The problems of foreknowledge and prophecy

The problem of foreknowledge is this: there is a plausible argument that God's having infallibly true beliefs about the future contingent actions of creatures is incompatible with those creatures having libertarian freedom, where libertarian freedom to do A implies an ability to bring it about that ~A. I follow Warfield's presentation of this argument, which relies upon the following three principles:

• Past: Past truths are accidentally necessary.

• Consequence: If P is accidentally necessary, then no one is free to make it the case that ~P.

• Transfer: Necessarily, if P is accidentally necessary and P entails Q then Q is accidentally necessary.

Philosophical debate over the concept of accidental necessity has raged. All I will say here is that Past is supposed to capture the intuitive idea that the past is over and done with in a way the future is not. Because the past is over and done with, Consequence is plausible. Many also find Transfer attractive. Importantly, Transfer makes it possible for non-past truths to be accidentally necessary. Where Q is a present or future truth entailed by a past truth, Q will be accidentally necessary. With these principles, we can now present the foreknowledge argument precisely.

Begin by selecting some arbitrary action of yours in 2020 which is just as good a candidate for a free action as you can come up with. Here's the argument:

1. (1) In 1000BC God believed that you would perform A in 2020. [supposition]

2. (2) Necessarily, if God believes p, then p. [infallibility]

3. (3) (1) is a past truth. [premise]

4. (4) (1) is accidentally necessary. [(3), Past]

5. (5) Necessarily, if (1) then you perform A in 2020. [(1), (2)]

6. (6) You perform A in 2020 is accidentally necessary. [(4), (5), Transfer]

7. (7) No-one is free to make it the case that you don't perform A in 2020. [(6), Consequence]

(7) implies that you will not freely do A in 2020. Since your doing A in 2020 was supposed to be as good a candidate as you could come up with for a free action, it follows that no action of yours which you take to be a free action is in fact free, by the foreknowledge argument.

The prophecy argument is very similar:

1. (1′) In 1000BC a prophet prophesied that you would perform A in 2020. [supposition]

2. (2′) Necessarily, if a prophet prophesies that p, then p. [infallibility of prophecy]

3. (3′) (1′) is a past truth. [premise]

4. (4′) (1′) is accidentally necessary. [(3′), Past]

5. (5′) Necessarily, if (1′) then you perform A in 2020. [(1′), (2′)]

6. (6′) You perform A in 2020 is accidentally necessary. [(4′), (5′), Transfer]

7. (7′) No-one is free to make it the case that you don't perform A in 2020. [(6′), Consequence]

The prophecy argument, if successful, shows that no prophesied action is a free action. Some authors have thought that it presents a special problem over and above that presented by the foreknowledge problem. To see why, we must look at the strategies for diffusing the foreknowledge and prophecy problems which Warfield labels the Ockhamist strategy and the Molinist strategy.

The Molinist's strategy is to deny the Transfer principle in these arguments. The arguments fail at (6) and (6′). The Molinist can thus retain Past, Consequence, the infallibility of foreknowledge and prophecy, and the claims that (1) and (1′) are past truths.

The Ockhamist's strategy is to put a halt to the arguments at (3) and (3′). Despite appearances, (1) and (1′) are not past truths. And, since they are not past, nor are they entailed by any past truths, we have no simple argument from our Past and Transfer principles that they are accidentally necessary. So, we cannot conclude (7) and (7′).

There are two reasons for why there has been independent motivation for looking into the prophecy argument. The first reason has to do with the Ockhamist's strategy for escaping from the problem posed by this argument. Some find the Ockhamist's strategy far less plausible when applied to the problem of prophecy than they find it when applied to the problem of foreknowledge.Footnote ² The prophet's prophecy, after all, seems to be as much a part of the causal history of the world as anything. So, there is some special pressure on the Ockhamist to explain why its occurrence doesn't count as a past truth. I return to this topic in the fourth section.

To see the second reason for this special motivation, we must look at Warfield's two anti-Molinist arguments. The first is an attack on the Molinist's denial of Transfer in both arguments. Warfield argues that the Molinist's denial of Transfer is unmotivated. For, Transfer is a simple closure principle. The only kinds of modalities for which closure principles are known to fail are epistemic or subjective modalities. Yet, accidental necessity is a metaphysical property, not an epistemic or subjective one. And, all varieties of metaphysical necessity we are familiar with, including the most plausible attempts to capture the notion of accidental necessity, do satisfy closure.

