If you say this, then you believe in backwards causality (or a breakdown of the very notion of causality, as in Kevin’s comment below). I agree that if causality doesn’t work, then I should take only Box B, but nothing in the problem as I understand it from the original post implies any violation of the known laws of physics.
If known physics applies, then Omega can predict all it likes, but my actions after it has placed the boxes cannot affect that prediction. There is always the chance that it predicts that I will take both boxes but I take only Box B. There is even the chance that it will predict that I will take only Box B but I take both boxes. Nothing in the problem statement rules that out. It would be different if that were actually impossible for some reason.
I will not regret taking only one box.
I knew that you wouldn’t, of course, since you’re a one-boxer. And we two-boxers will not regret taking both boxes, even if we find Box B empty. Better $1000 than nothing, we will think!
If known physics applies, then Omega can predict all it likes, but my actions after it has placed the boxes cannot affect that prediction. There is always the chance that it predicts that I will take both boxes but I take only Box B. There is even the chance that it will predict that I will take only Box B but I take both boxes. Nothing in the problem statement rules that out. It would be different if that were actually impossible for some reason.
Ah, I see what the probem is. You have a confused notion of free will and what it means to make a choice.
Making a choice between two options doesn’t mean there is a real chance that you might take either option (there always is at least an infinitesimal chance, but that it always true even for things that are not usefully described as a choice). It just means that attributing the reason for your taking whatever option you take is most usefully attributed to you (and not e.g. gravity, government, the person holding a gun to you head etc.). In the end, though, it is (unless the choice is so close that random noise makes the difference) a fact about you that you will make the choice you will make. And it is in principle possible for others to discover this fact about you.
If it is a fact about you that you will one-box it is not possible that you will two-box. If it is a fact about you that you will two-box it is not possible that you will one-box. If it is a fact about you that you will leave the choice up to chance then Omega probably doesn’t offer you to take part in the first place.
Now, when deciding what choice to make it is usually most useful to pretend there is a real possibility of taking either option, since that generally causes facts about you that are more benefitial to you. And that you do that is just another fact about you, and influences the fact about which choice you make. Usually the fact which choice you will make has no consequences before you make your choice, and so you can model the rest of the world as being the same in either case up to that point when counterfactually considering the consequences of either choice. But the fact about which choice you will make is just another fact like any other, and is allowed, even if it usually doesn’t, to have consequences before that point in time. If it does it is best, for the very same reason you pretend that either choice is a real possibility in the first place, to also model the rest of the world as different contingent on your choice. That doesn’t mean backwards causality. Modeling the word in this way is just another fact about you that generates good outcomes.
It’s not really too late then. Omega can predict what you’ll do between seeing the boxes, and choosing which to take. If this is going to include a decision to take one box, then Omega will put a million dollars in that box.
TobyBartels:
If you say this, then you believe in backwards causality (or a breakdown of the very notion of causality, as in Kevin’s comment below). I agree that if causality doesn’t work, then I should take only Box B, but nothing in the problem as I understand it from the original post implies any violation of the known laws of physics.
I remember reading an article about someone who sincerely lacked respect for people who were ‘soft’ (not exact quote) on the death penalty … before ending up on the jury of a death penalty case, and ultimately supporting life in prison instead. It is not inconceivable that a sufficiently canny analyst (e.g. Omega) could deduce that the process of being picked would motivate you to reconsider your stance. (Or, perhaps more likely, motivate a professed one-boxer like me to reconsider mine.)
If you say this, then you believe in backwards causality (or a breakdown of the very notion of causality, as in Kevin’s comment below). I agree that if causality doesn’t work, then I should take only Box B, but nothing in the problem as I understand it from the original post implies any violation of the known laws of physics.
I don’t see what that link has to do with anything in my comment thread. (I haven’t read most of the other threads in reply to this post.)
I should explain what I mean by ‘causality’. I do not mean some metaphysical necessity, whereby every event (called an ‘effect’) is determined (or at least influenced in some asymmetric way) by other events (called its ‘causes’), which must be (or at least so far seem to be) prior to the effect in time, leading to infinite regress (apparently back to the Big Bang, which is somehow an exception). I do not mean anything that Aristotle knew enough physics to understand in any but the vaguest way.
