If we go with holding the laws fixed and changing the past, I would worry that our Freedom-counterfactuals become too dependent on random unknown chaotic factors. It's not obvious to me that we can ensure that there is an initial condition that would lead to my choosing something different for breakfast without changing a bunch of stuff that we wouldn't want to bear on the counterfactual. Or even one where I come into existence and choose something different for breakfast. But I don't think our counterfactuals should be hostage to these accidents of what our laws allow from initial conditions. So it seems like we should rather allow "miracles" to change our decision by breaking the laws, whlle holding the past fixed.
Yea this is Lewis’ worry. I plan to write something up about this in future because the reply is pretty in the weeds but here is a short version:
Our best dynamical theories have continuous dynamics. The best way to think of this is that there is a large space of possible states and our dynamics lets us chart a line from later to earlier states. Given the continuity of these theories, for any two connected points in that space, I can find another set of points that stay *arbitrarily close* to the first set.
Here is Cian Dorr (who I’m largely taking this argument from):
“Lewis is certainly right that in our universe, little differences tend to blow up quickly
into to much bigger differences. But this fact is not a good reason to doubt the existence
of nomically possible worlds of the relevant sort. Our best deterministic physical theor-
ies have continuous dynamics, which means that so long as the past is not infinite, we can
always find a nomically possible world which stays arbitrarily close to the actual world
throughout any finite initial segment of history, just by choosing an initial state that is
close enough to that of the actual world.”
At this point the question is whether such similar histories could actually lead to differences going into the future; but at this point, the Lewisian worry undercuts itself. The worry is predicated on the supposition that small changes rapidly lead to larger changes in the future. We circumvent that worry by essentially ‘outrunning’ this rate of escape by choosing a point for the initial conditions that’s as close as we need to maintain sufficient similarity through the requisite interval. Once we reach the end of that interval, I can just *agree* with the Lewisian. Yes, the rate of escape would be quick, so we can expect a wide array of different changes following the end of our interval, some which will result in minor departures from actuality, and some which will result in larger ones. But that’s exactly what we might want for counterfactual evaluation!
There are other reasons to motivate this second step which are also drawn from the mechanics literature that Dorr goes into as well but that would be much more work to articulate.
Okay maybe I didn't understand that response fully, but you need two things for any world with our laws, right. You need:
A) That it is arbitrarily close in the past up to some point before the decision. And
B) That the decision that the counterfactual stipulates actually happens.
So for the pancakes-cereal example, you don't just need that the past can be arbitrarily close, but that you also actually choose to have pancakes.
As far as I understand what you said, it only proves (A)--that you can always get an arbitrarily similar past up to any point. But it seems like it clearly doesn't entail that we can both get (A) and (B) for the cases we want.
For an extreme counterexample: We can't have the past be very very similar to the past up to 1 nanosecond ago, and then have me now be on the moon. For "if I were on the moon", any world that satisfies the antecedent would need to have a very different past.
But if that's right, then I don't see how you can rule out the problems. Yes, you can have the past be incredibly similar to the actual past up to 1 minute ago. But I don't see how you can ensure that any such past is one where I end up choosing pancakes. It might just be that any world that has our laws and satisfies (A) for choosing pancakes is one where JFK were never assassinated. In fact, it might be that any world where I "would have" chosen pancakes is one where my parents never met, so that it's actually impossible for me to choose pancakes given our laws. I don't see how your argument rules that out. And again, I wouldn't want our counterfactuals for freedom to be hostage to these kinds of unknowns.
I agree that I need (A) and (B) to be true. I need it to be compossible with the laws that the past be largely the same as in the actual world, while the antecedent of the counterfactual ends up being true relatively close to the point of substantial departure from actuality.
You are right that the argument I mainly gave only supports (A) but not (B). The paragraph at the end of the comment, about the lewisian reply undercutting itself, is what is supposed to motivate (B). I’ll try and say a little more about that idea.
The thought behind the reply is that there is ‘rate of change’ with respect to similarity between states of the universe, and that universes become less similar over time at a very high rate in deterministic worlds. What the first argument shows is that, no matter how fast this rate of departure is, I can always pick some initial conditions that will keep the resulting universe however close to the actual universe you like. But the lewisian presumably thinks this rate of departure is quite high, such that small changes quickly result in big differences. If that’s right, then at the end of the interval, a wide array of different possible futures stretch out, depending on our choice of initial conditions. But if there is a wide array of different future possibilities with large changes going into the future from the end of the interval, why think that none of those changes can involve the change in choice?
The main idea is that the Lewisian seems to need to think that the rate of departure is very fast in order for the problem to arise, but if the rate of departure is fast, then counterfactual dependence doesn’t need to go that far into the past (because of how I can choose the interval). If you think the rate is slow, then it’s hard to see how the worry about my parents can come into effect, since that seems as though it would require the rate of departure being fast, relative to the choice of the end of the interval.
I guess I don't quite see why the rate of departure needs to be high for the worry to get off the ground. If it's low can't it still be the case that a world with your brain in the state of choosing pancakes would need to have JFK not be shot or something? In fact, wouldn't that be even more likely if the rate of departure is low, since there would then only be few paths that lead to the correct result?
But even if we do say that it's high, I'd still be uncomfortable with that solution. After all, while that may make it very likely in any particular case that you could get the right sort of counterfactual without too crazy of a past. But couldn't state space still just sometimes happen to be so that there's no world where you exist and choose pancakes, or where you choose pancakes after JFK is shot? You don't just need that it diverges quickly, but that it suddenly diverges--and has the potential to suddenly diverge in to any number of counterfactuals you might want to evaluate. Not just pancakes, but choosing PB&J or choosing to jump out the window, or yell at the toaster, or rob a bank, or...
I'd like to be able to evaluate all those counterfactuals without the past being very different from what it is. And I'd like to do that in all cases. But it seems very hard to get a good reason to be assured that we *can* get that in all cases. In fact, it seems unlikelt to me that we can. But even if we can, it also just seems to me like we shouldn't have to depend on the shape of state space for our laws and the past in this way in order to evaluate whether I was free/responsible in choosing to do what I did; if it happens that I could never exist to choose pancakes given the laws, then that feels more like a frankfurt case than something that limits my control.
I’m still thinking through this so my response is tentative. For what it’s worth, entirely unrelated to this reply I think that the fixed laws approach can’t work because of an independent argument which is partly why I might be more comfortable with an incomplete ‘fixed-past’ view (that’s an entirely different bucket of worms, just wanted to make my epistemic situation clear).
Let me just restate what I think your worry is now (because I think it’s slightly different than the earlier one). Your worry is that, for all we know, it might be nomologically impossible for me to choose to perform an action, because there is no state sufficiently close to the actual world which will include my making the different choice. For all we know, an event which my existence counterfactually depends on might counterfactually depend on me choosing as I actually do! This makes us reliant an an incredibly unclear issue for adjudicating our counterfactuals, and thus risks our counterfactual knowledge.
Okay, my reply: Suppose the rate of departure is slow. I think we can then safely choose a point in time further away from the point of choice. We shouldn’t expect this to result in JFKs death because these histories depart from actuality much more slowly. JFKs death just can’t be such a small departure from actuality that it somehow necessitates the relevant interval ending somewhere before 1936. If the death of JFK is enabled 1 week after the end of the interval then my choosing otherwise certainly should not require a 70+ year delay. The slow rate of departure should be consistent.
