Fine, you said that causality itself somehow makes verified predictions, to which I pointed out that it’s not causality, but the regularities that make these predictions. The argument is structurally the same, though.
Now to reply to the rest of the post.
At this point, I am essentially just firefighting. There is nothing that I could say that would make Half_Man_Half_Wit concede that maybe his talking point about causality doesn’t work, so there just isn’t a debate happening here.
Regardless, I don’t like people making false statements about me, so here we go again.
For a third time now: I have never claimed that making predictions necessitates causation.
The point is, causality makes those predictions and so that is reason to gain confidence in that model. If there are alternative models that make the same predictions then it’s reason to gain confidence in them too, but note that the predictions need to flow naturally from the model itself. It’s not enough to say a given observation is not incompatible with a model – it must be an explicit consequence of the model itself to count as a prediction.
No, you have misunderstood the concept of the block universe. The block universe is saying that there is no moment of “now” and no distinction of past and future; it’s an implication of relativity and there being no such thing as true simultaneity. However, it absolutely includes time slices being causally linked.
Again, no, this is a rephrasing of the straw man.
I am saying if my model predicts that you’ll be wet, then that is supporting evidence for my model. It’s not conclusive, but it’s a reason to gain confidence, and additional data / observations can help to increase our confidence further.
Not about empirical claims.
“Inferred regularities” is your term, not mine. But when I have inferred that what you are alluding to by this is inductive reasoning, you have not objected. So, yeah, the validity of inductive reasoning is one of the starting pillars for being able to make empirical enquiries about our reality. It is, to empirical claims, what truth by definition and deductive logic are to formal logic and mathematics.
We were just talking about whether there are any alternatives to making decisions apart from some function of past information and randomness. The list of ideas on the nature of reality is irrelevant to this, and it’s quite telling that you dodge any attempt to talk about the specifics of how agents make decisions.
:rolleyes:
I haven’t said that causality is necessarily true, just that it has copious amounts of supporting data.
And you might notice that discussing evidence for a claim is the precise opposite of handwaving it as “mysterious ways”.
Yeah pretty much. I mean at this point you’re struggling to define the thing, let alone come up with a model, let alone use it to make concrete predictions, let alone have those predictions verified.
It’s garbage until we can at least start with step 1: definition.
You did claim that causality itself makes predictions. I interpreted that (in the only sensible way I could find) as implying an argument of the form:
- I have observed that B follows A.
- I stipulate that this is because A causes B.
- I predict that, hence, when we observe A, we should observe B (all else being equal)
- We observe A, followed by B, and hence, find our expectations confirmed.
I paraphrased this as ‘causation allows us to make verified predictions’, on the basis that I surmised you held 2 to be necessary. If you feel that this incorrectly encapsulates your position, I’d ask you to spell out the argument you actually had in mind.
My argumentation, now, is that premise 2 is replaceable by 2’: There exists a regularity such that B follows A. The argument, as above, clearly goes through as before. Hence, causation is dispensable for the prediction; consequently, it’s not causation that makes this prediction.
Causation, then, is an additional principle stipulated to give a reason for why the regularity exists. As such, any confirmation of the prediction is not a confirmation of the model including causation, it merely confirms the existence of the regularity, with causation being postulated as an explanatory principle for that regularity. Causation is just metaphysical icing on the top. Hence, any other explanatory principle will work just as well; in consequence, the empirical success of the model is in no way a confirmation of the existence of causation.
If you feel that this misrepresents your position, then please, give an example of a prediction made by causation.
Relativistic block universes aren’t the only flavor of block universe out there, but even in those, what you’ve written is highly questionable. My point was for a general block universe, such as the following one: ABABABABA…BABABXYZ. One might observe this universe for a time, conclude that B follows A, and A follows B, make an according prediction, and have it come out right; but that’s not because A causes B, it’s because I set things up like this. This is exemplified by the fact that the regularity runs out (in the example; it’s not necessary that it does—such a block universe might be indefinitely regular).
But the validity/applicability of inductive reasoning doesn’t depend on causality—it depends on there being regularities in the universe which we can derive via generalization from past observations. But these can exist without causation.
