Thursday, February 24, 2022

The replay argument against agential control

Van Inwagen’s replay experiment is supposed to show that indeterministic free will is problematic. We imagine someone choosing betweeen A and B, then we rewind the state of the universe to just how it was before their choice, and repeat. Van Inwagen thinks that as we continue the experiments, we will get the proportion of choices that are As converging to some number, say 30%, and that tends to make us think that the choices are random rather than something in the agent’s control.

Let’s imagine we’ve actually done this replay a very large number of times. Here are the three possibilities for what we might observe:

  • O1: The proportion of As settled down to some number strictly between 0 and 1.

  • O2: All the choices were As or all the choices were Bs.

  • O3: The proportion of As changed and did not settle down.

For familiar libertarian reasons, it seems that O2 would be evidence against the hypothesis that the choice is in the agent’s control: they both support the hypothesis that the agent is compelled or nearly compelled, either by their character or by external forces, to choose as they did.

Van Inwagen claims that observation O1 is evidence against the hypothesis that the choice is in the agent’s control. For Bayesian reasons, given that O1, O2 and O3 are exhaustive and mutually exclusive, and that O2 is also evidence against the agent’s control, the only way this could be is O3 favored the agential control hypothesis (unless our prior probability of O3 is equal to 1, which it’s not).

But I don’t think observation O3 would favor the agential control hypothesis. There are two reasons for my judgment.

First, let’s subdivide observation O3 into two suboptions.

  • O3a: There is some discernible pattern to the As and Bs that precludes the proportion of As from settling down, e.g., ABBAAAABBBBBBBBAAAAAAAAAAAAAAAA...,

  • O3b: It’s just a complete mess and the proportion doesn’t settle.

Now, O3a is a strange option. A pattern initially may seem like evidence of control. But once we recall that the experiment involved a rewinding of the universe’s state, we can see that any pattern that is not just all As or all Bs cannot be the result of agential control, since control of a pattern across time would require memory, and we have assumed that any memories are wiped. So, given the rewinding, we know that any pattern—other than the patterns that do not require memory, namely the patterns in options 2 and 3, is a fluke. Thus, 4a shouldn’t be evidentially different from 4b.

What about O3b? Well, O3b is more of a mess than O1. A mess is, if anything, more random than a sequence with a probabilistic structure, and hence if anything less indicative of agential control. Thus, O3b is either neutral with regard to the hypothesis of agential control or even evidence against it. And O3b is in the boat by the above remarks. Thus, O3 is either neutral with regard to agential control or evidence against it.

Second, the reason van Inwagen thinks O1 goes against the agential control hypothesis is because it favors the hypothesis that we simply have a probabilistic structure of independent identically distributed random experiments: I will call this the “iid hypothesis”. Now, suppose we observe option O3, and let’s consider the specific observed sequence. Let r be the final observed proportion of As. This is some number strictly between 0 and 1 (otherwise we would have O2). Of course, because we are in option O3, we didn’t actually observe convergence to r, but still there was some final proportion. Whatever that number r is, van Inwagen thinks that if we had observed convergence to r, that would have been evidence against the agential control hypothesis, because it would have indicated a probabilistic random structure. But now observe that on the iid hypothesis, if there are m of the As and n of the Bs in a sequence, and the probability of A is p, then the probability of the sequence is pm(1−p)n. Note that this does not depend on the order of the As and Bs in the sequence. Hence when we keep fixed the proportion of As in the sequence, any particular sequence that looks like it converges to that proportion and any particular sequence that simply happens, after some swings, to end at that proportion are equally likely. Further, the main competing hypothesis with the iid hypothesis is that no meaningful probabilities can be attached to the situation. In that case, we cannot say anything about whether O1 or O3 is more likely. Thus, any particular sequence we could get that exhibits O1 does not favor the iid hypothesis any more than any particular sequence we could get that exhibits O3.