Re: quick departure. I think there’s independent arguments for it other than the one i’m presenting now. I think baked in to quick departure is that it covers a wide range of possible future points in the state space that can be reached quickly from nearby states. Part of the idea is that by ‘quick departure’ I mean some rather radical changes from actuality, like tornados and earthquakes, such that people making different choices is sort of small potatoes.
Re: the last point about depending on the shape of the state space and such, I have to think more about this. I think what you say might be vulnerable to some counter examples possibly involving time travel. If you read my next post about the grandfather paradox let me know if you have any related thoughts (I’ll keep thinking about this as well).
Re: slow departure. Well, suppose rate of departure was maximally slow. Then that would mean something like that any notably different state now would also have to have a past that's just as notably different all the way back. Whether or not the JFK example is plausible, it just seems clear to me that decreasing rate of departure makes the problem worse, as it limits your options for pasts that can get you to the state stipulated in the counterfactual.
Re: quick departure. Sure, maybe most cases of people making different choices are small potatoes. But you need that *every* possible counterfactual you'd want to be able to evaluate in *every single case* be covered. That just seems incredibly unlikely to me, and I just don't see how we have strong reason to think that every case we want will be covered.
Also, you say that tornados and stuff is much bigger in comparison. But while the macroscopic effects are bigger, it's not at all clear to me that they're harder to get with similar pasts. Voluntarily dowsing myself in gasoline, pulling down my pants and shitting, all while singing a random bollywood song are just very far from what my brain would be disposed to do with any minor variation in neuron activations. It seems like I'd have to have been very differently wired. To get that while holding the laws fixed would presumably require a very different past--such as me learning hindi to be able to sing the bollywood song. Still, I want to be able to say something like "if I did what I described, I'd be morally responsible for traumatizing any children that happened to see me."
Re: time travel. That's interesting! I must say I don't see the connection right now, but I'll have to read that post when it comes out :)
I have two questions, more for me to help understand the point than to put pressure on the view.
You made the time-travel argument with John living in an indeterministic world, but does the argument require his world to be indeterministic? It feels like you’re positioning the argument for a person who believes John would have free will if he lived in an indeterministic world, but I don’t know if this is automatically true. For example, if every third decision was made by a random indeterministic dice roll would we call this free will? What if John could be coerced to shoot JFK even if the laws were indeterministic, surely the coercion implies he didn’t shoot him of his own free will.
Second, are you worried about the metaphysical possibility of these scenarios? Like what about the classic paradox where John travels back in time to shoot his grandfather and then prevent himself from being born?
The point of the time travel case is to show that the natural laws could be such that backwards counterfactual dependence occurs even though determinism is false. So, I’m trying to appeal to a case where the existence of backwards counterfactual dependence *doesn’t* intuitively undermine our attributions of freedom, and then argue by analogy that we should have the same judgement in the case of determinism. Assuming indeterminism makes that argument clear, but nothing technically turns on that assumption. I’m perfectly happy to make the time travel world a deterministic one. In that case the backwards counterfactual dependence would just be overdetermined (lol), but still partly due to the time travel friendly laws.
My next post is exactly about the grandfather paradox! Short answer: I disagree with the consensus that Tim can kill grandfather. I think he lacks the ability. Similarly, I actually think determinism *does* deprive us of some abilities (this part isn’t in the post, maybe I should include it?). Consider Tom: Tom lives at a deterministic world where the proposition P describes the initial state of the universe, and Q describes the natural laws. Suppose Tom never comes to know that P^Q despite attending a university where they specialize in educating their students on these facts. Tom can’t learn P^Q because any world where Tom does come to believe P^Q is a world where they are false, given the nature of deterministic laws. So determinism *does* deprive us of this ability. But I think this is a special case. It is a necessary condition of any ability that it can be exercised given the actual laws of nature. If I cannot perform an action A without the laws of nature being different then neither I or anyone else is able to A. Supposing that P^Q is the proposition that describes our own laws and initial state, that the laws are deterministic, and I don’t learn P^Q, I am unable learn P^Q; but this is because it’s nomologically impossible for me to learn P^Q. This is the same diagnosis I have for Tim and grandfather, so there is a nice symmetry. Tim can’t kill grandfather because it’s not nomologically possible, same with learning P^Q.
But this doesn’t hold for our ordinary abilities. Suppose I choose to stand. I could have continued sitting. If I had so chose, nothing about our laws would have to be different, the past would just have needed to be different (and given determinism, the very distant past) but as I mention in this post that poses no problem.
There *is* a worry Lewis gestures at about backtracking views. The worry is that there won’t be nomologically possible worlds where our backtracking counterfactuals turn out true, because the universe is a chaotic system and small changes blowup into big changes quickly. My answer to this worry is very technical and basically taken whole-cloth from Cian Dorr’s “against counterfactual miracles.” The short version is that Lewis is (mostly) provably wrong given the state space of the universe is continuous. You can choose a variation in initial conditions that stays as close to actuality as you like, for a long as you like.
Cool, I think this post clicked for me after reading your response.
If I understand it correctly, can resolve the grandfather paradox by positing that the backwards time traveller doesn’t “change” the past but simply returns to the same timeline and intervenes in ways globally consistent with the actual history. So more like the time-turner in Harry Potter than Back to The Future where backwards time travellers literally change the history. The point about Tom’s lack of ability to know P^Q is particularly cool because it shows this isn’t just special pleading.
So when you say “John sits on the knoll and reconsiders” this is a possible world, but it can’t be the actual world because the actual world is one in which JFK died in 1963 when John time travelled from 2150 to shoot him.
One residual worry I have is once John travels back to 1963 and shoots JFK, there’s a genuine counterfactual possible world where John travelled to 1963 and *didn’t* shoot JFK - which means the whole history of the world involved a JFK who lived much longer. Presumably that world would differ so substantially from the one which featured the original John that it’s not even clear how similar the 2150 worlds are or whether the 2150 versions of John are sufficiently close counterparts to adequately be considered ‘John’.
Maybe this is where the Dorr paper you referenced comes in?
> If I understand it correctly, can resolve the grandfather paradox by positing that the backwards time traveller doesn’t “change” the past but simply returns to the same timeline and intervenes in ways globally consistent with the actual history.
This is true but it isn't my resolution to the grandfather paradox. The grandfather paradox is always stated in terms of 1 dimensional time travel (intra-timeline time travel in my own terminology), and that is what generates the issue in the first place. The paradox is a paradox of ability. It seems, at the same time, that Tim can and cannot kill his grandfather. I argue that Tim just *can't* kill grandfather.
> So when you say “John sits on the knoll and reconsiders” this is a possible world, but it can’t be the actual world because the actual world is one in which JFK died in 1963 when John time travelled from 2150 to shoot him.
This is right
> One residual worry I have is once John travels back to 1963 and shoots JFK, there’s a genuine counterfactual possible world where John travelled to 1963 and *didn’t* shoot JFK - which means the whole history of the world involved a JFK who lived much longer. Presumably that world would differ so substantially from the one which featured the original John that it’s not even clear how similar the 2150 worlds are or whether the 2150 versions of John are sufficiently close counterparts to adequately be considered ‘John’.