The list was to impress on you the fact that in each of these cases, we don’t know how agents make decisions. But that is the same as with causality: we don’t know how A causes B. So in, say, an occasionalist view, an agent makes decisions in the same black box way in which the next state of the universe is produced; in a Humean view, an agent chooses a particular local element of the quilt of reality in the same way they’re chosen to set up the whole of reality; on Schmidhuber’s view, an agent chooses the next event from the probability distribution in the same way they’re chosen in the universe’s time evolution; and so on. Not all of these lead to universes where the agent is free; it depends on the nature of the black box whether they are. In a universe subject to strict causality, the black box is how one event causes the other; but it’s a given that nothing else, like volition, etc, plays a part. But it’s just as much of a black box.
And that’s the problem: it has none. That our universe has persistent regularities has supporting data; that these are due to causality is your stipulation.
All of which holds just as much for causation.
I am simply talking about the scientific method.
In science, it is not necessary to say that only my model can predict some observation. In fact, it’s more than unnecessary, it’s impossible to ever validly make this claim.
The simple point of science, is that with each confirmed prediction we gain confidence in a model. That’s all.
I would disagree with that.
When we describe observations in terms of causality, that gives us some basis for predicting what effects will happen. I find broken egg shell pieces, yolk and albumen in the place where I dropped an egg, based on our understanding of gravity, mechanics and chemistry. If I don’t find exactly that then that is immediately something to investigate and maybe part of the model has been falsified.
“Inferred regularities” in this context is just saying B follows A.
Now I think I know what you’ll say, that with causality we’re still saying B just follows A if we go down enough levels (e.g. to why matter is pulled by gravitational fields). But the point is, we have a good model at many levels, versus a model that tells us precisely nothing at any level. The former is of course preferred by science.
Sure, and this is your framing. Everyone else was talking specifics of how the brain works and what free will actually means.
You’ll note that your framing “works” with anything. Any topic whatsoever concerning objective reality could throw up objections about the nature of causality itself.
Nope. Causality is defined, and makes verified predictions.
Agreed. And as a direct logical consequence, for two models making all the same predictions, you can’t validly claim that one of them is preferred by the evidence. But that’s what you’re trying to do.
You can appeal to additional metaphyisical or methodological principles, of course; but then, the conclusion isn’t supported by the evidence, but by your metaphysical predilections.
By the way, appealing to Occam’s razor will not help you: for one, it’s questionable that the postulation of causation is actually ‘simpler’ in the relevant sense (of not adding extraneous theoretical entities) than the alternatives, but more importantly, Occam’s razor is relevant to enable the ability of making predictions—that is, if you have model A and model B, and both are in agreement with the evidence, but make different predictions in certain cases, you’re justified to use the simpler one as a means of generating a unique prediction; otherwise, every set of data would license you making every conceivable prediction. But in the present case, all models make exactly the same predictions.
You have the same basis in other models. Take Schmidhuber’s: there, you can actually calculate that you’ll be justified in making the assumption that if an egg is let go a ways above the ground, it’ll fall down and go splat, and the model gives you a precise reason—that any given regularity is exponentially more likely to persist, than not. All of our laws, and our conclusions drawn from them, will still hold (to any relevant degree of accuracy), because they’re mathematical formulae capable of compressing the sequence of observed events. Causality, once more, not needed.
So the models here work just as well at many levels.
Again, tell me one that’s made only by causality.
I think most people would interpret a concisely describable deterministic rule as fitting within “causation”.
And such a rule is, of course, simpler. It’s simpler to write an algorithm to compute the digits of pi than it is to “print” each individual digit separately with “free will”.
Last Thursdayism makes identical predictions with however you believe the world to work, but essentially everyone summarily dismisses the idea as ridiculous because it comes with an enormous penalty of outrageously complex initial conditions, which discounts the idea to such absurd implausibility that it isn’t even worth considering at all, except for the meta-purpose of illustrating absurd ideas that aren’t worth consideration, such as in this paragraph.
The Razor here can and does justify more probabilisitic weight on universes that can be described by simpler models, even when all models make identical predictions. That is a primary use of this Razor.
But such a rule can hold for a universe with causation just as well as for one without.
That’s actually a good illustration: there’s a deterministic rule for the sequence of events (digits of pi), but it would simply be a category error to then conclude that each prior digit must have caused the following one.
It’s in fact exactly equivalent to supplying the initial conditions for a deterministic universe, because you can equivalently supply the data on any Cauchy surface—one in the far past, in the far future, or even last Thursday. (This also works for quantum mechanics, as long as there is no objective collapse, where the unitarity of the dynamics ensures that every state of the complete system, at any point in time, contains the complete information about the system—in other words, the dynamics is reversible, and no information is created or destroyed.)
