Why Molinism Does Not Help with the Rollback Argument

Peter Van Inwagen’s Rollback Argument presents the libertarian with a puzzle: the libertarian insists that freedom is incompatible with determinism, but the Rollback Argument purports to show that freedom is also incompatible with indeterminism.¹ Van Inwagen asks us to consider what would happen if God were to roll the universe back over and over again to a point just before an agent makes an indeterministic choice. In some repetitions the agent acts one way, in some another, evoking the sense that what she does is a matter of mere chance. Last year, at the SCP meeting in Georgetown, Robert Hartman gave an excellent paper in which he seeks to show that Molinism provides a solution to Van Inwagen’s puzzle. He claims that the fixed truth values of Molinism’s “Counterfactuals of Creaturely Freedom” (CCFs) sidestep the central mechanism of the thought experiment.² I agree with Hartman’s solution to van Inwagen’s problem as it stands but I will argue that he unfortunately pushes the threat of chanciness to elsewhere in his ontology. To show this, we will need to rework van Inwagen’s original thought experiment into a modal version. Rather than God rolling the universe back, I describe God picking at random from a set of possible worlds with identical histories up to the point when the agent makes her choice. While Hartman can respond to the original version, he cannot respond in the same way to the new.

I must confess at the outset that I agree with van Inwagen’s assessment: the force of the Rollback Argument does not give us reason to doubt that we are free. Neither does it give us reason to suppose that our freedom is, after all, compatible with determinism. Van Inwagen, Hartman, and I all subscribe to a libertarian view of free will—making this response something of a family squabble. All that the thought experiment shows is that libertarians have some explaining to do. We must give a clear account of how the indeterminacy of free action is something other than mere chance. Van Inwagen’s original argument and my modal version of it should both be read, then, as an instrument in the hand of the libertarian to cut away any component of his theory that, in the final analysis, understands freedom as luck. I think Hartman’s response helps but ultimately fails, and for this reason I am still on the hunt for a convincing solution to the problem of luck.

Van Inwagen’s Version

In the Rollback Argument, van Inwagen describes a girl named Alice who faces a choice either to tell the truth or to lie. Let L refer to the state of affairs in which Alice tells a lie and T refer to the state of affairs in which Alice tells the truth. At some time t₁ Alice is at the point of decision, when either option is still available. At t₁ it is within Alice’s power to bring about L and it is within Alice’s power to bring about T. This description appeals to the general Principle of Alternate Possibilities:

PAP

An agent S is free with respect to state of affairs x at time t iff at t, S is able to bring about x and S is able to bring about ¬x.

Further, the libertarian holds that we must gloss “able to bring about” in such a way that an agent’s being able to bring about x is incompatible with it being physically or nomologically impossible that he bring about x given the maximal state of affairs that obtains at t. This means that, if Alice is free with respect to T at t₁, there must be nothing about the state of the universe at t₁ that precludes Alice’s bringing about L. To say otherwise would be to say that there is something about the universe at t₁ that makes Alice tell the truth, but suppose that as a matter of contingent fact she does bring about T after t₁.

Now, at some later moment t₂ God steps in and preforms a little experiment, reverting the entire universe to its exact state at t₁. t₁ is numerically distinct from t₂ but the state of the universe at these two times is qualitatively identical. Now we can reasonably ask the question, “What will Alice do after t₂? Will she lie or will she tell the truth?” The stakes are exactly the same, her reasons for taking either course are the same, and she is still free with respect to both outcomes. If there is nothing about the state of the universe at t₁ that determines her choice, then there must not be anything about the state of the universe at t₂ that determines her choice either. Let us suppose that this time she lies. Thus we have a single time line in which after t₁ Alice tells the truth and after t₂ Alice lies. Now suppose that God repeats this procedure over and over again one thousand times. In some repetitions Alice brings about T and in some Alice brings about L. According to van Inwagen, as the number of repetitions increases, we are very likely to observe the ratio between T-type repetitions and L-type repetitions converge on some definite proportion. Let us say that after one thousand repetitions we observe the proportion of T-type repetitions to total repetitions converging on 0.7:1.

Imagining such a scenario we can already sense that this kind of indeterminism is not what the libertarian wants. The real difficulty that van Inwagen employs to pump our intuitions is the question:

Is it not true that as we watch the number of replays increase, we shall become convinced that what will happen in the next replay is a matter of chance?…If we have watched seven hundred and twenty-six replays, we shall be faced with the inescapable impression that what happens in the seven-hundred-and-twenty- seventh replay will be due simply to chance.³

After we (from a God’s-eye perspective) observe Alice going through her choice over and over again, sometimes lying, sometimes telling the truth, we get the strong impression that the outcome of the next repetition will be just as “chancy” as a dice roll. Finally, van Inwagen concludes,

Now, obviously, what holds for the seven-hundred-and-twenty- seventh replay holds for all of them, including the one that wasn’t strictly a replay, the initial sequence of events.⁴

But this will not do for a libertarian account of free will. By claiming that free actions are indeterminate, the libertarian does not intend to claim that they are metaphysically of the same sort as decaying Uranium atoms or coin flips. The libertarian therefore faces two unacceptable options: (i) the outcomes of an agent’s choices are determined beforehand and are therefore not free or (ii) the outcomes of an agent’s choices are not determined beforehand, are therefore a matter of mere chance, and are therefore not free. Determinism or chance: neither is freedom.