I think tiome travel counterfactuals are super hard to evaluate because we have backwards counterfactual dependence between two time periods, and are evaluating counterfactual worlds where there could be a huge departure from actuality in that intervening gap. Notably, I don't think this is a problem in deterministic worlds (this is where the Dorr part comes in). But one way to think of the problem you ask is to imagine someone who goes back in time to kill Hitler in the year 2500. Presumably, he is motivated by things he has read in the history books and such. If he succeeded, what could have possibly motivated him to go back and time and do the killing in the first place? This problem is obviously greater the bigger you make the distance between the time travelers point of departure and the event they effect. That's all to say: Your worry makes sense, counterfactuals are really hard to evaluate in time travel worlds in some scenarios. But! I don't think this problem extends to my resolution of compatibilist questions.
I am with you with regard to it being nomologically impossible for Tom to learn P^Q, given that his is stipulated to be a deterministic world, but I am not convinced that it is different for ordinary abilities. As far as I can tell, determinism does not rule out you thinking about whether to stand (or whether to chose the burger rather than the pasta, to take the example from your conclusion), but, by the definition of 'deterministic' apparently being used for the first case, the worlds where you choose one over the other seem to me to be just different possible worlds at any past time; there was no time when they were identical. The outcome of your decision process merely reveals some information about how the actual world always was and was going to be.
I tentatively think that Boris Kmet is on to something when he writes, in the abstract of 'Counterfactuals and Causal Reasoning' [1] "I offer an alternative account of the role of counterfactuals in causal thought that is consistent with these data: counterfactuals are used in a common method of causal reasoning related to John Stuart Mill’s method of difference. The method uses background beliefs about causal relationships, history, and the natural laws to establish a new causal claim. Counterfactuals serve as a convenient tool for stating certain intermediate conclusions in this reasoning procedure, and that is part of what makes counterfactuals useful. This account yields a functional explanation of why our language contains a construction with the truth-conditions of counterfactuals."
Personally, I'm not wedded to the idea that our world is deterministic, anyway.
It's true that deterministic worlds have the same universal description at all points in time, or never. I don't see why this makes you think that our ordinary abilities cannot be utilized in ways we don't actually use them, or why that would be nomologically impossible.
Great article! What I find interesting in the discussion surrounding the free will debate is that there is almost like this presumption of pessimism (the worst possible thing i.e., absence of free will is presumed true until proven otherwise). Hard determinists often come into the conversation thinking that compatibilists *have* to show them something. But given the fact that it pre-theoretically seems to most people like there is free will, *that* should be the starting point of the conversation. And if compatibilists can then provide a reasonable account of how free will works (like you just did!) it seems like the debate is kinda over in their favor right there and then (barring some internal issues with the account or some further arguments for hard determinism).
First I'd note an interesting facet of the definition of determinism.
"Supposing the laws are deterministic, a sufficiently sophisticated inference machine, that knew the state of the universe and the laws, could figure out what has happened, is happening, and will happen, with perfect accuracy."
I agree this would be sufficient to make a universe deterministic. The thing I have to note is that it seems as though due to things like self-reference, the halting problem being insoluble etc. that even if determinism were true such perfect prediction would be impossible (some things would not be predictable by such an inference machine).
So a particularly skeptical person might claim we can never know whether failure of prediction is due to self-reference problems etc. (limits of prediction) or simple failure of determinism. And indeed some people seem to treat determinism as a question of prediction (Karl Popper for example).
Clearly there is some sense to this in terms of understanding the counterfactual dependence of the future on the past, the way we don't recognize the present's dependence on the deep past (we can't predict how the present depends on the deep past) and so on. How we can and should deliberate depends on what we could know (about our actions and their implications, about what we are able to do given current resources etc.) Although clearly one can separate the issues somewhat.
I'm not sure how much it means, but I'd define fatalism as the view that some future outcome (set of outcomes) is fixed no matter what you do in the interim. A typical statement would be something like it is invitable that the glass will break so there is no point in trying to protect the glass. So a standard fatalism will be just contrary to determinism, since determinism says that things in the further future are only determined because things in the interim are a certain way if one did things different in the interim the final outcome might change. There is a form of fatalism that is a form of determinism.
It is true that if your actions are completely ineffectual they have "no point" (it becomes inadvisible). For example there is no point in trying to deflect an incoming city killer asteroid by swinging at with the a baseball bat as if it were a fastball. It would be inadvisible, stupid even. However the generalied fatalist idle argument (there is no point in doing anything so best to remain idle), is a very different proposition and doesn't really follow if we are talking about the overlap between fatalism and determinism. If fatalism is true because we only do one thing in the interim, then what we do in the interim isn't necessarily pointless etc.
Now I'd state free will in terms of moral responsibility (saying we have free will is saying we have moral responsibility or responsibility to do otherwise). If determinism does not imply every action is pointless like fatalism does, is that different from moral responsibility? If every action were equally pointless as in fatalism clearly we could not be responsible for doing otherwise. Does responsibility require more than being able to evaluate given actions as having a point or not (being advisible or inadvisible etc.) is that sufficient or just necessary.
I think this is just a complementary analysis to what you said. What it means to do otherwise or to be able to do otherwise is just a question of what range of counterfactuals are appropriate and this informs our sense of the point or pointless of actions, deliberations and so on. It seems like the arguments for incompatibilism are often arguments for fatalism and so on or overlap or subtlely share the same fallacies etc.
I have some thoughts on halting problem / computation related isssues.
1. The halting problem and related impossibility results only apply to infinite (or at least unbounded) processes. Any question concerning what will happen in a particular fixed finite amount of time is computable. If I'm interested if I have free will for the decision I'm going to make in 5 minutes, that should be computable. However, it is still possible that human decisions are uncomputable despite the finite time limit (say because of the continuous nature of reality).
2. There is an even stronger version of this prediction idea foiling determinism. Substacker Disagreeable Me believes that both consciousness and physical reality are fundamentally functional / computational in nature. If this is true, this may undermine determinism. This is because in order to predict my future decision, you'd have to simulate it, but the simulation and reality are made of the same thing (functional / computational states), and hence there is no difference between reality and the prediction, and hence there is no way to predict my decision without me actually making the decision.
First we are interested only in versions of the halting problem that can be solved by actual residents of the universe, so only by finite computers of indeterminate but not unbounded size. If it is only soluble by infinite devices then that would suffice to show that no inference machine exists (the inference machine has to give results in a finite time, with finite materials etc.), since the inference machine that can do it would need to be infinite and so can not exist. Given your premise that the halting problem impossibility rests on infinite machines and your other premise that there are no infinite machines in reality (or no infinite machines that give results in finite time) you are premising that all actual halting problems can be solved by actual finite machines.
Grant all that, it is the case that there is a general solution to the halting problem for all finite machines that can be run on finite machines. If any actual halting problem for an actual computer is finite (bounded) and such that it so computable (by our finite computers) then there is a finite algorithm that solves the halting problem and can be run as a program on our computers. Given that finite program one can easily construct another program P that has the solution to the halting problem as a subroutine H + feeding the code for this very program P into that subroutine H and perform the following conditional branch on the output of H, if it returns 0 (does not halt) halt and if it returns 1 (does halt) enter an infinite* loop (and so defy the prediction that it halts).