That’s a metaphysical commitment, but it has nothing to do with Occam’s razor. The razor is justified in the situation where you have experimental data, with a potential infinity of models to account for that data, and likewise with a potential infinity of predictions given the data. There is only one algorithm that will eventually converge to the model (or models) accurately accounting for all the data: taking the simplest (in regards to something like algorithmic complexity) explanatory hypothesis, computing its predictions, and checking them against experiment; if the prediction is falsified, take the remaining most simple hypothesis, and so on.
But it’s not justified for metaphysical pictures. Take the issue of interpretation of quantum mechanics: we can’t decide whether Bohmian mechanics or the Copenhagen picture is right simply because one is (according to whatever measure) simpler. Why should simplicity track metaphysical aptness? That’s a huge assumption without any proper justification (again, in the case of finding an accurate scientific model, there’s a clear justification for the simplicity hypothesis, but it fails here).
Which is why I picked it, yes.
Wrong.
Out of curiosity, are you using an atypical, term of art, or ‘house rule’ definition of causality? Because it seems trivially demonstrable that it is impossible to make predictions with certainty if there is not something that is causing you to be right.
Now, this doesn’t mean that A caused B. Maybe C caused both A and B. Or C was caused by A and then caused B. But something has to have caused B to be the way it is, or else you would not be able to predict B with any level of certainty.
The post of yours that the above quote is from includes a whole passel of alternate reality models, all of which includes a ‘black box’ that is causing things to be how they are. How is this not causality? Sure, it’s not linear causality from A to B (well, in some of the models it is), but something is still causing B to be the way it is.
The only model where B is not caused to be the way it is is if B is random, and in that case the predictions are erroneous - the coin has landed on heads ten times in a row, but it’s a fair coin and might land on tails next time.
Well, I suppose I have been less than explicit here, yes, so let’s try to remedy that. First of all, I think we need to distinguish between reasons and causes: just because something is a reason, doesn’t mean it’s a cause (while all causes are reasons—proper causes are necessary reasons, and sufficient causes are, well, sufficient reasons). So the irrationality of the square root of 2 is the reason it doesn’t have a finite decimal representation, but it would be odd, to me, to claim that the irrationality causes the expansion to be infinite. Similarly, that David Hume was born on May 7, 1711 is the reason he was born on a Thursday, but it didn’t cause him to be born on a Thursday. More generally, the truth of the premises of an argument is the reason its conclusion comes out right (provided it is formally valid), but I wouldn’t say that it’s the cause of this correctness.
So I can predict that, if you try to write down the decimal expansion of 2, you won’t ever get to an end; but I wouldn’t say it’s causation that allows me to make this prediction—it’s just logic, ultimately. Sure, this is what ‘causes’ me to be right—I’m right because of certain mathematical facts—but that’s just an unfortunate accident of language. Perhaps it comes into play here that my native German doesn’t conflate the two quite as much—‘cause’ would be something like ‘Ursache’, literally ‘primordial thing’, while ‘reason’ is ‘Grund’, ‘ground’. You wouldn’t say that the irrationality of the square root of two verursacht (causes) that its decimal expansion is infinite, but you might say that it is its Begründung, reason.
Additionally, as a physicist, my notion of causality is rooted in (maybe even caused by) Bohr’s use of the term ‘claim of causality’ for a description of a system in terms of energy-momentum variables (as opposed to the ‘spacetime picture’ of temporal and spatial coordinates), and Bell’s ‘local causality’ as proposing that the sufficient reason for the state of a system at t is the state of a small area containing that system at some t’ < t, which of course derives from the relativistic notion of causality as basically ‘influences transmitted at (maximally) the speed of light’.
So in this sense, I wouldn’t say it’s causation that allows me to make predictions in something like, for instance, Schmidhuber’s algorithmic universes. Each new event is drawn, independently, from a probability distribution; hence, it is independent from the history of the universe before, and thus, not due to causal influences. True, that means that predictions are, strictly speaking, approximate—but so are almost all predictions in the real world: I predict that if you run towards a wall, you’ll probably bounce off of it, but there’s of course a small chance you might tunnel through and come out the other side. If you want to include this in a notion of ‘causality’, then it seems to me that your coin throw is likewise subject to causality—the coins fairness ‘causes’ it to eventually come up heads.
