Sometime ago I posted to decision-theory-workshop an idea that may be relevant here. Hopefully it can shed some light on the “solution to free will” generally accepted on LW, which I agree with.
Imagine the following setting for decision theory: a subprogram that wants to “control” the output of a bigger program containing it. So we have a function world() that makes calls to a function agent() (and maybe other logically equivalent copies of it), and agent() can see the source code of everything inclucing itself. We want to write an implementation of agent(), without foreknowledge of what world() looks like, so that it “forces” any world() to return the biggest “possible” answer (scare quotes are intentional).
Then a possible algorithm for agent() may go as follows. Look for machine-checkable mathematical proofs (up to a specified max length) of theorems of the form “agent()==A implies world()==U” for varying values of A and U. Then, after searching for some time, take the biggest found value of U and return the corresponding A. For example, in Newcomb’s Problem there are easy theorems, derivable even without looking at the source code of agent(), that agent()==2 implies world()==1000 and agent()==1 implies world()==1000000.
The reason this algorithm works is very weird, so you might want to read the following more than once. Even though most of the theorems proved by the agent are based on false premises (because it is logically impossible for agent() to return a value other than the one it actually returns), the one specific theorem that leads to maximum U must turn out to be correct, because the agent makes its premise true by outputting A. In other words, an agent implemented like that cannot derive a contradiction from the logically inconsistent premises it uses, because then it would “imagine” it could obtain arbitrarily high utility (a contradiction implies anything, including that), therefore the agent would output the corresponding action, which would prove the Peano axioms inconsistent or something.
To recap: the above describes a perfectly deterministic algorithm, implementable today in any ordinary programming language, that “inspects” an unfamiliar world(), “imagines” itself returning different answers, “chooses” the best one according to projected consequences, and cannot ever “notice” that the other “possible” choices are logically inconsistent with determinism. Even though the other choices are in fact inconsistent, and the agent has absolutely perfect “knowledge” of itself and the world, and as much CPU time as it wants. (All scare quotes are, again, intentional.)
I’m skeptical that it will get many upvotes, though.
You seem to be either pathologically under-confident (considering that the comment your post was based on was voted up to 9, and people were explicitly asking you to make a top post out of it), or just begging for votes. :)
I’m nervous about reposting stuff from the workshop list as top-level posts on LW. I’m a pretty minor figure there and it might be seen as grabbing credit for a communal achievement. Yeah, this specific formalization is my idea, which builds on Nesov’s idea (ambient control), which builds on Wei Dai’s idea (UDT), which builds on Eliezer’s idea (TDT). If the others aren’t reposting for whatever reason, I don’t want to go against the implied norm.
(The recent post about Löbian cooperation wasn’t intended for the workshop, but for some reason the discussion there was way more intelligent than here on LW. So I kinda moved there with my math exercises.)
If the others aren’t reposting for whatever reason, I don’t want to go against the implied norm.
It is much more likely that people aren’t posting because they haven’t thought of it or can’t be bothered. I too would like to see top-level posts on this topic. And I wouldn’t worry about grabbing credit; as long as you putting attributions or links in the expected places, you’re fine.
For a bit of background regarding priority from my point of view: the whole idea of ADT was “controlling the logical consequences by deciding which premise to make true”, which I then saw to also have been the idea behind UDT (maybe implicitly, Wei never commented on that). Later in the summer I shifted towards thinking about general logical theories, instead of specifically equivalence of programs, as in UDT.
However, as of July, there were two outstanding problems. First, it was unclear what kinds of things are possible to prove from a premise that the agent does X, and so how feasible brute force theories of consequences were as a model of this sort of decision algorithms. Your post showed that in a certain situation it is indeed possible to prove enough to make decisions using only this “let’s try to prove what follows” principle.
Second, maybe more importantly, it was very much unclear in what way one should state (the axioms of) a possible decision. There were three candidates to my mind: (1) try to state a possible decision in a weaker way, so that the possible decisions that aren’t actual don’t produce inconsistent theories, (2) try to ground the concept (theory) of a possible decision in the concept of reality, where the agent was built in the first place, which would serve as a specific guideline for fulfilling (1); and (3) try to live with inconsistency. The last option seemed less and less doable, the first option depended on rather arbitrary choices, and the second is frustratingly hairy.