Let us recapitulate. Option O3 either is neutral on whether there is agential control or is some evidence against it. Option O2 opposes agential control. Thus, option O1 must either be neutral on whether there is agential control or be some evidence for agential control. And so van Inwagen’s replay argument does not work.


Wesley C. said...

Why would O2 be evidence against free will of the agent? Like, isn't one of the common libertarian principles that free will means the agent COULD choose otherwise, even if he is disposed in such a way that he would and does always choose one option over another?

Heck, indeterminism in O2 could still technically exist even with a statistical distribution of 99.9999...%, with arbitrary many nines in the decimal spot, since it's not a pure 100%. But even if it actually WERE a full 100%, it still wouldn't go against the ontological claims of libertarianism which are fundamentally about the ontological nature of choices, which don't depend on the amount of times a choice is made or how strong a disposition in favour of it is.

Wesley C. said...

Another thing worth mentioning is that we can speak of a person having free will and being able to have chosen otherwise even in cases where a certain desire or disposition is so strong such that it is very hard to resist giving in to it. Of course, being addicted or ill in such a way that choosing otherwise is extremely hard to the point of being an inability does diminish culpability and so seems to not be truly free will in the proper sense, but intuitively there also seem to be cases where a person could still truly choose otherwise, even though it's very hard to the point where it's a moral certainty that he will always choose that thing, and really does do so. This may or may not be related to the 99% statistical disposition aspect above, but I just thought it was worth mentioning.

Alexander R Pruss said...

I think that cases where it is close to certain that the agent will act a certain way are more likely to be cases of compulsion than cases of freedom. O2 is compatible with agential control, but it still seems to be evidence against agential control.

Walter Van den Acker said...


If the agent always chooses X over Y, the agent has no libertarian free will, because there is no sense in which he could choose otherwise.
It comes down to "there is no possible world in which the agents chooses Y", which is equivalent to "it is impossible that the agent chooses Y" or "necessarily, the agent chooses Y".
I agree that in the case of 99.9999...%, there "could" still be LFW, but it would be a strong indication against it. But 100 % means no LFW.

Wesley C. said...

To Alex: Well I guess it depends on what we mean by close to certain - you could have moral certainty that a person will choose a certain way all the time for the same reason we can often easily predict what people would do in situations in general, but it still wouldn't be a certainty that requires necessitation or no possibility of acting otherwise. I guess it depends on what's behind the certainty.

The intuition of being able to act otherwise isn't excluded or incompatible with the idea that an agent will always choose to act a certain way and we can be certain about it. Indeterminism seems to go deeper than the question of how often and how certain one chooses A and not B.

Wesley C. said...

Regarding contrastive or propositional explanation of free choices, you said once in your book on PSR that agent choosing A is explained by being impressed by reasons R for it, whilst choosing A* is explained by being impressed by reasons R* for it, and the agent is aware of both R and R* at the time, and so is impressed by both R and R*. Now you said that a contrastive explanation wouldn't say choice is explained by being impressed by both reasons, but by one in paritcular.

However, it occurs to me that maybe one could add to this by having a sort of quasi-contrastive or clarifying explanation of indeterministic free choice by explaining a particular choice also by appealing to the principles behind indeterminism. Basically, an agent chose A for reasons R and not in a contrastive way because of the reasons why his choices are indeterministic - so one doesn't need to fret about it not being contrastive, as there are good background reasons for why it doesn't need to be contrastive.

The basic nature of indeterminism would be applicable to any specific choice, so it can explain all of them in this sense, being both general in a sense but also being adaptable to the specifics of specific choices as well in some way. What do you think?

Alexander R Pruss said...


Merely moral certainty is unlikely to be probability 1. It's more like 0.999999. So if that's all we have, and we replay the experiment enough times (say, a billion times), then we can be pretty confident that there will be choices that go against what one is morally certain of.

Wesley C. said...

To Alex: One counterexample though might be a man saving his wife from death in a particular case, and no matter how many times it's replayed (even infinitely many) the man always saves the wife with no outliers. Considering the man is still under original sin or concupiscence, this means he can still theoretically choose otherwise as his virtue isn't perfect as in the next life.