It is Warfield's second anti-Molinist argument which furnishes the additional motivation we are looking for, though. Warfield's second argument purports to show that the Molinist's commitments in solving the problem of prophecy are inconsistent with others of the Molinist's beliefs. To present the argument, let me introduce some symbols. Read ◊p/□p as it is broadly logically possible/necessary that p; and read F_Sy as S freely does y. Let H stand for the conjunction of all past truths together with the laws of nature; let D stand for the claim that determinism is true; let x stand for your performance of A in 2020; and let p stand for the claim that you perform A in 2020. Warfield argues that the Molinist is committed both to affirming and to denying □((D&p)⊃~F_Youx). Without the symbols: if determinism is true and you do A in 2020, then you do not freely do A in 2020.

Begin with Warfield's claim that the Molinist must deny □((D&p)⊃~F_Youx). She must deny this principle because of her commitments in the problem of prophecy case. For, according to the Molinist, this case is one where F_Youx. Further, it is one where □(H⊃p). For the prophet's prophesying that p is one conjunct of H. Yet, the prophet's prophesying that p entails p, by the infallibility of prophecy. So, H, too, entails p. Now, a standard definition of determinism is just that ∀q□((D&q)≡□(H⊃q)). So, as the Molinist accepts that the prophecy case is one where □(H⊃p), she must accept that it is a case where (D&p). But, then, it is a case where ((D&p) & F_Youx). But from this it plainly follows that ~□((D&p)⊃~F_Youx).

Now for Warfield's simpler argument that the Molinist accepts □((D&p)⊃~F_Youx). The Molinist is an incompatibilist. Thus, she accepts ∀y□((D&S does y)⊃(~F_Sy&~F_S~y)). By universal elimination, □((D&p)⊃(~F_Youx&~F_You~x)). But, the latter of course implies □((D&p)⊃~F_Youx). So, the Molinist is committed both to □((D&p)⊃~F_Youx) and to ~□((D&p)⊃~F_Youx).

The □((D&p)⊃~F_Youx)&~□((D&p)⊃~F_Youx) argument

Neither of Warfield's arguments poses a special problem for the Molinist, I argue. Begin in this section with his second argument. Warfield's second argument fails because Warfield has failed to distinguish between logical laws and causal laws. He defines H as the conjunction of all past truths and the laws of nature. But, he does not specify which laws are to be included in the laws of nature. If it is only causal laws, the Molinist will not have to embrace ~□((D&p)⊃~F_Youx); but, if it is both causal laws and logical laws, the Molinist will not have to embrace □((D&p)⊃~F_Youx).

Recall Warfield's argument that the Molinist must embrace ~□((D&p)⊃~F_Youx), due to her commitments in the prophecy case. The argument purports to show that in the prophecy case, the Molinist is committed both to (D&p) and to F_Youx. The Molinist's commitment to F_Youx is obvious; it is the former commitment that takes some work. Warfield argues that the Molinist is committed to (D&p) in this case by showing that the Molinist is committed to □(H⊃p), since by definition ∀q□((D&q)≡□(H⊃q)). He argues that the Molinist is committed to □(H⊃p) as follows. The prophet's prophesying that p is a past fact, and hence a conjunct of H. But, the prophet's prophesying that p entails that p. So, H entails p.

What I want to point out about this argument is that we need to ask why the prophet's prophesying that p entails p. The answer is that the prophet's prophesying that p entails p because prophesy is infallible and because modus ponens holds. That is to say, the prophet's prophesying that p entails p by virtue of the infallibility of prophecy together with a logical law. But, now, if H is to entail p, then not only will H need to have as a conjunct that the prophet prophesied that p, but also that prophecy is infallible and that modus ponens holds. I will not argue here that the proposition that prophecy is infallible is not a conjunct of H; I will focus my attention on the question of whether the logical laws, including modus ponens, are conjuncts of H. Either the logical laws are or are not conjuncts of H; but, either option spells ruin for Warfield's argument.