*Of course infinite loops on a finite machine won't be infinite as the machine will eventually break (or run out of power or storage or something). However this is no help because the general solution or prediction that all machines will halt will thus be true and will technically be a general solution to the halting problems, but is not really specific enough. Really the halting problem we want to solve is how many steps will it take to halt (if we want to show that everything is predictable how many steps until halting is one of those things in everything). For definite algorithms (ones that will halt after a definite number of steps) one might predict the number of steps until halt by some modified halting solution algorithm and some modified program P' call the subroutine that runs that H' (that tells us the number of steps until the program halts) based on the code for P'. We can obviously easily create a branch or other operation that responds to the output of H' by then causing P' to do a different number of steps than predicted by H'. For example just take the output of H' add 1 and then do a loop with that number of steps, now the general solution to the modified halting problem (how many steps until halt) is guaranteed to give the wrong number of steps for P' (it is greater by 1 + the number of steps it took to perform H' etc.) even though P' does halt in a definite number of steps. Also for finite machines that are trying to perform an infinite loop but break down they won't have a definite number of steps until they halt, when they halt will depend on either random quantum events or microphysical events so obscure that they can not be ferreted out in a finite amount of time (if we are limiting machines to be finite, then the data entered into them must also be finite) and so on.
The basic problem is that for determinism to be definitively and unequivocally demonstrated what we need to show is that inference machines can exist (we can construct them and consult them) such that even if you had access to an inference machine your actions could be predicted by such a machine. If inference machines are impossible you can never come up with predictions to falsify or verify that everything is predictable (there will be some cases where either you can't generate a prediction or if you do it is prone to being wrong). If inference machines are possible and so it is possible to predict anything you will do in the next 5 minutes, then one of the things that you may do (it is possible for you to do) in the next 5 minutes is consult the inference machine since per stipulation consulting inference machines is possible. However such a scenario realizes the self-reference paradox roughly equivalent to a subset of the halting problem blocking prediction and blocking full simple verification that every human action is predictable thus showing inference machines are impossible. If inference machines are possible (if it is possible to consult inference machines) then inference machines are impossible, paradox and so a nice reducto of inference machines, inference machines must be impossible in worlds like ours.
Inference machines would be possible in a world unlike ours, if we knew there was a world A that was a subset of a world B and there were no inference machines for A in A, but there were inference machines for in B that worked only for A and if we maintained total separation of A from B (but not total separation of B from A asymmetrically B can observe A, just never alter it) then you could predict everything in A, show that everything in A is predictable (by inference machines) and there would be no danger of a self-reference paradox. However we know we are not in that situation when I ask if I have free will, I'm not asking if some system weirdly segregated from me has free will I'm asking if a system I have total interaction with has free will and so on.
I see, I misunderstood your original point. I agree, that if the goal is to build an inference machine within universe A to predict a future state of universe A, then that is subject to self-reference/halting type limitations even if universe A is finite (or infinite). I think you demonstrate this well, but just as another example, suppose their was a perfect predictor Alice, and Alice was asked to predict what number Bob will say immediately after seeing her prediction. If Bob was feeling contradictory, Bob could just say a number one larger than whatever Alice predicts. In this case it would be impossible for Alice to make a perfect prediction. Thanks for the correction!
Yeah sorry I could have made the point more succinctly. Note perfect prediction is ambiguous between perfect inference from facts about the past and laws and perfect guessing.
Even if every event outcome were completely random (but somehow specifiable) it might turn out that every guess about future events by some oracle turns out to be correct by coincidence (a coincidence of about 0 probability but not actually ruled out as "impossible" in some sense). This wouldn't be subject to self-reference because no one could deliberately include the guessing process in an algorithm (there is no algorithm for this kind of guessing). Presumably we can make something like that work for a world more like our own (with actual laws/causal succession of events). Yet this doesn't imply determination (predetermination) because while every guess is right, no guess is thus determinate (a determinate inference from facts and laws or something like that), also its not clear how you could reasonably conclude that the oracle can correctly "predict" (correctly guess) everything. This probably raises an underdetermination problem (are we making principled inferences or a series of expanding lucky guesses) at some point. Many complexities.
The laplacian idea isn’t supposed to be definitional (I included it more to provide a vivid example of what determinism might *allow*). I agree, consequently, with basically everything you say concerning the limits of computation.
The way you define fatalism is different from how I do, but it’s certainly a way the word is used. I think the fatalism you describe is very different from incompatibilism though. Incompatibilists certainly don’t think that your choices aren’t causally efficacious given determinism (or they shouldn’t think that anyway).
that version of fatalism is dubious. why think that a particular outcome can happen regardless of whatever happens prior to it? i will be utterly jacked at time t even if prior to t i never exercised? i don't think that there are many fatalists who hold this version.
the counterfactual claim is just the claim that if reality were different, it'd be different, or a claim about how a formal model works, eg. one that physicists use where initial conditions + laws uniquely necessitate all outcomes.
but why think that reality could've been different? i certainly won't believe that because of some dubious discourse of what would be the case if the case wouldn't be what it is.
I think I could have thrown the ball a bit higher because, when I stood in the same spot and tried harder, the ball went up further. So it seems like I could have tossed the ball higher. So reality could have been such that the ball went higher.
You’re free to deny any step in that argument, I just don’t see why I would.
yeah i don't see how it follows from the fact that several different but similar things happen at different instances that at any given instance, multiple things / something other than what actually does, can happen. it's not compatible with determinism. if it comes to you framing my rejection to make that step as denying your seeming, and me framing it as not seeing why i would make the step, now what? like with negative atheism, i am just waiting here for some consideration that doesn't require me to start with not-negative atheism.
"When we evaluate counterfactuals, we cannot hold all facts fixed. If we do, then every counterfactual will turn out false."
but... but... i thought that counterfactuals are literally all false... by definition? what does it even mean to not hold a fact fixed? are you suggesting delusion? if one takes seriously the physicist's model of determinism, then one can't accurately assess counterfactual conditionals, since even the tiniest change would entail immense differences in ways we can't ever compute. this insistence on what feels normal and natural and good for you to say isn't a reliable guide to either counterfactual consequences or the mere possibility of counterfactual events.
Counterfactuals aren’t all false. The antecedent of a counterfactual is definitionally false. To hold a fact fixed when evaluating a counterfactual means that we evaluate the counterfactual, using the standard Lewis-Stalnaker method for evaluating counterfactuals, and only look at worlds where the fixed facts are true. The point you make about whether we can know counterfactuals are true is related to the asymmetry point I make at the end. I think it’s wrong for technical reasons. The universe is a chaotic system on standard dynamical theories, but the state space is continuous and its (provably) possible to select an initial set of values that stays arbitrarily close to the actual universe in state space up until a specified point in time. That’s a lot of jargon but it basically means there are possible values to the initial conditions which keeps the resulting universe qualitatively *as close as you’d like* to the actual universe, for as long as you’d like. So the objection from chaos theory isn’t damning for backtracking theories of counterfactuals.
that is again a feature of a kind of model. but your claim is about free will in this world, not just how we may tinker with a model. are you saving the view by committing to each free choice changing the initial conditions of the universe? i still don't see the move that lets you infer that anything actual could've been otherwise.
also, how do possible worlds help in establishing how this world works or if there is intra-world contingency? lewis was a necessitarian about each possible world. i'm confused about how you wanna use them to help your conclusions about this world.
