Free will is "compatible" with determinism not because of chaos. Free will requires both determinism and predictability, as one can determine the future according to own preferences exactly because the future is predictable to a sufficient extent (for each possible action). The future is mathematically definite, it never changes, just as past never changes (for that would require the confused meta-time). You determine the future, with your freedom to determine your own actions (for the actions are defined in terms of your thoughts; you are stuff physics). Chaos, making predictability more difficult, is actually a force against free will.
Also, existence of Laplace's demon is perfectly epiphenomenal to what happens within physics, not affecting anything.
Well, chaos has more than one effect, but I was thinking primarily of the unpredictability of systems that carry out arbitrary computations (halting problem etc). Of course, computational systems do indeed depend on the future being at least somewhat deterministic.
You'd need to unpack this and explain in what sense you expect this "unpredictability of systems" (what systems, examples?) to help with "free will" (ability to make decisions according to own preference). What do you refer to about halting problem? How are "arbitrary" computations relevant, being arbitrary?
You seem to be trying to explain a mysterious phenomenon with mysterious explanations.
Certainly I would need to unpack all those terms if I were writing an essay that fully explained the matter, something suitable for a top-level post on the main site. In this case, I'm assuming the reader either has read or will/may be motivated to read what's already been written here on the topic, and I'm just posting (unedited and unembellished) an actual case study where it came up in conversation with someone who is neither a philosopher nor a scientist. I find a sloppy actual example is worth more than a perfectly polished hypothetical example, but if you find otherwise, fair enough.
In this case, I'm assuming the reader either has read or will/may be motivated to read what's already been written here on the topic [...]
Where? I don't recall arguments on LW that support chaos as explaining free will. You should've linked to them in any case if you believe they exist, but at least do so now.
It is possible for universes to exist that allow what we'd call free will but don't have determinism or predictability. Quantum mechanical universes, for example (as long as the universe really contains everything).
Quantum mechanics has both determinism (in many-worlds) and predictability (of probability). There are ways to salvage your argument, but unless you signal otherwise, I'll assume it was as simple as this.
Maybe you could help me out here then :P After all, if a proof of a theorem exists, then the theorem is true.
Quantum mechanics has determinism in MWI except when choosing which point in world-space you see - you see one point in the space, at random. Since all observers obey these rules (which is why I added that caveat), MWI produces non-deterministic answers to questions, because the answer depends on the observer's point in world-space. I'd agree that probability can be predicted, and if you mean "something can be predicted" by "predictability," thats okay, I just thought you meant "the entire universe can be predicted."
Perhaps the way you saw to "salvage" this was by saying that if a universe running on classical physics can have free will, any ol' sort of universe that reproduces classical physics in the macroscopic limit will have free will?
Quantum mechanics has determinism in MWI except when choosing which point in world-space you see - you see one point in the space, at random.
No, you see all outcomes simultaneously, it's just that different decohered copies of you see different outcomes. And each copy is associated with an "objective" probability value that is morally relevant, which is why you care about predicting (subjectively) this "objective" probability value.
I'd agree that probability can be predicted, and if you mean "something can be predicted" by "predictability," thats okay, I just thought you meant "the entire universe can be predicted."
Predicting "something" is enough, but the details you pointed out trouble with prediction of can also be predicted.
Perhaps the way you saw to "salvage" this was by saying that if a universe running on classical physics can have free will, any ol' sort of universe that reproduces classical physics in the macroscopic limit will have free will?
Preference can be about mathematical structures that are not processes, that don't have time in them, so that the notion of "predictability" becomes inapplicable, while decision-making is still possible. Alternatively, preference could be about a mathematical structure that is a process, and in which "predicting" is not possible in some sense, but preference cares about some aspect of that structure other than what requires predictability.
Quantum mechanics has determinism in MWI except when choosing which point in world-space you see - you see one point in the space, at random.
No, you see all outcomes simultaneously, it's just that different decohered copies of you see different outcomes. And each copy is associated with an "objective" probability value that is morally relevant, which is why you care about predicting (subjectively) this "objective" probability value.
Simple difference in the definition of "you." If we translated my statement into your set of definitions, we'd have your statement "each copy is associated with an "objective" probability value." MWI seems deterministic because if it was possible to see the whole universe at once, it wouldn't be nondeterministic. But it's not, so it is.