So it seems that the ability to do otherwise isn't always reducible to saying he would do otherwise in (even infinitely many) replays - the modality of contingency here is deeper than replayability. What do you think?

Alexander R Pruss said...

I find it hard to believe that anything in fallen humanity would be 100%. The possibility of rebellion against God, isn't that always available, even if in some cases extremely unlikely?

After all, given quantum mechanics suggests that there is a non-zero (but astronomically small) chance of a rock turning into a bird, is it plausible that human free will wouldn't have all sorts of outlandish possibilities?

Wesley C. said...

Well, the very idea of someone having such a conviction that they'd always do one thing in any replay (even if we assume this requires non-fallen humans) seems intuitively plausible. A man may always save his wife from certain death no matter how many times that situation is replayed - and that doesn't seem to violate free will; in fact, free will seems to still intuitively be there.

Firmness of decision to the point where a person would definitely always choose one course of action can even be said to be the fulfillment of free choice given that the decision is made firmly and with no second-guessing.

And I think this seems to suggest that free will isn't reducible to the probability of tendencies, and even the certainty of eventually doing otherwise in arbitrarily many replays - the ontological nature of free choice (not being strictly determined towards an object) to have the ability to have done otherwise seems to be rooted in something deeper and irreducible to those. What do you think?

Alexander R Pruss said...

Either the man has a deliberatively available undominated reason not to save his wife or he doesn't. If he has such a reason, then I wouldn't expect him to save his wife every time the case comes up. If he doesn't have such a reason, then I don't think he is choosing (whether freely or not) to save his wife over not saving her, because one only chooses A over B when one deliberates *between* A and B, and one only deliberates between A and B when one has deliberatively available undominated reasons reasons for both.

That said, I agree that free will isn't reducible to probabilities of tendencies. I also think that it may be logically possible to have a case where one is freely choosing A and the probability of that choice is 1. Imagine that one has an uncountable infinity of options that one is choosing from. Then at least one of the options will have probability zero (that's a theorem). So, the choice NOT to go for that option will have probability one.

Wesley C. said...

Sounds reasonable. Though my intuition is that even when a man doesn't have undominated reasons to choose otherwise, his choosing of A instead of B is still free - maybe because the will isn't pulled with absolute irresistibility, or the object isn't so great as to infallibly force the will to it; say because one's wife isn't the infinite ultimate good (God) which would pull our will without ability to do otherwise.

Or because the will views goods under the universal aspect of goodness, so any non-divine good is only a particular good among others and can't irresistibly attract the will. What do you think of that view?

Wesley C. said...

a) Also, does this view - that deliberation requires undominated deliberatively available reasons for both A and B - require that the attraction or intrinsic preference for both be absolutely equal? Or can there be a very strong preference for A over B, say 99.99999....%, whilst it still being a case of having deliberatively available undominated reasons for both?

b) Finally, what would be the libertarian account of cases where a person has such a strong inclination to A over B that he finds it very hard to resist and choose B, and so almost always chooses A as he finds it simply too hard to exercise himself for B? Assuming he could still choose B over A but that this requires immense effort, would this type of choice-difficulty be compatible with still having freedom?

Wesley C. said...

1) My intuition here though is that even when a man doesn't have undominated reasons to choose otherwise, his choosing of A instead of B is still free - maybe because the will isn't pulled with absolute irresistibility or the object isn't so great as to infallibly force the will to it.

2) Heck, if a person is free because he could have done otherwise, then he's also free because he also has the ability to always choose A over and over again. The ability of the will to choose otherwise also requires the ability to always choose A infinitely many times, so free will is in no way compromised with always choosing one thing over another in all replays.

3) Finally, what would be the libertarian account of difficulty in resisting A? Say a person has such a strong inclination to A over B that he finds it extremely hard to resist and choose B, and so always chooses A, though he still technically could choose B?