If we go with holding the laws fixed and changing the past, I would worry that our Freedom-counterfactuals become too dependent on random unknown chaotic factors. It's not obvious to me that we can ensure that there is an initial condition that would lead to my choosing something different for breakfast without changing a bunch of stuff that we wouldn't want to bear on the counterfactual. Or even one where I come into existence and choose something different for breakfast. But I don't think our counterfactuals should be hostage to these accidents of what our laws allow from initial conditions. So it seems like we should rather allow "miracles" to change our decision by breaking the laws, whlle holding the past fixed.
Yea this is Lewis’ worry. I plan to write something up about this in future because the reply is pretty in the weeds but here is a short version:
Our best dynamical theories have continuous dynamics. The best way to think of this is that there is a large space of possible states and our dynamics lets us chart a line from later to earlier states. Given the continuity of these theories, for any two connected points in that space, I can find another set of points that stay *arbitrarily close* to the first set.
Here is Cian Dorr (who I’m largely taking this argument from):
“Lewis is certainly right that in our universe, little differences tend to blow up quickly
into to much bigger differences. But this fact is not a good reason to doubt the existence
of nomically possible worlds of the relevant sort. Our best deterministic physical theor-
ies have continuous dynamics, which means that so long as the past is not infinite, we can
always find a nomically possible world which stays arbitrarily close to the actual world
throughout any finite initial segment of history, just by choosing an initial state that is
close enough to that of the actual world.”
At this point the question is whether such similar histories could actually lead to differences going into the future; but at this point, the Lewisian worry undercuts itself. The worry is predicated on the supposition that small changes rapidly lead to larger changes in the future. We circumvent that worry by essentially ‘outrunning’ this rate of escape by choosing a point for the initial conditions that’s as close as we need to maintain sufficient similarity through the requisite interval. Once we reach the end of that interval, I can just *agree* with the Lewisian. Yes, the rate of escape would be quick, so we can expect a wide array of different changes following the end of our interval, some which will result in minor departures from actuality, and some which will result in larger ones. But that’s exactly what we might want for counterfactual evaluation!
There are other reasons to motivate this second step which are also drawn from the mechanics literature that Dorr goes into as well but that would be much more work to articulate.
Okay maybe I didn't understand that response fully, but you need two things for any world with our laws, right. You need:
A) That it is arbitrarily close in the past up to some point before the decision. And
B) That the decision that the counterfactual stipulates actually happens.
So for the pancakes-cereal example, you don't just need that the past can be arbitrarily close, but that you also actually choose to have pancakes.
As far as I understand what you said, it only proves (A)--that you can always get an arbitrarily similar past up to any point. But it seems like it clearly doesn't entail that we can both get (A) and (B) for the cases we want.
For an extreme counterexample: We can't have the past be very very similar to the past up to 1 nanosecond ago, and then have me now be on the moon. For "if I were on the moon", any world that satisfies the antecedent would need to have a very different past.
But if that's right, then I don't see how you can rule out the problems. Yes, you can have the past be incredibly similar to the actual past up to 1 minute ago. But I don't see how you can ensure that any such past is one where I end up choosing pancakes. It might just be that any world that has our laws and satisfies (A) for choosing pancakes is one where JFK were never assassinated. In fact, it might be that any world where I "would have" chosen pancakes is one where my parents never met, so that it's actually impossible for me to choose pancakes given our laws. I don't see how your argument rules that out. And again, I wouldn't want our counterfactuals for freedom to be hostage to these kinds of unknowns.
I agree that I need (A) and (B) to be true. I need it to be compossible with the laws that the past be largely the same as in the actual world, while the antecedent of the counterfactual ends up being true relatively close to the point of substantial departure from actuality.
You are right that the argument I mainly gave only supports (A) but not (B). The paragraph at the end of the comment, about the lewisian reply undercutting itself, is what is supposed to motivate (B). I’ll try and say a little more about that idea.
The thought behind the reply is that there is ‘rate of change’ with respect to similarity between states of the universe, and that universes become less similar over time at a very high rate in deterministic worlds. What the first argument shows is that, no matter how fast this rate of departure is, I can always pick some initial conditions that will keep the resulting universe however close to the actual universe you like. But the lewisian presumably thinks this rate of departure is quite high, such that small changes quickly result in big differences. If that’s right, then at the end of the interval, a wide array of different possible futures stretch out, depending on our choice of initial conditions. But if there is a wide array of different future possibilities with large changes going into the future from the end of the interval, why think that none of those changes can involve the change in choice?
The main idea is that the Lewisian seems to need to think that the rate of departure is very fast in order for the problem to arise, but if the rate of departure is fast, then counterfactual dependence doesn’t need to go that far into the past (because of how I can choose the interval). If you think the rate is slow, then it’s hard to see how the worry about my parents can come into effect, since that seems as though it would require the rate of departure being fast, relative to the choice of the end of the interval.
I guess I don't quite see why the rate of departure needs to be high for the worry to get off the ground. If it's low can't it still be the case that a world with your brain in the state of choosing pancakes would need to have JFK not be shot or something? In fact, wouldn't that be even more likely if the rate of departure is low, since there would then only be few paths that lead to the correct result?
But even if we do say that it's high, I'd still be uncomfortable with that solution. After all, while that may make it very likely in any particular case that you could get the right sort of counterfactual without too crazy of a past. But couldn't state space still just sometimes happen to be so that there's no world where you exist and choose pancakes, or where you choose pancakes after JFK is shot? You don't just need that it diverges quickly, but that it suddenly diverges--and has the potential to suddenly diverge in to any number of counterfactuals you might want to evaluate. Not just pancakes, but choosing PB&J or choosing to jump out the window, or yell at the toaster, or rob a bank, or...
I'd like to be able to evaluate all those counterfactuals without the past being very different from what it is. And I'd like to do that in all cases. But it seems very hard to get a good reason to be assured that we *can* get that in all cases. In fact, it seems unlikelt to me that we can. But even if we can, it also just seems to me like we shouldn't have to depend on the shape of state space for our laws and the past in this way in order to evaluate whether I was free/responsible in choosing to do what I did; if it happens that I could never exist to choose pancakes given the laws, then that feels more like a frankfurt case than something that limits my control.
I’m still thinking through this so my response is tentative. For what it’s worth, entirely unrelated to this reply I think that the fixed laws approach can’t work because of an independent argument which is partly why I might be more comfortable with an incomplete ‘fixed-past’ view (that’s an entirely different bucket of worms, just wanted to make my epistemic situation clear).
Let me just restate what I think your worry is now (because I think it’s slightly different than the earlier one). Your worry is that, for all we know, it might be nomologically impossible for me to choose to perform an action, because there is no state sufficiently close to the actual world which will include my making the different choice. For all we know, an event which my existence counterfactually depends on might counterfactually depend on me choosing as I actually do! This makes us reliant an an incredibly unclear issue for adjudicating our counterfactuals, and thus risks our counterfactual knowledge.
Okay, my reply: Suppose the rate of departure is slow. I think we can then safely choose a point in time further away from the point of choice. We shouldn’t expect this to result in JFKs death because these histories depart from actuality much more slowly. JFKs death just can’t be such a small departure from actuality that it somehow necessitates the relevant interval ending somewhere before 1936. If the death of JFK is enabled 1 week after the end of the interval then my choosing otherwise certainly should not require a 70+ year delay. The slow rate of departure should be consistent.