Besides, it also seems, to me, to be the right notion of causality to use in the free will debate: if we were to just admit any of my above pictures as a causal one, including for instance the occasionalist view, then we’d just end up including volition as a cause, too, and hence, there’s no sense in which causation is opposed to free will. But I don’t think this would satisfy @Mijin.
This isn’t quite an idiosyncratic notion, I think. It seems to me that this is what Russell had in mind when he wrote (in ‘On the Notion of Cause’):
in advanced sciences such as gravitational astronomy, the word “cause” never occurs. […] the reason why physics has ceased to look for causes is that, in fact, there are no such things. The law of causality, I believe, like much that passes muster among philosophers, is a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm.
It’s also not unusual to distinguish between causality and laws of nature. This is an argument Sean Carroll is fond of (see his discussion in ‘The Big Picture’, in the chapter ‘The World Moves by Itself’): the notion of cause is problematic, but thankfully, in physics, things occur according to fixed fundamental laws, and hence, we can dispense with it. More accurately, he appeals to conservation of momentum, and is explicit that causes are ‘no longer part of our best fundamental ontology’. The problem with that is, of course, that it substitutes one black box for another, but that’s not the present point.
Likewise, a block universe (contrary to @Mijin’s assertion above) is also often held up as incompatible with causality. In fact, D’Ariano believes he can prove this:
[T]he scenario of the ‘block Universe’ and the connected ‘past hypothesis’ are incompatible with causality, and thus with quantum theory: they are both doomed to remain mere interpretations and, as such, are not falsifiable, similar to the hypothesis of ‘super-determinism’.
(From here.)
Nevertheless, of course, in a relativistic block universe, and in a universe governed by the laws of physics, you will have ample opportunity to make predictions that come out right. So there’s at least precedent for using the notion of causation in the way I did, as there is for being skeptical about it.
No, I said the exact opposite: I explicitly said that two models making the same predictions are supported equally.
The point you missed however, is that a prediction means something quite specific in science. It’s not enough to post-hoc look at a phenomenon, find something consistent with a model, and claim it as a prediction. A prediction must flow as a direct implication from a model, and must be falsifiable.
By your own admission, your concept of a block universe, for example, is not falsifiable. Because, if B follows A, then fine, that’s an “inferred regularity”. But if Z follows A, well, that’s consistent too, again I’m just quoting from the example you gave.
This is not the case for causality. Causality gives us a reason to make detailed scientific models expecting only B.
If I drop an egg and anything other than what our models suggest will happen then, at first, we will try to find the problem with our models of mechanics, gravity etc. We wouldn’t immediately question causality because it has been useful so, so many times.
But if enough weird non sequiturs happened, sure, we might think causality is flawed and find other concepts that may better explain what we were seeing. Plus of course there are hypothesized physics that explicitly break causality such as wormholes, negative mass etc.
So yeah, causality has made verified predictions, the others have not. That doesn’t make them wrong. But it is wrong to say we’re arbitrarily assuming causality for no reason.
We have confidence in causality just like we have confidence in the theory of gravity.
This is a bit confused: predictions aren’t falsifiable, they’re either right or wrong. Models are falsifiable by making predictions that may be wrong.
Of course it isn’t. Like causation, it’s a metaphysical assumption, and hence, not subject to empirical investigation. What is falsifiable is the hypothesis that there exist consistent regularities—just as is the case with causation. If there are no such regularities, then eventually, the coincidences run out, and our observations will diverge from our predictions.
Consequently, the block universe stands on exactly the same footing.
So does, for instance, Schmidhuber’s view, or Sean Carroll’s above, where causes are supplanted by laws, or the mathematical universe, or the Humean view, or even occasionalist views—provided one assumes, for instance, that regularities in the universe please whatever agent decides its next instance. In the same way, one may predict, for instance, regularities in a piece of music: the next note isn’t caused by the prior one, but the whole composition shows regularities due to the aesthetical judgment of the composer. An assumption, sure, and one that would be just as falsified as the assumption of causation if it turned out that the regularities ran out at some point.
You’re still stuck claiming that somehow, causality is necessary for there to be reliable regularities in the world (and all the predictions you cite are simply due to the presence of reliable regularities, not due to their being due to causality). But that’s simply false. Reliable regularities are a mathematical theorem of Schmidhuber’s view, and thus, the adoption of this view would prompt us to make exactly the same prediction as a causal view does.