However, in a thread on decision-theory-workshop, your comments prompted me to make the observation that consequences always appear consistent, that one can’t prove absurdity from any possible action, even though consequences are actually inconsistent (which you’ve reposted in the comment above). This raises the chances for option (3), dealing with inconsistency, although it’s still unclear what’s going on.
Thus, your input substantially helped with both problems. I’m not overly enthused with the results only because they are still very much incomplete.
Thanks, but after my last post I don’t think there’s enough informed interest here for this kind of stuff. Pretty much everyone who could take the ideas further is already participating in the workshop. Besides, even though this particular formalization may belong to me, UDT is Wei Dai’s idea and I leave it up to him to report our progress elsewhere.
It is not news that, with ingenuity, (apparent) Alternative Possibilities can be accommodated within
determinism. It is even less news that Alternative Possibilities can be accommodated
(without the need for ingenuity) within indeterminism.
The question is why the determinism based approach is seen around here as “the” solution, when the evidence for the actual existence of (in)determinism remains unclear.
Indeterminism can accommodate “alternate possibilities”, but it cannot accommodate meaningful choice between them. As Eliezer said:
My position might perhaps be called “Requiredism.” When agency, choice, control, and moral responsibility are cashed out in a sensible way, they require determinism—at least some patches of determinism within the universe. If you choose, and plan, and act, and bring some future into being, in accordance with your desire, then all this requires a lawful sort of reality; you cannot do it amid utter chaos. There must be order over at least over those parts of reality that are being controlled by you. You are within physics, and so you/physics have determined the future. If it were not determined by physics, it could not be determined by you.
Also, starting from “extreme determinism” has been very intellectually fruitful for me. As far as I know, the mathematical part of my comment above (esp. the second to last paragraph) is new—no philosopher had generated it before. If I’m mistaken and your words about it being “not news” have any substance, please give a reference.
“Some patches of determinsim” is perfectly compatible with “some patches of indeterminism”. We need more-or-less determinism to carry out decisions, but that
does not mean it is required to make them.
The second part of EY;s comment is too vague. If I am being controlled by “physics”
outside my body, I am un-free. I am not unconditionally free just because I am physical.
We need more-or-less determinism to carry out decisions, but that does not mean it is required to make them.
That sounds inconsistent. What’s the relevant difference between the two activities? They look like the same sort of activity to me. Both require making certain things correlate with other things, which is what determinism does. (Carrying out a course of action introduces a correlation between your decision and the outside world; choosing a course of action introduces a correlation between your prior values and your decision.)
The difference is that if we tried to carry out decisions indeterministically, we wouldn’t get the results we wanted; and if we made decisions determistically, there would be no real choice.
if we made decisions determistically, there would be no real choice
I don’t understand this statement. Isn’t it drawing factual conclusions about the universe based on what sort of choice some philosophers wish to have? Or do you trust the subjective feeling that you have “real choice” without examining it? Both options seem unsatisfactory...
Determinism does not enforce rationality. There are more choices than choices about what to believe. Since naive realism is false, we need to freely and creatively generate hypotheses before testing them.
The part of your mind that generates hypotheses is no less deterministic than the part that tests them. (It’s not as if they used different types of neurons!) The only difference is that you don’t have conscious access to the process that generates hypotheses, so it looks mysterious and you complete the pattern that mysterious=indeterministic. But even though you can’t introspect that part of yourself, you can still influence what options it will offer you, e.g. by priming).
Maybe the two stages are in a time domain, not a space domain.
The “it only seems indeterministic” story is one of a number of stories. It is not a fact. My central point is that to arrive at The Answer, all alternatives have to be considered.