Hartman’s Solution

Facing this difficult dilemma, the libertarian needs some way of either ensuring that Alice will choose to tell the truth in each revision or explain how Alice’s choice is something more than mere chance despite its outcome being indeterminate. Hartman is able to give a plausible account that takes the first of these two options. To account for God’s middle knowledge, Molinism already posits Counterfactuals of Creaturely Freedom (CCFs). These counterfactuals take the form:

CCF

If an agent S were in circumstance C, she would freely bring about state of affairs x.

Molinism claims that some relevant CCF is true with respect to each instance of free creaturely agency. In Alice’s case, the relevant CCF would be:

A

If Alice were in the circumstance that obtains at t₁, she would freely bring about T.

Lest he appear to be a compatibilist, Hartman is quick to point out that he does subscribe to PAP. According to Hartman, there is nothing about C or S that necessitates that S bring about x. It is simply a contingent truth in the actual world that S would bring about x given circumstance C, but there are other possible worlds in which S, in the same circumstances, brings about ¬x. Thus, given that A is true, it is simply a fact about the actual world that under the right circumstances Alice will tell the truth. Nevertheless, Alice is able to lie because there are other possible worlds in which, facing exactly the same circumstances, she does lie.

This is a neat trick for Hartman because it allows him to get quite a bit of what the libertarian wants in an account of free will while also preserving such things as God’s exhaustive foreknowledge and definite truth values for propositions about the future. He can accomplish the first by insisting that there is nothing about the universe or the laws of nature that makes A true. There is nothing even about God that makes A true. Both T and L are therefore metaphysically, nomologically, and theologically possible for Alice and this seems to be just what the libertarian asserts when he maintains his allegiance to PAP. In addition, however, Hartman can account for how it is that God knows what Alice will do, even though she has multiple routes open to her. Because A is a fact about the actual world an omniscient God knows it. Further, because he knows the exact circumstance that obtains at t₁ he knows that Alice will bring about T.

This is a doubly neat trick for Hartman because it allows him to easily solve van Inwagen’s conundrum. In any CCF, the variable C ranges over states of affairs rather than times. It does not matter, therefore, whether t₁ is numerically distinct from t₂. Ex hypothesi, the state of affairs that obtains at t₁ is the same state of affairs that obtains at t₂. Alice will definitely tell the truth after t₂ because A is timelessly true in the actual world. God can revert the universe to its t₁-state as many times as he likes, and Alice will tell the truth every single time. This escapes the impression that Alice’s action is a matter of chance because she reliably does the same thing every time. And yet, the Molinist is also able to escape the charge of determinism because it is nothing about this state of the universe alone that fixes this outcome. The reliability of Alice’s choice derives from the state of the universe taken together with the truth of A and there is nothing that determines A or forces it to be true. A is simply a contingent fact about our world. If Molinism is true, van Inwagen’s original problem quickly dissolves, and this (ceteris paribus) makes Molinism more attractive.

Modal Version

Unfortunately for Hartman we can rework van Inwagen’s original problem so that the same sense of chanciness reappears. This modification requires a simple shift from times in a single possible world to different worlds that share an identical past. As will become clear, the force of this problem derives from the difficulty the Molinist has accounting for the truth-values of his CCFs.

Consider Alice’s situation at t₁. An infinite set of logically possible worlds share the exact history of the world up to and including this point. Call this set H (for “shared history”), and let W refer to the actual world. If determinism is false, then some subset of H larger than {W} will be not only logically possible but also metaphysically and nomologically possible. That is, there must be multiple ways that the world could play out that are consistent both with the history of the world up to and including t₁ and the laws of nature. Call this subset H′.⁵ If Alice is free with respect to T and PAP is true, there must be at least one world, W′ that is a member of H′ in which Alice brings about L. This characterization seems to be a fair way of capturing what the libertarian means by the thesis that freedom is incompatible with determinism. If H′ were to include only worlds in which Alice brings about T, then there would be something about the history of the world taken together with the laws of nature that precludes her from bringing about L. On this model, we are simply claiming that there are multiple ways in which the world can legitimately unfold after t₁ some of which include Alice telling the truth and some of which include Alice lying, putting a possible world’s gloss on PAP.