I really don’t know what else to do to make that clear to you. It’s as Russell has it:
The law of causality, I believe, like much that passes muster among philosophers, is a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm.
And later on:
there is no a priori category of causality, but merely certain observed uniformities
Finally concluding:
the law of causality, as usually stated by philosophers, is false, and is not employed in science.
This is not an outsider view; it’s well regarded in the philosophy of science. We can postulate ‘uniformities’, but we can’t claim that they are due to causation, and whether they are is not an empirical matter, but a metaphysical one; and there are good grounds to reject the metaphysical notion of causation.
Actually, it’s even questionable whether what I’ve been calling ‘robust regularities’ or the like are a distinct consequence of causality, and thus, whether their absence would really give us reason to dismiss causality. Consider the cellular automaton Rule 30. I think you’d be happy to describe it as causal: the state of each cell at t+1 is determined by its state at t, and that of its two immediate neighbors, using a simple rule. The time evolution of this automaton is merely the continued application of that rule.
But Rule 30 is anything but regular. In fact, it’s so highly irregular that it’s used as a random number generator—it passes standard tests for randomness, and was even used to generate random numbers in the computer algebra software Mathematica. Of course, like all algorithmic methods, it doesn’t generate true randomness, but it certainly doesn’t generate anything very regular, either. Somebody observing, say, its center column as a proxy for performing measurements on some part of the universe won’t really be met with anything very regular; but it’ll still be something perfectly causal. So they wouldn’t be justified in concluding from this apparent irregularity that their world isn’t causal.
We’re actually faced with the same issue in the real world, in quantum mechanics. On different interpretations, quantum mechanics is either genuinely random, or completely deterministic—hence, conceivably causal. It’s in fact not hard to see that for any probabilistic theory, we can always come up with a deterministic one giving the same predictions.
So how, exactly, is causality supposed to be falsifiable? It’s not; just like any other metaphysical stance, it’s not an empirical matter.
Just because something is complex doesn’t mean it isn’t causal, and that definitely applies to Rule 30, even if the results are impossible to predict without perfect knowledge of prior conditions. Chaotic systems don’t violate causality just because they are hard to model.
Quantum mechanics may or may not violate causality - we just don’t know yet. But I think it is far premature to declare that this is inherently unknowable; as our understanding of the behavior of subatomic particles develops, we may find that in fact there is an underlying causal structure to quantum mechanics.
Centuries ago people looked at the sky and couldn’t predict the weather, so they declared that the gods decide whether it will rain or where lightning will strike. We now know that in fact weather is an entirely emergent behavior caused by the interactions of an enormous number of tiny particles. The number of variables involved is staggering and we currently have no way to accurately model this in the long term. But that doesn’t mean it violates causality. It just means that an enormous number of simple interactions can quickly snowball into an incredibly complex emergent system.
It’s provable that all interpretations of quantum mechanics yield the same predictions, so if quantum mechanics is right, then we will, in fact, never know whether the world is causal or not. Now, quantum mechanics may be wrong, but that doesn’t detract from the point: the assertion that causality makes falsifiable predictions is shown not to hold in general by exhibiting a single case where it doesn’t hold, and for that, quantum mechanics suffices. (And in general, it should be true that one can always find a deterministic theory giving the same predictions as an indeterministic one, by virtue of the fact that indeterministic Turing machines can be simulated on deterministic ones; so I would be surprised if it wasn’t the case that every extension of quantum mechanics consistent with known facts does admit a Bohm-like interpretation. But I don’t know of any proof one way or the other offhand.)
Actually it’s both. Models need to be falsifiable, and so do predictions.
Because, yes, a prediction is either right or wrong after being tested. But prior to being tested, it needs to be falsifiable in the first place i.e. there needs to be a possibility of it being proven wrong. If I make a prediction that says that if we see a bright flash of light, it confirms my model, and if we don’t see a bright flash of light, that’s confirmation too, then there is no test to perform since it’s an unfalsifiable prediction (neither right nor wrong, “not even wrong”).
A couple posts ago though you said it did make verified predictions. Either you were not using any scientific idea of “prediction” in this context, or were simply being disingenuous.
I think this is the fourth post in a row where I need to again point out I have said no such thing.
This gets to an interesting point though.
