Free Will with a Little Bit of Science! (TM)(C)(R)

Great Debates
41

Imagine we perform a Gallilean transformation on a particle undergoing simple harmonic motion, such that the velocity at every other pass through the equilibrium postion is zero. It’s clear that at every other pass through the equilibrium position the particle is at rest and the net force applied is zero. It’s also clear there’s no points along its trajectory where its velcoity is zero and there is a net force applied. The particle still manages to move, and I bring this up to demonstrate that the idea that a net force is applied to a particle at rest in order to get it to move is actually too simplistic to be a general rule in Newtonian mechanics. You need further clarification and Norton’s dome is consisitent with Newton’s 2nd law as usually stated nowadays, unless you place additional restrcitions.

I would avoid the term random as that is often taken to mean stochastic. The net force is not indeterminate* in Norton’s dome and is always zero at the apex, as mentioned above it is the 2nd derivative of force wrt to time that is indeterminate at the apex.

It is correct to say that this is a highly unstable situation in the sense that any peturbation takes us away from the situation that we are interested in. As I said though I’m making a point about the theory not reality, so that is not important.

The basic argument of the link you posted is that Norton’s dome demonstrates that Newtonian mechanics is incomplete. This is not an unreasonable opinion, but its not a rebuttal.

*NB this depends on how the problem is set up, but the important thing is it can be set so the force is always defined.

42

That’s just not true, all of science is our understanding of how A causes B.
If you’re making a wider philosophical point about inductive logic, then you’re right; deductive and inductive logic are basically starting assumptions we begin from otherwise no reasoning is possible.
However, if you’re using that argument as a defense for free will then that is really admitting failure, since that’s an argument you could use to defend any hypothesis on anything.

This sentence ignores the point I just put to you.
Causality has made and continues to make countless verified predictions and inferences. Free will hasn’t.

That isn’t free will though, that’s illustrating that the brain state of desiring water can cause actions to obtain water (yet more support for causality)!
This is not an illustration of free will. You can notice this by the fact that you could have substituted anything for free will in your argument and it would have equal (zero) explanatory power. X makes me desire water, therefore I go get some water, therefore X.

43

Wouldn’t 100% accuracy just indicate it was perfect at predicting human behavior? I’m not sure how free will fits into it. It’s possible I misunderstood the original post.

44

People tend to be very willing to talk about free will without first defining what it is - and often without having even the vaguest idea of what they think it is.

I think that free will is when an agent makes choices itself. Which is to say, without being directly compelled or controlled by an outside force. Randomity isn’t necessary for a choice to be free, and in fact doesn’t help - if I choose to eat apple pie because I like it that’s more of a real choice than if something in the back of my brain flips a coin. Unpredictability doesn’t help - the fact that you can be pretty darned confident that I won’t choose to run into traffic doesn’t mean that I’m not consciously choosing not to commit suicide.

So yeah - I’m what they call a compatiblist, largely because I consider “it acts unpredictably!” to be a stupid and incoherent definition of free will. So yeah, under my definition of the term there’s nothing problematic about being able to model a brain with 100% accurate predictive power - no matter what method you use to do so.

45

I freely admit to being confused by the idea that a stochastic model could have 100% accurate predictive capability. Doesn’t being stochastic mean that you can run the model twice on exactly the same input data and get different outcomes? How could the varying outcomes always be perfectly correct?

(Note that I know almost nothing about stochastic models - it just sounds self-contradictory on the face of it to me.)

46

I agree, and I think you’ve put it better than I did

47

It comes down to how you measure the accuracy.

If the model says “The most likely outcome is A with probability of 60%.” and A is the state, then you can consider that to be correct.

Alternatively, you have the model produce the top 5 choices, and see if the top 5 choices match.

You can also check the probability accuracy. If A occurs 60% of the time, and the model says A should occur with a probability of 57% this is good. If it says it should occur with a probability of 99% or 5%, then that’s bad.

48

Talking about acceleration. How is it accelerating, i.e. changing it’s velocity if it has no net force?

Ultimately, either there is intrinsic randomness or things or deterministic. If things are deterministic there can’t be free will. Outside of semantic trickery.

With general relativity, correct me if I’m wrong, but the existence of curved space time strongly implies eternalism does it not?

49

I’ve never heard any sort of argument supporting this at all, ever, that didn’t rely entirely on semantic incomprehensibility - or bald-faced tautology. ‘Free will is when you’re utterly unpredictable. Only a completely insane person who plausibly might choose to do anything at any moment has free will.’