Using this framework we can alter van Inwagen’s thought experiment so that God picks a random possible world from H′ rather than reverting the universe within a single world. From the description of H′, we—and Hartman—must say that such a world could be one in which Alice brings about T or one in which Alice brings about L. Suppose further that God does this over and over again 1,000 times, revealing to us in sequence the history of one world after another randomly selected from H′. We see worlds in which Alice lies and worlds in which Alice tells the truth. As the number of worlds increases, the proportion between these two outcomes tends to converge on some determinate ratio just as it does in van Inwagen’s original case. Here again, the conviction inescapably arises that what Alice will do in any given world is merely a matter of chance. As God selects the 1,001^st world we could take bets on whether it is an L-type world or a T-type world. This is relevantly similar to the original case because the scope of H′ is restricted precisely by those factors which would count as violating Alice’s free will with respect to her choice. Nothing about Alice’s history, deliberations, or character at t₁ could affect which kind of world God selects because, ex hypothesi, these factors are identical in all members of H′. That the actual world happens to be a T-type world—a world in which she does the right thing—turns out to be quite lucky for Alice.

It is important to see that Hartman’s trick does not work a second time. He cannot appeal to the truth-value of the relevant CCF because this truth-value varies across worlds. An initial route of escape may be to insist that H′ contains only worlds in which A is true. If he does this, however, Hartman gives up any pretense of offering an incompatibilist account of free will. When he describes the nature of CCFs, he insists on inserting “freely” into the consequent (S would freely bring about…). Ostensibly, he is licensed to do this because—by his own lights—there is nothing about the universe or the laws of nature that determines the truth value of a CCF. But these are just the factors that restrict the scope of H′. The Molinist cannot consistently hold (i) that nothing about the history of the world or the laws of nature determines the truth value of A and (ii) that A is true in all possible worlds that share their history and the laws of nature. Assuming that Hartman concedes varying truth-values of A across the worlds in H′, he has little left with which to resist the impression that Alice’s choice is a matter of mere chance.

Instead, Hartman may try to restrict the set from which God can choose to some subset of H′. Something like this seems to be going on in the Molinist account of middle knowledge. After all, according to Molinism, God’s knowledge of which CCFs are true is logically prior to his decision to actualize this world. All the worlds that belong to H′ where A is false are worlds that God could not create because he knows that A is true antecedent to his creative act. While these worlds are all logically, nomologically, and metaphysically possible, they are not theologically possible because God’s actualization of any one of them would violate some creature’s freedom. If God is picking, then, from the pool of worlds that he could create, there will be no chance that Alice will lie because all of these worlds are worlds in which A is true.

This response, however, dodges the real source of our sneaking sense of chanciness, and this source lurks as a consistent problem for all accounts of Molinism: the grounding of CCFs. The thought experiment is not meant to reveal anything about the chanciness of God’s creative act. It is meant to reveal something about the chanciness of Alice’s choice. God’s creative act does not appear chancy, but rather that A should be true. After all, A’s truth is extraordinarily contingent. Nothing about logic, mathematics, the laws of nature, the history or initial position of the universe, the past deeds of Alice, or even her character can possibly determine the truth value of A. No event in Alice’s brain prior to her choice or even anything about the knowledge of God makes it the case that Alice will tell the truth in these circumstances. Nevertheless, Molinism insists, it is a fact about the actual world (and any world God could have created) that Alice would tell the truth in these circumstances.

The problem is that Hartman cannot point to anything sensible that would ground the truth value of A without his Molinism collapsing into a compatiblist account of free will. Instead (and I think this is his best move), he may simply describe CCFs as brute facts within his system. Every comprehensive philosophical account must, at some point, appeal to brute facts that ground the other truths in the system. Why should not CCFs play this role? This is a legitimate move for him to make, but such a move increases rather than removes our worry about chance. On this version of Molinism, it is a matter of sheer contingency that Alice would tell the truth in these circumstances. If anything counts as something which is not “up to Alice” surely it will be matters of sheer contingency and brute fact. Hartman, therefore, faces a difficult choice: he may either (i) give a thorough account of what grounds the truth values of CCFs and, in doing so, risk turning his theory into a kind of compatibilism or (ii) maintain an incompatibilist account of free will while conceding that Molinism does not remove the impression of chanciness in rollback-style thought experiments.

Conclusion

Van Inwagen’s thought experiment forces the libertarian to face this difficulty: actions are either determined or probabilistic and neither are compatible with freedom. At first glance, it seems that Hartman’s Molinism provides a convenient and clean response to this problem without adding anything to the theoretical machinery Molinism already employs in other contexts. If there are true CCFs, Hartman is able to describe how Alice is both free and yet preforms the same action each and every time God rolls the universe back. The main project of this paper has been to show that this response is too easy. While it does respond to the thought experiment as given, it does not solve the deeper problem facing libertarian accounts of free will. Hartman fails to do this because he simply pushes the area of mystery back from the realm of undetermined action to the grounding of CCFs. This is an old objection to Molinism, but I have hoped to show how the grounding problem is related to the larger problem of luck. Molinism is, therefore, on level footing with other libertarian theories with respect to the Rollback Argument.