I can conceive of this alternative description. To continue your analogy, let’s say the music is just simply ascending and descending C maj scales. It seems somewhat arbitrary whether we consider “D” to have been played because it was caused by “B” and “C” being played previously or because that was the whole theme of the piece of music.
Because: let’s bring it back to the concrete discussion of free will. When it comes to discussing minds’ decision making, the distinction between “B caused C caused D” and “D had to come next, because the overall theme demanded the C maj sequence” seems entirely moot. In both cases what came before does entail what comes next. If a God changed the prior states, but wanted to preserve the theme, the next state necessarily must change.
It’s not just a matter of interpretation. For example, we know that the full quantum state cannot be determined from local hidden variables. So it goes deeper than just a matter of perspective.
And yeah, if we ruled out non-local hidden variables too then we would essentially have shown that the quantum state would not be fully determined from the past state.
I did? I thought I had been consistent in saying that it’s the regularities, not causation, that makes predictions, and thus, causation only does so in so far as it leads to regularities.
Yet you did not object to my attempt at reconstructing your argument above, nor provide one you consider more fitting, so what else am I supposed to go on? If you aren’t of the opinion that causality is the driving force behind the regularities of the world, then I just don’t see what you’re arguing for, because then, our experimental confirmation of (or failure to disconfirm) the regularities of the world is just flat-out unconnected with causality, but that’s a claim you seem to want to object to.
Well, I would rather say that the overall theme, the overall harmony, determines what comes next. But yes, such a model is one without free will—I never claimed otherwise. Any model in which the next instant is uniquely determined by non-volitional considerations won’t include free will; but that doesn’t mean that there are no models in which the next moment is due to volition. Volition, in these models, is necessarily a primitive notion, not further analyzable in terms of other elements, because any such analysis would entail a determination in non-volitional terms; but in this unanalyzability, it stands on the same footing as all of the other black boxes—causation, random choice, laws, block univereses, etc.
It’s just a matter of interpretation. There’s an equivalent description of quantum mechanics that’s fully causal, known as Bohmian mechanics, and leads to all the same predictions as quantum mechanics. Yes, it’s a non-local theory—but the existence of this theory also entails that (provided quantum mechanics is right) we can never exclude non-local hidden variables: we have a theory equivalent to quantum mechanics in these terms, so any demonstration within quantum mechanics of the impossibility of non-local hidden variables would equivalently extend to Bohmian mechanics, and hence, be wrong.
All of which just reinforces the main point you’ve sort of managed to skip over: causation isn’t falsifiable, because there’s causal and acausal models giving exactly the same predictions.
This isn’t much of a shock, of course: causality is just a metaphysical principle postulated to explain the existence of persistent regularities in the world.
By the way, @Asympotically_fat above already mentioned John Norton and his dome; his paper, ‘Causation as Folk Science’ (link to pdf), is rather interesting in this regard:
I urge that the concepts of cause and effect are not the fundamental concepts of our science and that science is not governed by a law or principle of causality. […] What I do deny is that the task of science is to find the particular expressions of some fundamental causal principle in the domain of each of the sciences. […] This form of causal skepticism is not the traditional Humean or positivistic variety. It is not motivated by an austere epistemology that balks at any inference to metaphysics. It is motivated by taking the content of our mature scientific theories seriously. Mature sciences, I maintain, are adequate to account for their realms without need of supplement by causal notions and principles. The latter belong to earlier efforts to understand our natural world, or to simplified reformulations of our mature theories, intended to trade precision for intelligibility. In this sense I will characterize causal notions as belonging to a kind of folk science, a crude and poorly grounded imitation of more developed sciences.
I think this, and the above quotes, are quite sufficient to show that there’s serious issues, or at least a widespread perception of serious issues, with the idea that the success of science in some way entails a belief in causal notions—if Norton’s argument is correct, it in fact serves to refute them.
Note that I’m not taking a stance on the matter. I’m not nearly knowledgeable enough of the state of the debate to have any sort of settled opinion. But what I think this does show is that it’s not as simple as you make it out to be, and whether science is supportive of causation or not is a complex issue.
