Prediction, incentive, and free will

Originally posted by tojo
Of course, there is also the theory that time splits reality into an infinite number of alternate realities, where not only is everything possible, but can and will happen, in at least one of these realities.

By this, I mean, you make one decision, you follow one path in time, but at the same instant, you also make the opposite desicion, and continue ...[text shortened]... ll existed for the test subject. Therefore, no paradox?

Or is this a bit of a cop-out theory?

I think it may be a cop-out. I think the paradox applies in one universe only, however many universes there are.

Originally posted by Pawnokeyhole
That's odd: I thought my machine might be a counterexample to determinism.

No - a counter-example to that would be someone choosing to defy the machine. But that may not be possible. The existence of the machine is a counter-example to non-compatibilist accounts of free will.

Originally posted by dottewell
No - a counter-example to that would be someone choosing to defy the machine. But that may not be possible. The existence of the machine is a counter-example to non-compatibilist accounts of free will.

Sorry, ignore my silly last post. Absinthe makes the mind grow duller...

I see what you mean.

However, I submit that the machine, if it worked, would be merely proof of determinism, not of the compatibilist view of the determinism/free will debate, viz. that both determinism and free will can co-exist. That is, the existence of the machine would no more support compatibilism than it would support non-compatibilism.

However, the existence of the machine would, I believe, support determinism over indeterminism--if predictability implies determinism--and hence would rule out free will as libertarians conceive it (or, at least, try to conceive it, as they have trouble)--the last being the point I believe you were trying to make.

Originally posted by Pawnokeyhole
Such a reason seems a priori very unlikely, based on a knowledge of (ironically, somewhat predictive and deterministic) human psychology.

It seems odd that, just to "please the machine", an extraordinary reason would emerge that would override greed or selflessness.

Would nature just produce such reason on demand in this situation?

This strikes me as one key point, so I reiterate:

Doesn't it strike you as dreadfully convenient, dottewell, that nature would oblige the machine by producing reasons/causes capable of overriding subjects' natural tendency to take the $1,000,000 that I am offering them for defying the prediction?

Originally posted by Pawnokeyhole
This strikes me as one key point, so I reiterate:

Doesn't it strike you as dreadfully convenient, dottewell, that nature would oblige the machine by producing reasons/causes capable of overriding subjects' natural tendency to take the $1,000,000 that I am offering them for defying the prediction?

It does.

Originally posted by dottewell
It does.

And does not convenient, in this context, imply implausible?

Originally posted by Pawnokeyhole
And does not convenient, in this context, imply implausible?

Not necessarily. But it seems to show that the consequences of determinism can be counter-intuitive.

Originally posted by Pawnokeyhole


Dr. Scribbles opined that the machine cannot exist. I think his reason was that

My reason is based on the following sort of proof.

Claim: The machine described in the original post cannot logically exist.

Proof by Contradiction:

Suppose the machine does exist. Call it M.

Construct a much simpler machine M' that reads the output of M and negates it. If M says Yes about anything, then M' says No.

Then, ask machine M to predict whether the next output of machine M' will read Yes. Machine M must make a wrong prediction, for if M answers Yes, M' will answer No, and vice versa.

But this is a contradiction, because M, by definition, does not make wrong predictions. Therefore, the supposition is false, and M cannot in fact exist.

Thus, the claim is true.

Originally posted by DoctorScribbles
My reason is based on the following sort of proof.

Claim: The machine described in the original post cannot logically exist.

Proof by Contradiction:

Suppose the machine does exist. Call it M.

Construct a much simpler machine M' that reads the output of M and negates it. If M says Yes about anything, then M' says No.

Then, ask mach ...[text shortened]... s. Therefore, the supposition is false, and M cannot in fact exist.

Thus, the claim is true.

Nicely done. It has a sort of Turing flavour to it. I'm surprised its like did not appear in GEB.

Originally posted by royalchicken
I'm surprised its like did not appear in GEB.

I'm not convinced that it is actually a sound proof. I think it requires some further assumptions about the universe or M.

In particular, as is, a refutation of the proof could be the observation that the universe and M may be such that the existence of M yields conditions such that M' cannot be constructed - I haven't given an existence proof for M'. That is, my assumption that M' can be constructed is tantamount to assuming the crux of the original problem, that the man can take the money and exercise his will to defy the machine. However, I have a rebuttal in mind if somebody cares to make that refutation.

Another refutation concerns the decidability of the problems that M solves. How is my proof affected if M spins ad infinitum? Is M allowed to be asked undecidable questions? If so, then my proof is in big trouble.

In contrast, everything in GEB is sound.

Originally posted by DoctorScribbles
I'm not convinced that it is actually a sound proof. I think it requires some further assumptions about the universe or M.

In particular, as is, a refutation of the proof could be the observation that the universe and M may be such that the existence of M yields conditions such that M' cannot be constructed - I haven't given an existence proof ...[text shortened]... l in mind if somebody cares to make that refutation.

In contrast, everything in GEB is sound.