It’s not wrong, and it;’s not intended as a mirror-image of the LW official dogma. It’s a suggestion. I cannot possibly say it is The Answer, since, for one thing, I don’t know if indeterminsim is actually the case. So my central point remains: the solution space
remains unexplored, and what I put forward is an example of a neglected possibillity
If physics randomly decides whether an agent in state S at time t will evolve into state A or state B at time t+dt, then the cause of “A rather than B” cannot be the agent’s preferences and values, or else these would already have been different at time t. The agent could not be held morally accountable for “A rather than B” (assuming S were known to the judge). Indeterminism being present in the ‘cogs and gears’ of the agent is more like an erosion of personal autonomy than a foundation for it.
If the ‘problem of free will’ has a solution (resp. dissolution) at all, then it can be solved (resp. dissolved) under the assumption of physical determinism.
“Physics chooses” is vague. An agents physical state will evolve under the laws
of physics whether they are deterministic or not. If an agents state never contained the slightest inkling of committing murder, for instance, then they will not choose to do that—deterministically or not. A choice, random or not, can only be made from the options available, and will depend on their values or preferences.
That FW can be dissolved under determinism does not mean it should be disolved under determinism or disolved at all. A case has to be made for dissolution over solution.
“Physics chooses [between A with probability p and B with probability 1-p]” is vague.
It means nothing other than “a Laplacean superbeing, given complete knowledge of the prior state and of the laws of physics, would calculate that at time t+dt, the state of the system will either be A with probability p or B with probability 1-p”. (You can see why I tried not to write all of that out! Although this may have been unwise given that you’ve now made me do just that.)
Complete knowledge of the prior state includes complete knowledge of the agent. Hence, there is no property of the agent which explains why A rather than B happens. The Laplacean superbeing has already taken all of the agent’s reasons for preferring A (or B) into account in computing its probabilities, so given that those were the probabilities, whatever ultimately happens has nothing to do with the agent’s reasons.
You should read chapter VII of Nagel’s book The View From Nowhere. He explains very clearly how the problem of free will arises from the tension between the ‘internal, subjective’ and ‘external, objective’ views of a decision. From the ‘external, objective’ view, freedom in the sense you want inevitably disappears regardless of whether physics is deterministic.
The explanation about the Laplacian Daemon does not take into account the fact that the very varied pre-existing states of people’s minds/brains has a major influence on their choices. Physics cannot make them choose something they never had in mind. Their choices evolve out of their dispositions under both determinism and indeterminism.
If the choice between A and B is indeterministic, it is indeterministic, but the particular values of A and B come from the particular agent. Whatever happens has a huge amount to do with those reasons since your personified “physics” cannot implant brand new reasons ex nihilo.
I am quite capable of arguing my case against Nagel or anybody else.
Imagine a ‘coarse-grained’ view of the agent, where we don’t ask what’s inside the agent’s head. Then the agent has a huge spectrum of possible actions—our uncertainty about the action taken is massive.
Finding out what’s inside the agent’s head resolves either ‘most’ or ‘all’ of the uncertainty, according as physics is indeterministic or deterministic respectively. If physics is indeterministic then some uncertainty remains, and the resolution of this uncertainty cannot be explained by reference to the agent’s preferences, and cannot serve as a meaningful basis for freedom.
The point is: that extra bit of uncertainty on the end, which you only get with indeterministic physics, doesn’t give any extra scope whatsoever for ‘free will’ or ‘moral responsibility’.
I heartily agree with you that
the very varied pre-existing states of people’s minds/brains has a major influence on their choices. Physics cannot make them choose something they never had in mind. Their choices evolve out of their dispositions under both determinism and indeterminism.”
I can’t figure out why you’re making disagreement noises while putting forward the same exact view as mine!
Some irresoluble uncertainty about what an agent will do is the only meaningful basis for freedom. (Other solutions are in fact disolutions) The point is how an agent can have that freedom without complete disconnection of their actions from their character, values, etc. The answer is to pay attention to quantifiers. Some indeterminism does not mean complete indeterminism, and so does not mean complete disconnection.
Sorry but I think that’s confused, for reasons I’ve already explained.