Re: quick departure. I think there’s independent arguments for it other than the one i’m presenting now. I think baked in to quick departure is that it covers a wide range of possible future points in the state space that can be reached quickly from nearby states. Part of the idea is that by ‘quick departure’ I mean some rather radical changes from actuality, like tornados and earthquakes, such that people making different choices is sort of small potatoes.
Re: the last point about depending on the shape of the state space and such, I have to think more about this. I think what you say might be vulnerable to some counter examples possibly involving time travel. If you read my next post about the grandfather paradox let me know if you have any related thoughts (I’ll keep thinking about this as well).
Re: slow departure. Well, suppose rate of departure was maximally slow. Then that would mean something like that any notably different state now would also have to have a past that's just as notably different all the way back. Whether or not the JFK example is plausible, it just seems clear to me that decreasing rate of departure makes the problem worse, as it limits your options for pasts that can get you to the state stipulated in the counterfactual.
Re: quick departure. Sure, maybe most cases of people making different choices are small potatoes. But you need that *every* possible counterfactual you'd want to be able to evaluate in *every single case* be covered. That just seems incredibly unlikely to me, and I just don't see how we have strong reason to think that every case we want will be covered.
Also, you say that tornados and stuff is much bigger in comparison. But while the macroscopic effects are bigger, it's not at all clear to me that they're harder to get with similar pasts. Voluntarily dowsing myself in gasoline, pulling down my pants and shitting, all while singing a random bollywood song are just very far from what my brain would be disposed to do with any minor variation in neuron activations. It seems like I'd have to have been very differently wired. To get that while holding the laws fixed would presumably require a very different past--such as me learning hindi to be able to sing the bollywood song. Still, I want to be able to say something like "if I did what I described, I'd be morally responsible for traumatizing any children that happened to see me."
Re: time travel. That's interesting! I must say I don't see the connection right now, but I'll have to read that post when it comes out :)
Great post!
I have two questions, more for me to help understand the point than to put pressure on the view.
You made the time-travel argument with John living in an indeterministic world, but does the argument require his world to be indeterministic? It feels like you’re positioning the argument for a person who believes John would have free will if he lived in an indeterministic world, but I don’t know if this is automatically true. For example, if every third decision was made by a random indeterministic dice roll would we call this free will? What if John could be coerced to shoot JFK even if the laws were indeterministic, surely the coercion implies he didn’t shoot him of his own free will.
Second, are you worried about the metaphysical possibility of these scenarios? Like what about the classic paradox where John travels back in time to shoot his grandfather and then prevent himself from being born?
The point of the time travel case is to show that the natural laws could be such that backwards counterfactual dependence occurs even though determinism is false. So, I’m trying to appeal to a case where the existence of backwards counterfactual dependence *doesn’t* intuitively undermine our attributions of freedom, and then argue by analogy that we should have the same judgement in the case of determinism. Assuming indeterminism makes that argument clear, but nothing technically turns on that assumption. I’m perfectly happy to make the time travel world a deterministic one. In that case the backwards counterfactual dependence would just be overdetermined (lol), but still partly due to the time travel friendly laws.
My next post is exactly about the grandfather paradox! Short answer: I disagree with the consensus that Tim can kill grandfather. I think he lacks the ability. Similarly, I actually think determinism *does* deprive us of some abilities (this part isn’t in the post, maybe I should include it?). Consider Tom: Tom lives at a deterministic world where the proposition P describes the initial state of the universe, and Q describes the natural laws. Suppose Tom never comes to know that P^Q despite attending a university where they specialize in educating their students on these facts. Tom can’t learn P^Q because any world where Tom does come to believe P^Q is a world where they are false, given the nature of deterministic laws. So determinism *does* deprive us of this ability. But I think this is a special case. It is a necessary condition of any ability that it can be exercised given the actual laws of nature. If I cannot perform an action A without the laws of nature being different then neither I or anyone else is able to A. Supposing that P^Q is the proposition that describes our own laws and initial state, that the laws are deterministic, and I don’t learn P^Q, I am unable learn P^Q; but this is because it’s nomologically impossible for me to learn P^Q. This is the same diagnosis I have for Tim and grandfather, so there is a nice symmetry. Tim can’t kill grandfather because it’s not nomologically possible, same with learning P^Q.
But this doesn’t hold for our ordinary abilities. Suppose I choose to stand. I could have continued sitting. If I had so chose, nothing about our laws would have to be different, the past would just have needed to be different (and given determinism, the very distant past) but as I mention in this post that poses no problem.
There *is* a worry Lewis gestures at about backtracking views. The worry is that there won’t be nomologically possible worlds where our backtracking counterfactuals turn out true, because the universe is a chaotic system and small changes blowup into big changes quickly. My answer to this worry is very technical and basically taken whole-cloth from Cian Dorr’s “against counterfactual miracles.” The short version is that Lewis is (mostly) provably wrong given the state space of the universe is continuous. You can choose a variation in initial conditions that stays as close to actuality as you like, for a long as you like.
Cool, I think this post clicked for me after reading your response.
If I understand it correctly, can resolve the grandfather paradox by positing that the backwards time traveller doesn’t “change” the past but simply returns to the same timeline and intervenes in ways globally consistent with the actual history. So more like the time-turner in Harry Potter than Back to The Future where backwards time travellers literally change the history. The point about Tom’s lack of ability to know P^Q is particularly cool because it shows this isn’t just special pleading.
So when you say “John sits on the knoll and reconsiders” this is a possible world, but it can’t be the actual world because the actual world is one in which JFK died in 1963 when John time travelled from 2150 to shoot him.
One residual worry I have is once John travels back to 1963 and shoots JFK, there’s a genuine counterfactual possible world where John travelled to 1963 and *didn’t* shoot JFK - which means the whole history of the world involved a JFK who lived much longer. Presumably that world would differ so substantially from the one which featured the original John that it’s not even clear how similar the 2150 worlds are or whether the 2150 versions of John are sufficiently close counterparts to adequately be considered ‘John’.
Maybe this is where the Dorr paper you referenced comes in?
Let me take this in parts.
> If I understand it correctly, can resolve the grandfather paradox by positing that the backwards time traveller doesn’t “change” the past but simply returns to the same timeline and intervenes in ways globally consistent with the actual history.
This is true but it isn't my resolution to the grandfather paradox. The grandfather paradox is always stated in terms of 1 dimensional time travel (intra-timeline time travel in my own terminology), and that is what generates the issue in the first place. The paradox is a paradox of ability. It seems, at the same time, that Tim can and cannot kill his grandfather. I argue that Tim just *can't* kill grandfather.
> So when you say “John sits on the knoll and reconsiders” this is a possible world, but it can’t be the actual world because the actual world is one in which JFK died in 1963 when John time travelled from 2150 to shoot him.
This is right
> One residual worry I have is once John travels back to 1963 and shoots JFK, there’s a genuine counterfactual possible world where John travelled to 1963 and *didn’t* shoot JFK - which means the whole history of the world involved a JFK who lived much longer. Presumably that world would differ so substantially from the one which featured the original John that it’s not even clear how similar the 2150 worlds are or whether the 2150 versions of John are sufficiently close counterparts to adequately be considered ‘John’.