50

Imagine a particle at rest at the origin subject to constant force, you could equally ask how the particle ever moves from the origin when its velocity is zero at the origin, but this line of reasoning is similiar to the demonstrably false reasoning in Zeno’s paradoxes. It’s the same thing in Norton’s dome but with higher order derivatives. Though for dome the indeterminacy comes from intial conditions failing to uniquely define the 4th deriviative of position wrt time (the ‘jounce’).

FWIW I think Norton’s dome points to unphysical, but it is still a valid situation in Newtonian theory unless you place restrictions to prevent it.

In general relativity you need to formulate the initial value problem on a something called a Cauchy surface. A Cauchy surface is about a close as you can get to a global instant of time in general relativity (NB Cauchy surfaces intersect, so global time can only be subjective rather than absolute). However you may have a surface that looks like a Cauchy surface in all ways locally, lets call it a local Cauchy surface, but at some point in the future it undergoes a non-Cauchy devlopment, such a wormhole opening up to previously disconnected region of spacetime, bringing influences that were not on the original local Cauchy surface*.Therefore to know that your initial state gives a unique solution, you already have to know that your local Cauchy surface undergoes Cauchy development only for the entire future (and past) and is therefore truly a Cauchy surface.

I wouldn’t say curved spacetime suggests eternalism, but being able to create an initial value problem is not necessary for this point of view.

*In Newtonian physics you can set up a not dissimilar indeterminate situation where objects are able to arrive from infinity in finite time bringing influences from infinity that are independent of the initial state.

51

I honestly have no idea about that. If the position is fixed and the velocity is 0 and the acceleration is 0 and there are no net forces all derivatives should be 0. If they aren’t 0 the sometime in the past the item wouldn’t be balanced on top of the dome with 0 velocity for an indeterminate amount of time. It sort of sounds like some voodoo physics to be honest.

But like I said, I don’t really know. It just logically doesn’t make sense to me.

52

Science yields generalizations from observed regularities; this does not imply any understanding of how those regularities come about. Indeed, if it did, science would be very different: if we could, from looking at an electron, directly infer that it will always alter its path in such-and-such a way when a magnetic field is applied, due to the ‘causal power’ exerted by that magnetic field, then the theory that it does move in this way would not be open to falsification—instead of provisional knowledge, science would then yield certain knowledge.

Consider a very simple world. All you have hitherto observed is two distinct events, A and B, in alternating succession: ABABABABABAB. That may prompt you to confidently predict that the next event in this series is, again, A; but that’s of course not certain. It might even prompt you to formulate a natural law according to which A causes B, which causes A; but that doesn’t mean that the world is necessarily obliged to obey this law. There is nothing that says that the next event couldn’t be C, say. In that case, your earlier theory would be falsified—big deal.

But importantly, this doesn’t make any claims about how A causes B. You could get fancy in your formulation of your natural law and say, well, A has a ‘B-causing power’. But that’s just giving the mystery a name. And that’s exactly what’s done in physics: what does the work of causation there is energy (more abstractly, action), typically defined as something like ‘the capacity to perform work’. ‘Work’, then, is something like producing a change of state in some object—so energy is just the capacity of causing changes. Do we now understand how causation works? How energy imbues an object with ‘the capacity of causing changes’? No, we don’t; all we know is that we have successful theories based on this idea. But these, like all theories, could be proven wrong tomorrow—which would, of course, just prompt us to find new ones, but these would just as much depend on stipulated powers like ‘the capacity of causing changes’.

You might think of the process of finding laws of physics like the process of finding the best compression of the data you’ve taken. ‘Physics’ in the AB world is completely described by the law ‘A causes B, and B causes A’, combined with the initial condition ‘A’ (until it isn’t, that is)—which is just a way of finding the maximally compressed version of the string ‘ABABABABABABABA…’. It does not, thereby, tell us what it is about A that causes B, or how it does so. This is the same situation with the electron in the magnetic field, or any other physical system.

Again, that’s just you accepting causality as a primitive notion—it would be just as well supported to use free will instead. It’s not evidence for causality—you can use the concept of causality as a fig leaf for how a state at a certain time led to a state at another; but you can equally well support the concept of free will. Both are just as unanalyzable—it is only habit that causes you to prefer causation (or perhaps, it is only your free will that does).