Suppose, first, that the logical laws, including modus ponens, are conjuncts of H. In this case, it follows that □(H⊃p) and hence by the definition of determinism that (D&p). So, the Molinist will have to embrace ~□((D&p)⊃~F_Youx). However, she will lose all impetus to accept □((D&p)⊃~F_Youx). For, by the definition of determinism, that claim is equivalent to □(□(H⊃p)⊃~F_Youx). Without the symbols, this says that necessarily, if H entails that you do A in 2020, then you are not free to do A in 2020. But, remembering now that H includes not only facts about the past and laws of nature, but also logical laws, the former says that necessarily, if all past truths together with all causal and logical laws entail that you do A in 2020, then you are not free to do A in 2020. However, the Molinist will not accept this claim. For, she allows that such claims as:

1. (1″) In 1000 BC it was true that p

count as past truths. Since she will think that it is true that:

1. (2″) Necessarily, for all actual times t, if p is true at t, then p,

she will think that the past together with all causal and logical laws entails that you do A in 2020. But, this will not give her any reason to think that you will not freely do A in 2020. For, she is not moved by the argument for logical fatalism. Thus, if H includes the logical laws as conjuncts, then the Molinist will have no reason to accept □((D&p)⊃~F_Youx). (An alternative way of making this point is as follows. Just say that if H includes as conjuncts the logical laws, then Warfield's definition of determinism is false and for that reason the Molinist need not accept □((D&p)⊃~F_Youx), since D as defined by Warfield is not determinism.)

Suppose then that H does not include as conjuncts the logical laws. In this case, the Molinist's commitments in the prophecy case will not give her reason to deny □((D&p)⊃~F_Youx). For, the prophecy case will no longer be such that □(H⊃p). H doesn't entail p because H only includes the claims that a prophet prophesied that p and that if a prophet prophesies that p, then p; it doesn't include the logical laws, e.g. modus ponens, which are necessary for these claims to entail p. So, if H does not include the logical laws, then the Molinist will have no reason to accept ~□((D&p)⊃~F_Youx). The prophecy case won't offer an example in which (D&p) & F_Youx, since it isn't an example where □(H⊃p).

I have argued that Warfield's second argument against the Molinist fails to distinguish between logical and causal laws and that, because of this, the argument fails. In the next section I show a similar problem with his first anti-Molinist argument.

The transfer principle argument

Return now to Warfield's first argument – the argument against the Molinist's strategy of denying the transfer principle used in both the foreknowledge and prophecy arguments. As it turns out, this argument fails due to similar considerations to those which led to the demise of the second argument. Whereas in the second argument, Warfield failed to distinguish between causal and logical laws, in the first he fails to distinguish between causal and logical modalities. Or, rather, he overlooks causal modalities altogether. But, once we see this, his argument against the Molinist's strategy of denying the transfer principle is no longer appealing.

Here's why. Warfield makes two central points against the Molinist's strategy. First, the only modalities we know of for which closure under entailment fails are either epistemic or subjective modalities, but accidental necessity is a metaphysical modality. Second, all metaphysical modalities we know of are ones which are closed under entailment. In particular, this is so for broad logical necessity as well as the most plausible attempts to capture accidental necessity. But we will see that each of these claims is implausible, once we consider causal modalities.

First, it is implausible that the only modalities for which closure under entailment fails are epistemic or subjective modalities. For, causal modalities are neither epistemic nor subjective modalities and they are not closed under entailment. Consider, for instance, the causal modality of being uncausable: p is uncausable for S just in case S cannot causally bring about p; (more generally, p is uncausable just in case no agent can causally bring it about that p). In 2021, p – the claim that you do A in 2020 – is uncausable, for instance; nobody can cause p to be the case in 2021. But, uncausability is not closed under entailment. For, all contradictions are uncausable, and each one implies everything; but it is false that everything is uncausable. Nor will restricting the principle to say ‘if p is not a contradiction and is uncausable, and p entails q, then q is uncausable’ help. For, though it is uncausable that I leap over the moon, and my leaping over the moon entails my leaping, it is false that my leaping is uncausable. So, it is implausible that the only modalities for which closure under entailment fails are epistemic or subjective modalities.Footnote ³

Second, it is implausible that all metaphysical modalities – especially those which are plausible candidates for accidental necessity – are closed under entailment. For, uncausability is a metaphysical modality, and closure under entailment fails for it. Further, it is a plausible account of accidental necessity. For, recall that the term ‘accidental necessity’ is a term of art invented to capture the way in which the past is somehow asymmetrically more fixed than the future. Yet, one plausible view about what it is that makes the past and future asymmetric, and about what makes it such that the past is in a certain way more fixed than the future, is that we cannot causally affect the past, whereas we can causally affect the future. In other words, the past is uncausable, whereas the future is not uncausable. Prima facie, then, uncausability is a promising account of accidental necessity. Yet, as we have seen, uncausability is not closed under entailment. So, it is false that all metaphysical modalities – especially those which are plausible candidates for accidental necessity – are ones which are closed under entailment. Accordingly, Warfield's first argument fails.