I see what you mean now about predictability. The problem was that you were using the same word as the original post in a different way - you meant "prediction made by the free-willed agent in order to make a decision," rather than "prediction of a supposedly free-willed agent's actions ahead of time." And so what I meant was that quantum mechanics outlaws the second one.
Well, given the horrible things you might do to the definition of "agent," I guess I should specify "how a copy of you would measure the agent" :D
MWI seems deterministic because if it was possible to see the whole universe at once, it wouldn't be nondeterministic. But it's not, so it is.
If you don't see something, it's still there. If you know what it is, you don't need to observe it to know what it is. There is no uncertainty about which copy is you, you are both. There is no uncertainty about what outcome is observed, both outcomes are observed. Everything is perfectly deterministic in the relevant sense.
you meant "prediction made by the free-willed agent in order to make a decision," rather than "prediction of a supposedly free-willed agent's actions ahead of time." And so what I meant was that quantum mechanics outlaws the second one.
It doesn't, because the concept of "future agent's actions" is incoherent, there is no unique agent to refer to, there are multiple copies instead. And everything is in principle known about all the copies.
If you don't see something, it's still there. If you know what it is, you don't need to observe it to know what it is. There is no uncertainty about which copy is you, you are both. There is no uncertainty about what outcome is observed, both outcomes are observed. Everything is perfectly deterministic in the relevant sense.
Okay, so you've shown that you can indeed make the world deterministic, for suitable definitions of "you," "world," and "deterministic." You're right.
Now try swapping definitions for a second. This may be even harder for you than it is for me. All it takes to make the universe nondeterministic is a definition change to "you" that is, in fact, totally undetectable, since all our measurements fall within the memory of just one point in world-space. And since the difference is undetectable, why not try thinking with it for a while?
you meant "prediction made by the free-willed agent in order to make a decision," rather than "prediction of a supposedly free-willed agent's actions ahead of time." And so what I meant was that quantum mechanics outlaws the second one.
It doesn't, because the concept of "future agent's actions" is incoherent, there is no unique agent to refer to, there are multiple copies instead. And everything is in principle known about all the copies.
For my clarification, please refer to the last sentence of my previous post.
EDIT: Being less of a jerk.
Now try swapping definitions for a second. This may be even harder for you than it is for me. All it takes to make the universe nondeterministic is a definition change to "you" that is, in fact, totally undetectable, since all our measurements fall within the memory of just one point in world-space.
Not just a question of definitions, since one of the alternatives doesn't make sense. The question of which of the copies is "you" doesn't define a correct answer, whatever notion of "you" is used. (By the way, I don't understand what do you mean by ""you" that is totally undetectable".)
For my clarification, please refer to the last sentence of my previous post.
As far as I see, the last statement is as follows, and I don't see how it helps:
Well, given the horrible things you might do to the definition of "agent," I guess I should specify "how a copy of you would measure the agent" :D
Hm, perhaps I should try to flesh out the parallels in measurement theory between MW and Copenhagen, and see if you agree.
Before measurement is considered, one possible outcome in Copenhagen is exactly identical to one point in world-space in MWI.
And even for the act itself, measurement is measurement. You find the wavefunction of your detector at some time, and this gives you a probability distribution over your Hilbert space, with each point in Hilbert space being one possible outcome/one world.
The difference is in (surprise) interpretation and surrounding procedures. MWI only lets you measure the wavefunction of the entire universe, but in exchange it lets the universe just evolve deterministically. Copenhagen lets you measure small parts of the universe, simplifying many computations, but this 1) often requires the complicated machinery of collapse and entanglement and 2) treats these parts of the universe as real.
Since we don't know the state of the universe, MWI makes predictions by conditioning on the statement of the problem at hand, e.g. "given that the spin of an electron points along x at t=0..." This makes it trickier to talk about "you." The machinery of the Copenhagen interpretation lets us talk about "you" quite easily, you're handled as a part of the universe, and our classical experience translates nicely. But MW makes it a bit harder - the most useful approach I know is to just to construct a hypothetical "you" state, relying on empirical evidence that you have one. But what is the "real you" with known distribution in Hilbert space that gets conditioned on in order to actually predict things? Which points in this very general space still qualify as a possible "you?"