53

Just because the laws cannot be written down with 100% accuracy at this point in time doesn’t mean that the universe does not act according to physical law. And why does the why matter? If something just is and is deterministic then it follows all of biology is deterministic. If the universe is supernatural or has true sources of fundamental randomness then it would appear that that the universe is nondeterministic. What have experiments shown with regards to true randomness?

54

It’s not a practical issue, it’s a conceptual one: even if we knew the complete physical law ‘according to’ which the universe acts, we would not know by what powers said law makes the universe act accordingly. Whenever we say, A causes B, we’re in fact just using words to paper over a hole in our understanding—that’s what’s usually leveled against free will: nobody has a theory of how free will works, hence, you’re not really making sense by appealing to it. But it goes just as well for the notion of causation. So in particular, arguments that free will is nonsense because everything is just due to causality really just replace one mystery with another.

As for randomness, no experiment will ever demonstrate true randomness: you can always write down a deterministic system giving the same predictions to any degree of accuracy.

55

This kind of “generalization” goes beyond science, it’s necessary for any empirical rational thought whatsoever. A baby needs to make the same kind of generalization to learn to pick up a ball.

And, indeed, free will (however you eventually decide to define it) would also need to stand on this same edifice.

Oh, absolute certainty now.
Once again, this level of reasoning could be used to defend any hypothesis equally weakly.
What the bleep do we know, we don’t have certain knowledge of anything.

By this logic magic pixies controlling me is an equally good model.

In reality, science pares down models to the minimum required; unless and until the magic pixie model makes a prediction specific to their existence (e.g. predicting we’d find pixie dust), we Occam’s away that part of the model.
That’s where your idea of free will currently lies. Your idea of free will is essentially magic pixies until you define what you mean by free will and what the difference is between the current best model of past data and neurology resulting in our decisions.

56

I’m not defending the hypothesis of free will, I’m pointing out that the attacks levied against it can equally well be mounted against the notion of causation.

You claim that free will is ‘magical pixie dust’ unless I can define it. Fine—but then, so’s causation. What we have in terms of data is observed regularities. From these, you infer that there’s this mythical notion that something ‘causes’ something else. You could just as well claim that there’s an equally mythical notion of ‘free will’ by which these things happen.

That’s again not a defense of free will; I don’t know if such a thing exists. But that’s just the same with causation, so using the latter to attack the former just misses the plot.

57

This is true, but consider a gradual “upload” process by which, as you age and your neurons start to fail, they are gradually replaced with artificial neurons of whatever kind you want to posit. Certainly those neurons may function somewhat differently then regular old neurons subject to biochemistry, but what makes this of greater “concern” towards the continuity of consciousness then a sprinter who loses his legs in an accident but has them replaced with prosthetics, which are not subject to, for example, the buildup of lactic acid during strenuous physical exertion?

58

You guys are aware of ongoing debates about causality, and that other people have thought in great detail about it for a long time?
 

The Metaphysics of Causation (Stanford Encyclopedia of Philosophy)

Causation | Internet Encyclopedia of Philosophy

59

Besides, the general issue of inductive reasoning is somewhat beside the point (although Hume got there via his skeptical analysis of causation). You can still just as validly make the same inductive generalization from an observed regularity regarding its continuation into the future (which may, or may not, be true), but this won’t tell you anything about how causation works. If you could know the essence of causation, then the inductive generalization wouldn’t be necessary: instead of saying ‘because I have observed B reliably following A, hence, I infer that whenever I observe A, I will, all else being equal, observe B next’, you could say, ‘because of As B-causing powers, I know that whenever A, necessarily B’.

But allowing inductive reasoning does not entail the necessity of causation. Suppose there is free will, and suppose a free agent decides to follow every A with a B, and vice versa: then, the inductive conclusion that B will follow A will hold just as well. Indeed, we can conceive of a whole universe in this way: every state of the universe is due to the free choice of some entity (something like Malebranche’s occasionalism). Then, there will be natural laws, as long as the sequence of events isn’t maximally random, and we will be able to make inductive inferences, and we may talk about ‘causation’ and the like, just as we do in this world.

And no, I don’t know how that entity freely choses each new state of the world. But—and this is really the only point I’m making—I don’t know how a state of the world A causes a state of the world B, either. We’re just more used to accepting the mystery of the latter.

So no, I’m not questioning the basis of ‘any empirical rational thought whatsoever’; it’s just that causation doesn’t enter into this basis.

60

Huh, that’s a very interesting thought I had not considered.