Honestly, you’d enjoy reading Nagel. If it helps, he’s an anti-reductionist just like you, who doesn’t think in terms of ‘dissolving’ philosophical problems.
Um.
Sometime ago I posted to decision-theory-workshop an idea that may be relevant here. Hopefully it can shed some light on the “solution to free will” generally accepted on LW, which I agree with.
Imagine the following setting for decision theory: a subprogram that wants to “control” the output of a bigger program containing it. So we have a function world() that makes calls to a function agent() (and maybe other logically equivalent copies of it), and agent() can see the source code of everything inclucing itself. We want to write an implementation of agent(), without foreknowledge of what world() looks like, so that it “forces” any world() to return the biggest “possible” answer (scare quotes are intentional).
For example, Newcomb’s Problem:
Then a possible algorithm for agent() may go as follows. Look for machine-checkable mathematical proofs (up to a specified max length) of theorems of the form “agent()==A implies world()==U” for varying values of A and U. Then, after searching for some time, take the biggest found value of U and return the corresponding A. For example, in Newcomb’s Problem there are easy theorems, derivable even without looking at the source code of agent(), that agent()==2 implies world()==1000 and agent()==1 implies world()==1000000.
The reason this algorithm works is very weird, so you might want to read the following more than once. Even though most of the theorems proved by the agent are based on false premises (because it is logically impossible for agent() to return a value other than the one it actually returns), the one specific theorem that leads to maximum U must turn out to be correct, because the agent makes its premise true by outputting A. In other words, an agent implemented like that cannot derive a contradiction from the logically inconsistent premises it uses, because then it would “imagine” it could obtain arbitrarily high utility (a contradiction implies anything, including that), therefore the agent would output the corresponding action, which would prove the Peano axioms inconsistent or something.
To recap: the above describes a perfectly deterministic algorithm, implementable today in any ordinary programming language, that “inspects” an unfamiliar world(), “imagines” itself returning different answers, “chooses” the best one according to projected consequences, and cannot ever “notice” that the other “possible” choices are logically inconsistent with determinism. Even though the other choices are in fact inconsistent, and the agent has absolutely perfect “knowledge” of itself and the world, and as much CPU time as it wants. (All scare quotes are, again, intentional.)
Is there any way that this applies to me or you making a decision? If it does can you give an indication of how. Thanks.
This is brilliant. This needs to be a top-level post.
Done. I’m skeptical that it will get many upvotes, though.
You seem to be either pathologically under-confident (considering that the comment your post was based on was voted up to 9, and people were explicitly asking you to make a top post out of it), or just begging for votes. :)
It’s a little bit of both, I guess.
I’m nervous about reposting stuff from the workshop list as top-level posts on LW. I’m a pretty minor figure there and it might be seen as grabbing credit for a communal achievement. Yeah, this specific formalization is my idea, which builds on Nesov’s idea (ambient control), which builds on Wei Dai’s idea (UDT), which builds on Eliezer’s idea (TDT). If the others aren’t reposting for whatever reason, I don’t want to go against the implied norm.
(The recent post about Löbian cooperation wasn’t intended for the workshop, but for some reason the discussion there was way more intelligent than here on LW. So I kinda moved there with my math exercises.)
It is much more likely that people aren’t posting because they haven’t thought of it or can’t be bothered. I too would like to see top-level posts on this topic. And I wouldn’t worry about grabbing credit; as long as you putting attributions or links in the expected places, you’re fine.
Sorry for deleting my comment. I still have some unarticulated doubts, will think more.
For a bit of background regarding priority from my point of view: the whole idea of ADT was “controlling the logical consequences by deciding which premise to make true”, which I then saw to also have been the idea behind UDT (maybe implicitly, Wei never commented on that). Later in the summer I shifted towards thinking about general logical theories, instead of specifically equivalence of programs, as in UDT.
However, as of July, there were two outstanding problems. First, it was unclear what kinds of things are possible to prove from a premise that the agent does X, and so how feasible brute force theories of consequences were as a model of this sort of decision algorithms. Your post showed that in a certain situation it is indeed possible to prove enough to make decisions using only this “let’s try to prove what follows” principle.