I think tiome travel counterfactuals are super hard to evaluate because we have backwards counterfactual dependence between two time periods, and are evaluating counterfactual worlds where there could be a huge departure from actuality in that intervening gap. Notably, I don't think this is a problem in deterministic worlds (this is where the Dorr part comes in). But one way to think of the problem you ask is to imagine someone who goes back in time to kill Hitler in the year 2500. Presumably, he is motivated by things he has read in the history books and such. If he succeeded, what could have possibly motivated him to go back and time and do the killing in the first place? This problem is obviously greater the bigger you make the distance between the time travelers point of departure and the event they effect. That's all to say: Your worry makes sense, counterfactuals are really hard to evaluate in time travel worlds in some scenarios. But! I don't think this problem extends to my resolution of compatibilist questions.
I am with you with regard to it being nomologically impossible for Tom to learn P^Q, given that his is stipulated to be a deterministic world, but I am not convinced that it is different for ordinary abilities. As far as I can tell, determinism does not rule out you thinking about whether to stand (or whether to chose the burger rather than the pasta, to take the example from your conclusion), but, by the definition of 'deterministic' apparently being used for the first case, the worlds where you choose one over the other seem to me to be just different possible worlds at any past time; there was no time when they were identical. The outcome of your decision process merely reveals some information about how the actual world always was and was going to be.
I tentatively think that Boris Kmet is on to something when he writes, in the abstract of 'Counterfactuals and Causal Reasoning' [1] "I offer an alternative account of the role of counterfactuals in causal thought that is consistent with these data: counterfactuals are used in a common method of causal reasoning related to John Stuart Mill’s method of difference. The method uses background beliefs about causal relationships, history, and the natural laws to establish a new causal claim. Counterfactuals serve as a convenient tool for stating certain intermediate conclusions in this reasoning procedure, and that is part of what makes counterfactuals useful. This account yields a functional explanation of why our language contains a construction with the truth-conditions of counterfactuals."
Personally, I'm not wedded to the idea that our world is deterministic, anyway.
[1] https://www.princeton.edu/~bkment/articles/causal%20reasoning.pdf
It's true that deterministic worlds have the same universal description at all points in time, or never. I don't see why this makes you think that our ordinary abilities cannot be utilized in ways we don't actually use them, or why that would be nomologically impossible.
Great article! What I find interesting in the discussion surrounding the free will debate is that there is almost like this presumption of pessimism (the worst possible thing i.e., absence of free will is presumed true until proven otherwise). Hard determinists often come into the conversation thinking that compatibilists *have* to show them something. But given the fact that it pre-theoretically seems to most people like there is free will, *that* should be the starting point of the conversation. And if compatibilists can then provide a reasonable account of how free will works (like you just did!) it seems like the debate is kinda over in their favor right there and then (barring some internal issues with the account or some further arguments for hard determinism).
Thank you so much! I agree with everything you say here haha
stoked to read this. I think this is what you laid on me during our conversation and I don’t think I fully grokked it at the time.
First I'd note an interesting facet of the definition of determinism.
"Supposing the laws are deterministic, a sufficiently sophisticated inference machine, that knew the state of the universe and the laws, could figure out what has happened, is happening, and will happen, with perfect accuracy."
I agree this would be sufficient to make a universe deterministic. The thing I have to note is that it seems as though due to things like self-reference, the halting problem being insoluble etc. that even if determinism were true such perfect prediction would be impossible (some things would not be predictable by such an inference machine).
So a particularly skeptical person might claim we can never know whether failure of prediction is due to self-reference problems etc. (limits of prediction) or simple failure of determinism. And indeed some people seem to treat determinism as a question of prediction (Karl Popper for example).
Clearly there is some sense to this in terms of understanding the counterfactual dependence of the future on the past, the way we don't recognize the present's dependence on the deep past (we can't predict how the present depends on the deep past) and so on. How we can and should deliberate depends on what we could know (about our actions and their implications, about what we are able to do given current resources etc.) Although clearly one can separate the issues somewhat.
I'm not sure how much it means, but I'd define fatalism as the view that some future outcome (set of outcomes) is fixed no matter what you do in the interim. A typical statement would be something like it is invitable that the glass will break so there is no point in trying to protect the glass. So a standard fatalism will be just contrary to determinism, since determinism says that things in the further future are only determined because things in the interim are a certain way if one did things different in the interim the final outcome might change. There is a form of fatalism that is a form of determinism.
It is true that if your actions are completely ineffectual they have "no point" (it becomes inadvisible). For example there is no point in trying to deflect an incoming city killer asteroid by swinging at with the a baseball bat as if it were a fastball. It would be inadvisible, stupid even. However the generalied fatalist idle argument (there is no point in doing anything so best to remain idle), is a very different proposition and doesn't really follow if we are talking about the overlap between fatalism and determinism. If fatalism is true because we only do one thing in the interim, then what we do in the interim isn't necessarily pointless etc.
Now I'd state free will in terms of moral responsibility (saying we have free will is saying we have moral responsibility or responsibility to do otherwise). If determinism does not imply every action is pointless like fatalism does, is that different from moral responsibility? If every action were equally pointless as in fatalism clearly we could not be responsible for doing otherwise. Does responsibility require more than being able to evaluate given actions as having a point or not (being advisible or inadvisible etc.) is that sufficient or just necessary.
I think this is just a complementary analysis to what you said. What it means to do otherwise or to be able to do otherwise is just a question of what range of counterfactuals are appropriate and this informs our sense of the point or pointless of actions, deliberations and so on. It seems like the arguments for incompatibilism are often arguments for fatalism and so on or overlap or subtlely share the same fallacies etc.
I have some thoughts on halting problem / computation related isssues.
1. The halting problem and related impossibility results only apply to infinite (or at least unbounded) processes. Any question concerning what will happen in a particular fixed finite amount of time is computable. If I'm interested if I have free will for the decision I'm going to make in 5 minutes, that should be computable. However, it is still possible that human decisions are uncomputable despite the finite time limit (say because of the continuous nature of reality).
2. There is an even stronger version of this prediction idea foiling determinism. Substacker Disagreeable Me believes that both consciousness and physical reality are fundamentally functional / computational in nature. If this is true, this may undermine determinism. This is because in order to predict my future decision, you'd have to simulate it, but the simulation and reality are made of the same thing (functional / computational states), and hence there is no difference between reality and the prediction, and hence there is no way to predict my decision without me actually making the decision.
First we are interested only in versions of the halting problem that can be solved by actual residents of the universe, so only by finite computers of indeterminate but not unbounded size. If it is only soluble by infinite devices then that would suffice to show that no inference machine exists (the inference machine has to give results in a finite time, with finite materials etc.), since the inference machine that can do it would need to be infinite and so can not exist. Given your premise that the halting problem impossibility rests on infinite machines and your other premise that there are no infinite machines in reality (or no infinite machines that give results in finite time) you are premising that all actual halting problems can be solved by actual finite machines.
Grant all that, it is the case that there is a general solution to the halting problem for all finite machines that can be run on finite machines. If any actual halting problem for an actual computer is finite (bounded) and such that it so computable (by our finite computers) then there is a finite algorithm that solves the halting problem and can be run as a program on our computers. Given that finite program one can easily construct another program P that has the solution to the halting problem as a subroutine H + feeding the code for this very program P into that subroutine H and perform the following conditional branch on the output of H, if it returns 0 (does not halt) halt and if it returns 1 (does halt) enter an infinite* loop (and so defy the prediction that it halts).