Would the difficulty of exertion be explained as just another form of high inclination towards a certain distribution of outcomes?

Alexander R Pruss said...


If I don't have undominated reason to choose B over A, I can't deliberate between A and B, since deliberation is based on contrastive reasons, and if there is no B-rather-than-A reason available to the agent, there is no way to consider B deliberatively. It's just a shoo-in rather than a decision or choice.

Wesley C. said...

To Alex: Wait, what about saying a person simply has reasons to choose B, but not of the contrastive variety in relation to A? In other words, can one be said to have free choice in a non-contrastive state where one has reasons to choose A and reasons to choose B, but not any contrastive ones in relation to either?

Do you mean to say that reasons to choose B by itself entails its own contrastivity or that it even IS contrastive since it's NOT a reason for A?

Alexander R Pruss said...

Well, if A and B are incompatible, then an undominated reason for B is a contrastive reason for B. A dominated reason for B, however, is not deliberatively relevant when A is an option. Thus, if all you care about is the amount of money, and more is better, I think you can't choose between $5 and $3.

Dominik Kowalski said...

Nope that's definitely false. In fact the idea that probabilities to choices could be assigned are what's problematic. The libertarian aspect comes in due to the fact that a) the agent is metaphysically capable of choosing otherwise and b) the physical conditions prior to the choice weren't deterministic i.e. entailing of the subsequent action.

That the agent has two choices which each could have been chosen doesn't entail that there's actually a world in which the agent doesn't choose 1) instead of 2). This is because if we judge an option as good or better than the other one, then, under the same conditions, we will always choose the same, no matter how many times we should rewind. Everything else falls prey to the randomness objection. Theoretically you could choose to not rescue your child from the oncoming car, but it's something else entirely to claim there's actually a world where you wouldn't do so. However your claim would be that this would refute libertarianism. Frankly, this sounds ridiculous

Wesley C. said...

@Dominik, Could you go into more detail about what indeterminism / libertarianism would be, from what you describe at least? Because it's very common to assign probabilities to choices as if it's a proper accident of LFW?

2) When you say there isn't actually a world where you would choose otherwise than you did, do you mean that we actually can't choose otherwise? I think not as you clearly affirm LFW, so are you understanding worlds in the sense of possible world which includes all logical possibilities? Or in a different sense from that?

3) If a person would always choose the same if one option was just as good as the other one, where does the indeterminism come from? Why is it said that a person can choose otherwise if he will always choose A over B in the same situation? How could a person choose otherwise, and what's the source of that?

Wesley C. said...

To Dominik: To add to point one above, why exactly can't one assign probabilities to LFW choices, especially in the sense of inclinations (50% tendency overall, 90% tendency for A over B, etc.)?

Dominik Kowalski said...

1) Probabilities don't make sense unless for illustration. For every free choice with options I deny that there is a possible world with identical circumstances in which the agent will ever choose differently, what would compell him to choose differently in this instance?

2) No, but once the decision is made, it will be irreversible, even if we rewind time. The contemplation has happened, under these circumstances the agent will choose a specific way A and not B, and he would never choose B even though it was initially a real possibility.

Possible worlds are all logical coherent worlds, but in cases of free actions there are worlds which never will be actualized. Even on a view that affirms the reality of all such worlds, it will remain a possibilia.

3) The indeterminism is the lack of external determining force, neither the prior physical conditions nor internal biological effects determine the outcome, it's left to the self-determining intellect. And this is coherent even in a circumstance in which we really can't choose otherwise (if the soul sees God), since the reasons themselves are causally ineffacious, they are contemplated ans judged by the intellect which then acts for them. The indeterminacy is the intellect acting in such a way

Dominik Kowalski said...

Because the probabilities would have to hold afterwards as well, otherwise they are seemingly of an epistemic, rather than ontological nature. But I am convinced that the choice itself makes the probability 1, not just in this world but in every other world where the agent is in identical circumstances. Otherwise we need additional explanation why the reasons that seemed compelling in one world aren't in another