Actually, I think that may have been too quick. After all, there might be more than one way to carry on the theme—it’s certainly not typically the case that an entire piece of music is uniquely determined by its first few notes—and god might choose between those. Or, god might cease to want to preserve that particular theme, and opt for another; or even abandon the notion of preserving a theme altogether. Even if god chooses to preserve the theme, though, it doesn’t follow that he doesn’t do so freely—if I have the power to perform miracles such that I could act at any time against the laws of physics, thus genuinely choose between an option allowed by these laws and one that isn’t, yet never do so, I still have choice, and the attendant freedom.
Of course, I suppose you’ll want to ask—but how does god choose between these options? In such a way as to make his choice neither random, nor determined uniquely by prior considerations? And the only answer is that I don’t know, and don’t think we can know. You’ll find that unsatisfying, but the reality is that with causation and randomness, we stand at exactly the same problem.
If B follows A, and you stipulate that that’s because A causes B, then what is it about A that makes it cause B? Why could A not cause C instead? What sort of powers inhere in A that make it intrinsically a B-causing thing, rather than a C-causing thing?
And it’s the same with randomness. If A or B could equally well happen, but only A does, then what determined that it’s A to the exclusion of B that happens? There’s no way to choose, with any finite procedure, one over the other. Yet one gets chosen over the other. How does that work?
In these cases, you’re fine with ‘we don’t, and probably can’t, know’ as an answer. But then, there’s no real reason to reject the same answer in the case of volition, other than metaphysical prejudice and/or force of habit.
That doesn’t give you any positive reason to believe in free will, of course. But neither is there any positive reason to believe in causation, yet you do. So at least, it seems to me, you should be fine with others believing in free will—knowing that both you, and they, have the same lacuna in your worldview, the same question of, but how does it work?
You might have, of course, other reasons to believe in causation. Others have other reasons to believe in free will—believing that it’s necessary for moral responsibility, for instance, or being unable to reconcile its nonexistence with their impression of having it (which is evidence for free will, even if it by far isn’t incontrovertible or conclusive evidence), some might hold to it for theological reasons, and so on.
I’ve never really particularly cared, one way or the other (well, that’s not quite true; at the time I did care most, I was a staunch proponent of the notion that it’s incoherent in principle). But I think it’s important to fairly meet the options on the table, and the ‘no free will because causality’-stance fails to do so, in my opinion.
Oh dear, you said the f-word: “free will”. Which means that I’m obliged to point out that there are various definitions of “free will” that are entirely compatible with determinism. Specifically, all the ones that aren’t self-contradictory and/or incoherent.
Free will, as commonly defined, is “freedom of humans to make choices that are not determined by prior causes or by divine intervention”. The interesting thing about this definition is that it draws a distinction between the human and “prior causes”. It very explicitly presumes that the human is a black box, producing “free will” independent of the things the will is “free” of. Your will is “free” to choose without being controlled by outside forces.
And then people try to crack open that black box and figure out what part in there is producing this free will - while simultaneously requiring that will to be free of everything inside the box too.
This is, of course, stupid - it’s a very explicit movement of the goalposts from “nothing outside my mind controls what my mind does” to “my mind doesn’t doesn’t control what my mind does either”. And then they realize that they just said that there’s literally nothing that makes their decisions and get all confused, and rather than reassess their bad argument just claim that it’s magic or something.
You could’ve chosen not to 
I do agree that if you try to analyze free will, you won’t be left with any—but that just means that free will isn’t reducible to notions of causation (and/or randomness). Which really shouldn’t surprise anyone. And in fact, it’s the same with causation and randomness: if you try and analyze those, you’ll also be left with nothing sensible. It’s just that we’re habituated not to try and perform such analysis, because causation and randomness (the latter, more recently and reluctantly) are the notions we analyze others in terms of—they’re accepted as basic, primitive, given, a priori, what have you.
But now suppose, instead of causation and randomness, somebody took causation and free choice as fundamental. They’d be just as puzzled by the notion of randomness, if they were to try to give it an account in their terms—what, so there’s two alternatives, either of which could happen with equal justification, and then one… just happens? But how is it chosen? What decides, this one and not that one? How does this ‘randomness’ thing work?
And that’s essentially the same criticism leveled against free will: you can’t reduce it to causation and randomness, so it doesn’t make sense. But that’s only an argument if we had any reason to believe that causation and randomness are necessarily primitive; but I don’t see any reason that the world couldn’t be equally well described in terms of causation and free will, or free will alone (as in the occasionalist viewpoint), or causation, randomness, and free will (which indeed some think is the import of the Kochen-Conway free will theorem).