I'm not convinced there is a problem. Do you agree that for each sequence of questions, M will produce an unambiguous string of yes/no answers? This can clearly be written as a string of countably many 0s and 1s -- a real number m. The machine M' consists simply of an algorithm for generating another (unique) real number m' such that m+m' = 0, where '+' is digitwise addition mod 2. Why wouldn't such an algorithm be constructible?

By the last question, I mean 'Such an algorithm is trival to construct!'.

Originally posted by royalchicken
Why wouldn't such an algorithm be constructible?

My concern isn't with the existence of the algorithm. My concern is more of a metaphysical one - could the algorithm actually be implemented and brought into physical existence, given that M already physically exists?

That is, if one doesn't dismiss the original problem out of hand by saying that obviously the man has free will to defy the machine and thus it can't exist, then one believes that the existence of the machine may somehow negate man's free will. (On the other hand, if one does dismiss the problem out of hand and does not invoke that concern, then my proof is unnecessary. ) Man may not have the free will to bring M' into existence if M exists.

Physically bringing M' into existence is an instance of the man defying the machine's prediction - he can simply ask M' to tell him what to do, always defying M. I can't assume the feasibility of that class of acts in the proof, but question it in the problem. The only reason I'd need to furnish the proof is if somebody doubted that man could defy the machine's prediction, of which the construction of M' is an instance. I think this refutation can be dispatched with by creating M' first - then, either M can't be brought into existence due to M' already existing or it can, and in either case, the conclusion holds.*

Also, note my edits concerning decidability. While the metaphysical reservations I have may not logically refute the proof, the decidability issues do. The definition of M needs to specify its behaviour under undecidable questions. I need to know if M always terminates when asked for a prediction. (I suppose it could be argued that it must, since if it perfectly predicts what I will do X seconds from now, then presumably it must furnish an answer within X seconds, or else it is not predicting. Considering this, I think my proof may be sound after all. )

Finally, your new avatar throws me off balance. Seeing the flag, I initially thought that chancremechanic had worked his way through GEB.

Dr. S

EDIT: *GRRRR! This doesn't work either! In that case, I have only proved that M cannot exist in a universe that contains M'; I haven't proved that M cannot exist. Quick, somebody build M'.

P.S. Could any M have predicted that I would have required 19 edits to disprove its existence?

Originally posted by Pawnokeyhole
Suppose I make a machine that can predict your future behavior perfectly.

In the future, one minute from now, you will have to choose to take either a harmless purple pill, or not. Everything has been neatly prearranged and is going to plan, so barring very unlikely circumstances, you will be in position to make that choice, pill in hand, one minute ...[text shortened]... n practice)?

3) Does quantum uncertainty necessarily exist to prevent a paradox from forming?

Can you refuse to do what the machine predicts?

No, because if you could, the machine would not have been able to predict your behavior. Since it can, you WILL do whatever it predicts no matter what.

Originally posted by DoctorScribbles
My concern isn't with the existence of the algorithm. My concern is more of a metaphysical one - could the algorithm actually be implemented and brought into physical existence, given that M already physically exists?

That is, if one doesn't dismiss the original problem out of hand by saying that obviously the man has free will to defy the mac ...[text shortened]...
P.S. Could any M have predicted that I would have required 19 edits to disprove its existence?

Very interesting and nicely argued.

So, let's suppose that your basic argument is sound, and that we have taken care of the relevant decidability and metaphysical objections. Let's suppose that the machine can't exist.

But suppose--having as much disdain for logic as RBHILL--we then try to build one anyway. Suppose too that we have unlimited time and resources at our disposal to waste on this boondoggle.

Logic guarantees that our attempt will fail. But I'm wondering what would happen *in concrete terms* to guarantee that failure.

Would we be unable to implement algorithms on the machine that were up to the task (a software problem)?

Or would the construction of the actual physical device be impossible (a hardware problem)?

Or would there be a horizon of predictability, perhaps fueled by quantum uncertainty, that stops the machine (an "externalware" problem)?

Or would ANY of these have to happen, and not just one or the other?

My suspicion is that the software would be impossible to implement.

P.S.

If I was potentially willing to play the role of M' (and I am) would that be enough to stop M coming into existence in this universe? Would it, as it were, get scared?

P.P.S.

Can you make M' before M exists?

Originally posted by AThousandYoung
[b]Can you refuse to do what the machine predicts?

No, because if you could, the machine would not have been able to predict your behavior. Since it can, you WILL do whatever it predicts no matter what.[/b]

First, suppose a perfect predictive machine exists.

Now suppose you didn't know of the machine's prediction. Then there would be no logical obstacle to its predicting your behavior. (Note: there would also be no problem with the machine predicting the behavior of all conscious beings, like hamsters and babies, how cannot grasp the prediction. They cannot be aware of it; but you just happen not to be aware of it)

However, suppose that you now learned of the machine's prediction. Now the machine's perfect predictivity could run into trouble, if everyday intuitions about free will are correct (cf. "Minority Report"😉

But maybe what would happen is that circumstances would conspire, not to make you act in accord with the prediction, but to prevent you learning of the prediction in the first place! That would also be sufficient to stop the paradox arising.