Second, maybe more importantly, it was very much unclear in what way one should state (the axioms of) a possible decision. There were three candidates to my mind: (1) try to state a possible decision in a weaker way, so that the possible decisions that aren’t actual don’t produce inconsistent theories, (2) try to ground the concept (theory) of a possible decision in the concept of reality, where the agent was built in the first place, which would serve as a specific guideline for fulfilling (1); and (3) try to live with inconsistency. The last option seemed less and less doable, the first option depended on rather arbitrary choices, and the second is frustratingly hairy.
However, in a thread on decision-theory-workshop, your comments prompted me to make the observation that consequences always appear consistent, that one can’t prove absurdity from any possible action, even though consequences are actually inconsistent (which you’ve reposted in the comment above). This raises the chances for option (3), dealing with inconsistency, although it’s still unclear what’s going on.
Thus, your input substantially helped with both problems. I’m not overly enthused with the results only because they are still very much incomplete.
Thanks, but after my last post I don’t think there’s enough informed interest here for this kind of stuff. Pretty much everyone who could take the ideas further is already participating in the workshop. Besides, even though this particular formalization may belong to me, UDT is Wei Dai’s idea and I leave it up to him to report our progress elsewhere.
It is not news that, with ingenuity, (apparent) Alternative Possibilities can be accommodated within determinism. It is even less news that Alternative Possibilities can be accommodated (without the need for ingenuity) within indeterminism. The question is why the determinism based approach is seen around here as “the” solution, when the evidence for the actual existence of (in)determinism remains unclear.
Indeterminism can accommodate “alternate possibilities”, but it cannot accommodate meaningful choice between them. As Eliezer said:
Also, starting from “extreme determinism” has been very intellectually fruitful for me. As far as I know, the mathematical part of my comment above (esp. the second to last paragraph) is new—no philosopher had generated it before. If I’m mistaken and your words about it being “not news” have any substance, please give a reference.
“Some patches of determinsim” is perfectly compatible with “some patches of indeterminism”. We need more-or-less determinism to carry out decisions, but that does not mean it is required to make them.
The second part of EY;s comment is too vague. If I am being controlled by “physics” outside my body, I am un-free. I am not unconditionally free just because I am physical.
That sounds inconsistent. What’s the relevant difference between the two activities? They look like the same sort of activity to me. Both require making certain things correlate with other things, which is what determinism does. (Carrying out a course of action introduces a correlation between your decision and the outside world; choosing a course of action introduces a correlation between your prior values and your decision.)
The difference is that if we tried to carry out decisions indeterministically, we wouldn’t get the results we wanted; and if we made decisions determistically, there would be no real choice.
It’s a two stage model
I don’t understand this statement. Isn’t it drawing factual conclusions about the universe based on what sort of choice some philosophers wish to have? Or do you trust the subjective feeling that you have “real choice” without examining it? Both options seem unsatisfactory...
Determinism does not enforce rationality. There are more choices than choices about what to believe. Since naive realism is false, we need to freely and creatively generate hypotheses before testing them.
The part of your mind that generates hypotheses is no less deterministic than the part that tests them. (It’s not as if they used different types of neurons!) The only difference is that you don’t have conscious access to the process that generates hypotheses, so it looks mysterious and you complete the pattern that mysterious=indeterministic. But even though you can’t introspect that part of yourself, you can still influence what options it will offer you, e.g. by priming).
Maybe the two stages are in a time domain, not a space domain.
The “it only seems indeterministic” story is one of a number of stories. It is not a fact. My central point is that to arrive at The Answer, all alternatives have to be considered.
I was mostly trying to argue against the point that human minds need indeterminism to work as they do. Do you now agree that’s wrong?