I mean the flow of macroscopic entropy in a physical system.
The best reference that I know on the arrow of time is Huw Price’s 1996 book Time’s Arrow and Archimedes’ Point. But actually I didn’t understand how entropy flow leads to a physical concept of causality until several years after I read that, so that might not actually help, and I’m having no luck finding the Internet conversation that made it click for me.
But basically, I’m saying that, if known physics applies, then P(there is money in Box B|all information available on a macroscopic level when Omega placed the boxes) = P(there is money in Box B|all information … placed the boxes & I pick both boxes), even though P(I pick both boxes|all information … placed the boxes) < 1, because macroscopic entropy strictly increases between the placing of the boxes and the time that I finally pick a box.
So I need to be given evidence that known physics does not apply before I pick only Box B, and a successful record of predictions by Omega will not do that for me.
The Psychopath Button: Paul is debating whether to press the ‘kill all psychopaths’ button. It would,
he thinks, be much better to live in a world with no psychopaths. Unfortunately,
Paul is quite confident that only a psychopath would press such a button. Paul
very strongly prefers living in a world with psychopaths to dying. Should Paul
press the button? (Set aside your theoretical commitments and put yourself in
Paul’s situation. Would you press the button? Would you take yourself to be
irrational for not doing so?)
Newcomb’s Firebomb:
There are two boxes before you. Box A definitely contains $1,000,000. Box B definitely
contains $1,000. You have two choices: take only box A (call this one-boxing), or take
both boxes (call this two-boxing). You will signal your choice by pressing one of two
buttons. There is, as usual, an uncannily reliable predictor on the scene. If the predictor
has predicted that you will two-box, he has planted an incendiary bomb in box A, wired
to the two-box button, so that pressing the two-box button will cause the bomb to
detonate, burning up the $1,000,000. If the predictor has predicted that you will one-box,
no bomb has been planted – nothing untoward will happen, whichever button you press.
The predictor, again, is uncannily accurate.
I would suggest looking at your implicit choice of counterfactuals and their role in your decision theory. Standard causal decision theory involves local violations of the laws of physics (you assign probabilities to the world being such that you’ll one-box, or such that you’ll one-box, and then ask what miracle magically altering your decision, without any connection to your psychological dispositions, etc, would deliver the highest utility). Standard causal decision theory is a normative principle for action, that says to do the action that would deliver the most utility if a certain kind of miracle happened. But you can get different versions of causal decision theory by substituting different sorts of miracles, e.g. you can say: “if I one-box, then I have a psychology that one-boxes, and likewise for two-boxing” so you select the action such that a miracle giving you the disposition to do so earlier on would have been better. Yet another sort of counterfactual that can be hooked up to the causal decision theory framework would go “there’s some mathematical fact about what decision(decisions given Everett) my brain structure leads to in standard physics, and the predictor has access to this mathematical info, so I’ll select the action that would be best brought about by a miracle changing that mathematical fact”.
If you say this, then you believe in backwards causality (or a breakdown of the very notion of causality, as in Kevin’s comment below). I agree that if causality doesn’t work, then I should take only Box B, but nothing in the problem as I understand it from the original post implies any violation of the known laws of physics.
If known physics applies, then Omega can predict all it likes, but my actions after it has placed the boxes cannot affect that prediction. There is always the chance that it predicts that I will take both boxes but I take only Box B. There is even the chance that it will predict that I will take only Box B but I take both boxes. Nothing in the problem statement rules that out. It would be different if that were actually impossible for some reason.
I knew that you wouldn’t, of course, since you’re a one-boxer. And we two-boxers will not regret taking both boxes, even if we find Box B empty. Better $1000 than nothing, we will think!
Ah, I see what the probem is. You have a confused notion of free will and what it means to make a choice.