*Of course infinite loops on a finite machine won't be infinite as the machine will eventually break (or run out of power or storage or something). However this is no help because the general solution or prediction that all machines will halt will thus be true and will technically be a general solution to the halting problems, but is not really specific enough. Really the halting problem we want to solve is how many steps will it take to halt (if we want to show that everything is predictable how many steps until halting is one of those things in everything). For definite algorithms (ones that will halt after a definite number of steps) one might predict the number of steps until halt by some modified halting solution algorithm and some modified program P' call the subroutine that runs that H' (that tells us the number of steps until the program halts) based on the code for P'. We can obviously easily create a branch or other operation that responds to the output of H' by then causing P' to do a different number of steps than predicted by H'. For example just take the output of H' add 1 and then do a loop with that number of steps, now the general solution to the modified halting problem (how many steps until halt) is guaranteed to give the wrong number of steps for P' (it is greater by 1 + the number of steps it took to perform H' etc.) even though P' does halt in a definite number of steps. Also for finite machines that are trying to perform an infinite loop but break down they won't have a definite number of steps until they halt, when they halt will depend on either random quantum events or microphysical events so obscure that they can not be ferreted out in a finite amount of time (if we are limiting machines to be finite, then the data entered into them must also be finite) and so on.
The basic problem is that for determinism to be definitively and unequivocally demonstrated what we need to show is that inference machines can exist (we can construct them and consult them) such that even if you had access to an inference machine your actions could be predicted by such a machine. If inference machines are impossible you can never come up with predictions to falsify or verify that everything is predictable (there will be some cases where either you can't generate a prediction or if you do it is prone to being wrong). If inference machines are possible and so it is possible to predict anything you will do in the next 5 minutes, then one of the things that you may do (it is possible for you to do) in the next 5 minutes is consult the inference machine since per stipulation consulting inference machines is possible. However such a scenario realizes the self-reference paradox roughly equivalent to a subset of the halting problem blocking prediction and blocking full simple verification that every human action is predictable thus showing inference machines are impossible. If inference machines are possible (if it is possible to consult inference machines) then inference machines are impossible, paradox and so a nice reducto of inference machines, inference machines must be impossible in worlds like ours.
Inference machines would be possible in a world unlike ours, if we knew there was a world A that was a subset of a world B and there were no inference machines for A in A, but there were inference machines for in B that worked only for A and if we maintained total separation of A from B (but not total separation of B from A asymmetrically B can observe A, just never alter it) then you could predict everything in A, show that everything in A is predictable (by inference machines) and there would be no danger of a self-reference paradox. However we know we are not in that situation when I ask if I have free will, I'm not asking if some system weirdly segregated from me has free will I'm asking if a system I have total interaction with has free will and so on.
I see, I misunderstood your original point. I agree, that if the goal is to build an inference machine within universe A to predict a future state of universe A, then that is subject to self-reference/halting type limitations even if universe A is finite (or infinite). I think you demonstrate this well, but just as another example, suppose their was a perfect predictor Alice, and Alice was asked to predict what number Bob will say immediately after seeing her prediction. If Bob was feeling contradictory, Bob could just say a number one larger than whatever Alice predicts. In this case it would be impossible for Alice to make a perfect prediction. Thanks for the correction!
Yeah sorry I could have made the point more succinctly. Note perfect prediction is ambiguous between perfect inference from facts about the past and laws and perfect guessing.
Even if every event outcome were completely random (but somehow specifiable) it might turn out that every guess about future events by some oracle turns out to be correct by coincidence (a coincidence of about 0 probability but not actually ruled out as "impossible" in some sense). This wouldn't be subject to self-reference because no one could deliberately include the guessing process in an algorithm (there is no algorithm for this kind of guessing). Presumably we can make something like that work for a world more like our own (with actual laws/causal succession of events). Yet this doesn't imply determination (predetermination) because while every guess is right, no guess is thus determinate (a determinate inference from facts and laws or something like that), also its not clear how you could reasonably conclude that the oracle can correctly "predict" (correctly guess) everything. This probably raises an underdetermination problem (are we making principled inferences or a series of expanding lucky guesses) at some point. Many complexities.
The laplacian idea isn’t supposed to be definitional (I included it more to provide a vivid example of what determinism might *allow*). I agree, consequently, with basically everything you say concerning the limits of computation.
The way you define fatalism is different from how I do, but it’s certainly a way the word is used. I think the fatalism you describe is very different from incompatibilism though. Incompatibilists certainly don’t think that your choices aren’t causally efficacious given determinism (or they shouldn’t think that anyway).
I think we broadly agree though!
that version of fatalism is dubious. why think that a particular outcome can happen regardless of whatever happens prior to it? i will be utterly jacked at time t even if prior to t i never exercised? i don't think that there are many fatalists who hold this version.
the counterfactual claim is just the claim that if reality were different, it'd be different, or a claim about how a formal model works, eg. one that physicists use where initial conditions + laws uniquely necessitate all outcomes.
but why think that reality could've been different? i certainly won't believe that because of some dubious discourse of what would be the case if the case wouldn't be what it is.
I think I could have thrown the ball a bit higher because, when I stood in the same spot and tried harder, the ball went up further. So it seems like I could have tossed the ball higher. So reality could have been such that the ball went higher.
You’re free to deny any step in that argument, I just don’t see why I would.
yeah i don't see how it follows from the fact that several different but similar things happen at different instances that at any given instance, multiple things / something other than what actually does, can happen. it's not compatible with determinism. if it comes to you framing my rejection to make that step as denying your seeming, and me framing it as not seeing why i would make the step, now what? like with negative atheism, i am just waiting here for some consideration that doesn't require me to start with not-negative atheism.
"When we evaluate counterfactuals, we cannot hold all facts fixed. If we do, then every counterfactual will turn out false."
but... but... i thought that counterfactuals are literally all false... by definition? what does it even mean to not hold a fact fixed? are you suggesting delusion? if one takes seriously the physicist's model of determinism, then one can't accurately assess counterfactual conditionals, since even the tiniest change would entail immense differences in ways we can't ever compute. this insistence on what feels normal and natural and good for you to say isn't a reliable guide to either counterfactual consequences or the mere possibility of counterfactual events.
Counterfactuals aren’t all false. The antecedent of a counterfactual is definitionally false. To hold a fact fixed when evaluating a counterfactual means that we evaluate the counterfactual, using the standard Lewis-Stalnaker method for evaluating counterfactuals, and only look at worlds where the fixed facts are true. The point you make about whether we can know counterfactuals are true is related to the asymmetry point I make at the end. I think it’s wrong for technical reasons. The universe is a chaotic system on standard dynamical theories, but the state space is continuous and its (provably) possible to select an initial set of values that stays arbitrarily close to the actual universe in state space up until a specified point in time. That’s a lot of jargon but it basically means there are possible values to the initial conditions which keeps the resulting universe qualitatively *as close as you’d like* to the actual universe, for as long as you’d like. So the objection from chaos theory isn’t damning for backtracking theories of counterfactuals.
that is again a feature of a kind of model. but your claim is about free will in this world, not just how we may tinker with a model. are you saving the view by committing to each free choice changing the initial conditions of the universe? i still don't see the move that lets you infer that anything actual could've been otherwise.
also, how do possible worlds help in establishing how this world works or if there is intra-world contingency? lewis was a necessitarian about each possible world. i'm confused about how you wanna use them to help your conclusions about this world.