v (p-at-t10)) are logically equivalent. But these propositions would very likely be equivalent as well on any finer-grained way to distinguishing propositions.

Yes, of course, I deny that logically equivalent sentences express the same proposition. If logically equivalent sentences express the same proposition then everyone believes that God exists, since everyone believes some necessary truth.

I have no idea how you arrived at that. The fact that p and q express the same proposition certainly does not entail that, necessarily, S believes p iff. S believes q. The 'believes that' operator is hyperintensional, so you cannot substitute strictly equivalent propositions, s.v. You can't conclude that everyone believes that God exists simply because it is strictly equivalent to 2+2=4, or some other necessary truth. On the other hand, for perfectly rational beings such as God, the context is non-hyperintensional. Incidentally, Stalnaker (Lewis, too) believed that propositions are just sets of worlds. So, you'd be in good company.

If there is only one necessary proposition, then if Dawkins believes a necessary proposition and I believe a necessary proposition, then Dawkins believes every necessary proposition that I believe. But among the necessary propositions that I believe is the proposition that God exists. Let "p" be a name of that proposition. So Dawkins believes p.

What are being believed are propositions, so I need the propositional operator 'believes that' to be hyperI. It's clearly hyperintensional and obviously intensional. I don't know whether 'about' induces intensional, and I'm less sure it's hyperintensional. I have no idea how its being so would affect the argument negatively. I do know that if two propositions are strictly equivalent, I can believe one without believing the other. So I know how hyperintensionality negatively affects your counterexample.

Alex,