Making a choice between two options doesn’t mean there is a real chance that you might take either option (there always is at least an infinitesimal chance, but that it always true even for things that are not usefully described as a choice). It just means that attributing the reason for your taking whatever option you take is most usefully attributed to you (and not e.g. gravity, government, the person holding a gun to you head etc.). In the end, though, it is (unless the choice is so close that random noise makes the difference) a fact about you that you will make the choice you will make. And it is in principle possible for others to discover this fact about you.
If it is a fact about you that you will one-box it is not possible that you will two-box. If it is a fact about you that you will two-box it is not possible that you will one-box. If it is a fact about you that you will leave the choice up to chance then Omega probably doesn’t offer you to take part in the first place.
Now, when deciding what choice to make it is usually most useful to pretend there is a real possibility of taking either option, since that generally causes facts about you that are more benefitial to you. And that you do that is just another fact about you, and influences the fact about which choice you make. Usually the fact which choice you will make has no consequences before you make your choice, and so you can model the rest of the world as being the same in either case up to that point when counterfactually considering the consequences of either choice. But the fact about which choice you will make is just another fact like any other, and is allowed, even if it usually doesn’t, to have consequences before that point in time. If it does it is best, for the very same reason you pretend that either choice is a real possibility in the first place, to also model the rest of the world as different contingent on your choice. That doesn’t mean backwards causality. Modeling the word in this way is just another fact about you that generates good outcomes.
Alicorn:
TobyBartels:
I remember reading an article about someone who sincerely lacked respect for people who were ‘soft’ (not exact quote) on the death penalty … before ending up on the jury of a death penalty case, and ultimately supporting life in prison instead. It is not inconceivable that a sufficiently canny analyst (e.g. Omega) could deduce that the process of being picked would motivate you to reconsider your stance. (Or, perhaps more likely, motivate a professed one-boxer like me to reconsider mine.)
Beware hidden inferences. Taboo causality.
I don’t see what that link has to do with anything in my comment thread. (I haven’t read most of the other threads in reply to this post.)
I should explain what I mean by ‘causality’. I do not mean some metaphysical necessity, whereby every event (called an ‘effect’) is determined (or at least influenced in some asymmetric way) by other events (called its ‘causes’), which must be (or at least so far seem to be) prior to the effect in time, leading to infinite regress (apparently back to the Big Bang, which is somehow an exception). I do not mean anything that Aristotle knew enough physics to understand in any but the vaguest way.
I mean the flow of macroscopic entropy in a physical system.
The best reference that I know on the arrow of time is Huw Price’s 1996 book Time’s Arrow and Archimedes’ Point. But actually I didn’t understand how entropy flow leads to a physical concept of causality until several years after I read that, so that might not actually help, and I’m having no luck finding the Internet conversation that made it click for me.
But basically, I’m saying that, if known physics applies, then P(there is money in Box B|all information available on a macroscopic level when Omega placed the boxes) = P(there is money in Box B|all information … placed the boxes & I pick both boxes), even though P(I pick both boxes|all information … placed the boxes) < 1, because macroscopic entropy strictly increases between the placing of the boxes and the time that I finally pick a box.
So I need to be given evidence that known physics does not apply before I pick only Box B, and a successful record of predictions by Omega will not do that for me.
From Andy Egan.
I would suggest looking at your implicit choice of counterfactuals and their role in your decision theory. Standard causal decision theory involves local violations of the laws of physics (you assign probabilities to the world being such that you’ll one-box, or such that you’ll one-box, and then ask what miracle magically altering your decision, without any connection to your psychological dispositions, etc, would deliver the highest utility). Standard causal decision theory is a normative principle for action, that says to do the action that would deliver the most utility if a certain kind of miracle happened. But you can get different versions of causal decision theory by substituting different sorts of miracles, e.g. you can say: “if I one-box, then I have a psychology that one-boxes, and likewise for two-boxing” so you select the action such that a miracle giving you the disposition to do so earlier on would have been better. Yet another sort of counterfactual that can be hooked up to the causal decision theory framework would go “there’s some mathematical fact about what decision(decisions given Everett) my brain structure leads to in standard physics, and the predictor has access to this mathematical info, so I’ll select the action that would be best brought about by a miracle changing that mathematical fact”.