Fortunately, for most applications we can dodge the hard questions by just answering "me from 5 minutes ago" and "everything with reasonable probability is still me." A long series of this simplification gives the familiar image of a tree-ish volume in you-space plus time, all "you" at different times.
But notice that one point in MW's you-space equals one possible you in Copenhagen, just like one point in the Hilbert space of the universe can be either a possible state or a point in world-space. So "you" in MW corresponds to the entire set of possible yous in Copenhagen. Similarly, you in Copenhagen corresponds to one point in you-space.
Surely "you" could tell if you were a spread out function or a single point, right? Well, no. Why not? Because whenever you're measured, what matters are the properties of a single point in you-space, which are identical between MW and Copenhagen, as long as the statement of the problem was the same.
So you cannot tell by any measurement whether you are you(M) or you(C). That's what I meant by "a definition change to "you" that is... totally undetectable."
The question of which of the copies is "you" doesn't define a correct answer
So if you want to go from MWI to Copenhagen, what you do is make a measurement, thus choosing one point from the Hilbert space, and then treat that point as real. So there are no "copies," really, there are only "possible yous that didn't turn out to be you when measured."
There is no uncertainty about which copy is you, you are both.
However there's no one who can say "I am both copies".
Ok. There's no one who can truthfully say "I am both copies".
Let's ban word truth. There's no one who can say "I am both copies" and prove it has same sense as in "I am I (this living thing that speaks those words)" (e.g. I can control my body. I can react to external events in a way I'm previously described or agreed to do.)
one of the most important discoveries of 20th-century mathematics is that in general the behavior of a complex system cannot be predicted -- or rather, there is no easier way to predict it than to run it and see what happens.
Really? Please elaborate - what theorems are these?
I assume he was referring to the undecidability of the halting problem and Rice's Theorem, although it would be more accurate to say that the behavior of some complex systems cannot be predicted, full stop.
A practical albeit fictional application of the philosophical conclusion that free will is compatible with determinism came up today in a discussion about a setting element from the role-playing game Exalted
(5:31:44 PM) Nekira Sudacne: So during the pirmodial war, one Yozi got his fetch killed and he reincarnated as Sachervell, He Who Knows The Shape of Things To Come. And he reincarnated asleep. and he has remained asleep. And the other primordials do all in their power to keep him asleep. and he wants to be asleep.
For you see, for as long as he sleeps, he dreams only of the present. should he awaken, he will see the totaltiy of exsistance, all things past and future exsactly as they will happen. quantumly speaking he will lock the universe into a single shape. All things that happen will happen as he sees them happen and there will be no chance for anyone to change it. effectivly nullifying chance for change. Even he cannot alter his vision for his vision takes into account all attempts to alter it.
And there's a big debate over rather or not this is a game ending thing. Essentially, does predestination negate freewill or not
(5:32:17 PM) Nekira Sudacne: and this is important, because one of the requirements for Exaltation to function is freewill. if Sachervell is able to negate freewill, then Exaltations will cease to function
(5:32:44 PM) Nekira Sudacne: and maddenly enough the game authors are also on the thread arguing because THEY don't agree where to go with it either :)
(5:38:02 PM) rw271828: ah, well I happen to know the answer :-)
(5:39:23 PM) rw271828: one of the most important discoveries of 20th-century mathematics is that in general the behavior of a complex system cannot be predicted -- or rather, there is no easier way to predict it than to run it and see what happens. Note in particular:
(5:39:41 PM) rw271828: 1. This is a mathematical fact, so it applies in all possible universes, including Exalted
(5:40:01 PM) rw271828: 2. Humans and other sentient lifeforms are complex systems in the relevant sense
(5:41:33 PM) rw271828: so if you postulate an entity that can actually see the future (as opposed to just extrapolate what is likely to happen unless something intervenes), the only way to do that is for that entity to run a perfect simulation, a complete copy of the universe
(5:42:50 PM) rw271828: if you're willing to postulate that, well fine, continue the game, and just note that you are running it in the copy the entity is using to make the prediction - the people in the setting still have free will, it is their actions that determine the future, and thus the result of the prediction ^.^
(5:43:04 PM) Nekira Sudacne: Hah. nice one