It’s not wrong, and it;’s not intended as a mirror-image of the LW official dogma. It’s a suggestion. I cannot possibly say it is The Answer, since, for one thing, I don’t know if indeterminsim is actually the case. So my central point remains: the solution space remains unexplored, and what I put forward is an example of a neglected possibillity
This is equally far from being news:
If physics randomly decides whether an agent in state S at time t will evolve into state A or state B at time t+dt, then the cause of “A rather than B” cannot be the agent’s preferences and values, or else these would already have been different at time t. The agent could not be held morally accountable for “A rather than B” (assuming S were known to the judge). Indeterminism being present in the ‘cogs and gears’ of the agent is more like an erosion of personal autonomy than a foundation for it.
If the ‘problem of free will’ has a solution (resp. dissolution) at all, then it can be solved (resp. dissolved) under the assumption of physical determinism.
“Physics chooses” is vague. An agents physical state will evolve under the laws of physics whether they are deterministic or not. If an agents state never contained the slightest inkling of committing murder, for instance, then they will not choose to do that—deterministically or not. A choice, random or not, can only be made from the options available, and will depend on their values or preferences.
That FW can be dissolved under determinism does not mean it should be disolved under determinism or disolved at all. A case has to be made for dissolution over solution.
It means nothing other than “a Laplacean superbeing, given complete knowledge of the prior state and of the laws of physics, would calculate that at time t+dt, the state of the system will either be A with probability p or B with probability 1-p”. (You can see why I tried not to write all of that out! Although this may have been unwise given that you’ve now made me do just that.)
Complete knowledge of the prior state includes complete knowledge of the agent. Hence, there is no property of the agent which explains why A rather than B happens. The Laplacean superbeing has already taken all of the agent’s reasons for preferring A (or B) into account in computing its probabilities, so given that those were the probabilities, whatever ultimately happens has nothing to do with the agent’s reasons.
You should read chapter VII of Nagel’s book The View From Nowhere. He explains very clearly how the problem of free will arises from the tension between the ‘internal, subjective’ and ‘external, objective’ views of a decision. From the ‘external, objective’ view, freedom in the sense you want inevitably disappears regardless of whether physics is deterministic.
The explanation about the Laplacian Daemon does not take into account the fact that the very varied pre-existing states of people’s minds/brains has a major influence on their choices. Physics cannot make them choose something they never had in mind. Their choices evolve out of their dispositions under both determinism and indeterminism.
If the choice between A and B is indeterministic, it is indeterministic, but the particular values of A and B come from the particular agent. Whatever happens has a huge amount to do with those reasons since your personified “physics” cannot implant brand new reasons ex nihilo.
I am quite capable of arguing my case against Nagel or anybody else.
Imagine a ‘coarse-grained’ view of the agent, where we don’t ask what’s inside the agent’s head. Then the agent has a huge spectrum of possible actions—our uncertainty about the action taken is massive.
Finding out what’s inside the agent’s head resolves either ‘most’ or ‘all’ of the uncertainty, according as physics is indeterministic or deterministic respectively. If physics is indeterministic then some uncertainty remains, and the resolution of this uncertainty cannot be explained by reference to the agent’s preferences, and cannot serve as a meaningful basis for freedom.
The point is: that extra bit of uncertainty on the end, which you only get with indeterministic physics, doesn’t give any extra scope whatsoever for ‘free will’ or ‘moral responsibility’.
I heartily agree with you that
I can’t figure out why you’re making disagreement noises while putting forward the same exact view as mine!
Some irresoluble uncertainty about what an agent will do is the only meaningful basis for freedom. (Other solutions are in fact disolutions) The point is how an agent can have that freedom without complete disconnection of their actions from their character, values, etc. The answer is to pay attention to quantifiers. Some indeterminism does not mean complete indeterminism, and so does not mean complete disconnection.
Sorry but I think that’s confused, for reasons I’ve already explained.
Honestly, you’d enjoy reading Nagel. If it helps, he’s an anti-reductionist just like you, who doesn’t think in terms of ‘dissolving’ philosophical problems.
I didn’t say I was anti reductionist. I find this us-and-them stuff rather annoying.
OK. Replace the word “who” with “in that he” in my previous comment.
I don’t mind dissolving prolbems if all else fails. But you cannot reduce everything to nothing.