Warfield's Ockhamism

I have shown so far that, pace Warfield, the Molinist is not worse off in responding to the problems of foreknowledge and prophecy than the Ockhamist. In this section I offer two brief remarks about Warfield's own positive proposal about how to respond to the problems of foreknowledge and prophecy, in order to show that things between the Ockhamist and Molinist may even be the reverse of what he has said – it may be that the Molinist one-ups the Ockhamist. At the very least, I want to show that Warfield's proposal is in need of further defence.

First, if Warfield's proposal differs from other Ockhamist proposals, his proposal is in trouble. Warfield at times writes in a way that suggests that his proposal is different from other versions of Ockhamism. For, while Warfield's Ockhamist proposal targets premises (3) and (3′) of the above arguments, other Ockhamist proposals seem to target Past.Footnote ⁴ In particular, most Ockhamists distinguish between hard and soft past facts. Hard facts are the accidentally necessary past facts, while soft facts are past facts which are not accidentally necessary. On this type of Ockhamist view, (1) and (1′) are soft past facts – but they are still past facts. Warfield, however, writes as is (1) and (1′) are simply not past facts at all.Footnote ⁵ He never mentions the hard fact/soft fact distinction.

If Warfield's proposal does differ in this way from other versions of Ockhamism, his proposal is in trouble. For, there are serious difficulties for denying that (1) and its kin are past facts. First, it is hard to see what independent motivation one would have for claiming that (1) is not a past fact, while

1. (1*) In 1000BC Job believed that you would perform A in 2020

is a past fact. For, all we have done to change (1) to (1*) is to replace God with Job. Why does this make such a difference? Warfield suggests that the reason it makes such a difference is that (1) entails that a now-future time will exist, while (1*) doesn't. But, the view that p is a past fact only if p doesn't entail the existence of any future time surely cannot be the criterion which differentiates past propositions from future ones. For, in a deterministic world, many propositions which we are tempted to think are wholly about the past will end up not being past propositions. To see this, pick your favourite past time t in deterministic world D and let p be a maximally informative proposition about all of the physical goings-on at t together with a complete description of the causal laws of D. p will obviously entail that future times exist, but it is far from obvious that p is not a past truth.

Second, and more seriously, denying that (1) and its kin are past facts leads to a loss of explanatory power. For, when asked to explain why a claim like

1. (8) In 999BC God placed a bet with Gabriel that you would perform A in 2020

is true, we would often like to appeal to some past fact like (1) about God's mental states which led to (8)'s being true. This problem is especially pressing in the context of divine deliberation. We want to know, ‘Why did God do A at time t ₂?’ We want an answer in the form, God did A at t ₂ because he ultima facie wanted to do A at t ₁ or something along those lines. But, this sort of explanation is unavailable for Warfield if his view differs from other Ockhamist views, as I have suggested. For, the claim that God ultima facie wanted to do A at t ₁ entails that future times exist and hence is not a past truth. But, then, we cannot explain God's doing A at t ₂ in terms of some past truth. And this demonstrates a lack of explanatory power.

My second remark about Warfield's Ockhamism is as follows. Supposing Warfield does want to endorse the same Ockhamist position as those other Ockhamists I have described, his view will no longer be motivated. For, the motivation for denying Past, as these Ockhamists do, is that there seem to be cases where I can freely perform an action A such that some past proposition p is true and p wouldn't have been true if I hadn't performed A. It seems as though, in such cases, I have a certain kind of power over the past. Well, call it a power over the past if you like, but don't call it a causal power, I say. For, it isn't as if my doing A causally brings it about that some past proposition p was true. p was true prior to my doing A. But, then, my doing A couldn't have causally brought it about that p was true. For, causes make a difference, and my doing A didn't make a difference to whether p was true. So, if what Past says is just that all past truths are uncausable, as we proposed in the previous section, then there is no motivation to deny it. Thus, if Warfield's Ockhamism is different from other Ockhamist proposals on the table, it is in trouble. Yet, if it is just like those proposals, it is unmotivated.