Yes, that makes sense! Thanks for explaining.
I think it would have made more sense to me if the GL derivation was written as
joseph_c
Karma: 346
We also have another theorem of PA asserting that this theorem is provable:
Is this theorem a premise, or derived from another theorem? I disagree with the inclusion of this theorem.
I’m not disagreeing about what your argument would prove, if the premises were all correct. I agree that it does, indeed, prove an equivalence between the Payorian FairBot and the Löbian FairBot, modulo certain other assumptions. But those other assumptions are non-trivial, and the two FairBots are in fact different, precisely when those other assumptions break down.
Yes, I agree that the GL derivation, with both of those premises, establishes that the Löbian FairBot
cooperates at most as often as the Payorian FairBotis semantically a Payorian FairBot. But why are you allowed to have both premises? You don’t have both premises in the definition of either bot.Edit: I think there are edge cases where the second premise does not hold, and so the Löbian FairBot might behave differently from the Payorian FairBot.
I think that your GL derivation is correct, assuming the premises are true, though I haven’t looked at it very carefully. I’m confused about why you have both of the following premises, instead of just one of them:
I can see you choosing either one as a reasonable definition of “FairBot”, depending on whether you are describing its code or the implementation of that code as a running program (i.e., to actual run the agent, you need some kind of theorem prover—should our logical language describe the syntax of the agent’s code, or the semantics of how the agent runs on the theorem prover?). But how are you acquiring both premises simultaneously? I think that is mixing things up slightly, and in fact, this conflation is masking a real difference between the Payorian FairBot and the Löbian FairBot. The Löbian FairBot will, when run, depending on the implementation, either cooperate with
fewerother sorts of FairBots than the Payorian FairBot, or fail to terminate sometimes.
A few comments:
The statement
You seem to be doing one of two things: Either extracting
I think it makes sense to define the code of FairBot as simply
I think you are mixing up the implementation with the code, and this is where you are coming up with an additional assumption which you shouldn’t be.
We are assuming Löbian fairness, so we have available as premises
\begin{align*}
P \leftrightarrow \Box Q\
\Box(P \leftrightarrow \Box Q)
\end{align*}I thought that the Löb fairbot was simply
If we imagine that each player submits a computer program which takes in the source code of the other player, then the second premise is essentially an assertion that your program terminates on your opponent’s input. That seems like a reasonable goal of a correct program to have, but how can you actually guarantee that as the language designer? Perhaps you could make such a guarantee within the program itself (i.e., semantically it terminates, but you can’t prove it), but this seems like it would have to be a bare assumption about the program itself, not anything proved about itself.
Perhaps another way to go about this is to introduce GL modal logic. Instead of creating shares in
The part I’m confused about is why Bob converts
Also, I think a weak part of this idea in either conception is that you have to provide a proof to make these exchanges. I think it would be neat for an exchange to have a proof-verifier, but that doesn’t really seem to hold up to the promise of Alice and Bob working collectively to prove
Suppose you have a neural network which classifies handwritten digits. It has 10 outputs for 10 logits, and its “choice” is the highest logit it outputs, given an input image. This is what I mean by a choice.
I don’t understand what it means to say an entity “COULD HAVE” output a different action than what they outputted, other than talking about either (1) a stochastic function, or (2) a claim that there exists a hypothetical other function which would have output something else. I think the second case is the right picture to have in your head, but you seem to have some other picture in your head. Would you mind explaining it?
However, I think this is the wrong model to have for the possibility of choosing otherwise. Instead, you should imagine that a different choice function in your place might choose a different action
But do you know that? Surely establishing how the capacity for choice actually works requires empirical investigation.
You appear not to have answered that question.
I was using the word “model” to mean “picture in your head”, not “theorized laws which capacity for choice follow”. I was arguing that it was an error to define capacity for choice in a split-brain way, and that you should instead define it in a substitution-brain way. I didn’t answer your question because it wasn’t really engaging with what I had said. It’s probably my fault for being sloppy in my word choice.
I agree that establishing how choosing actually works in brains requires empirical investigation.
The only difference from your model is the inclusion of indeterminism
My model was agnostic about indeterminism, and still is.
Special, meaning it’s the only uncaused cause.
You’re sure using special to mean more than that later on!
Momentous things matter more than trivial thungs by definition.
If you read the second part of my sentence after the semicolon, and the sentence after that paragraph, it is clear that I am just saying that being more momentous doesn’t affect the truth value of a proposition, not that momentous things matter less.
But not to the same extent , as I argued at length.
Not really. You mostly just repeated “more momentous” in various ways, such as more real, more special, and so on. If you want me to care more about choices in the world where choices are non-deterministic than the world where choices are deterministic, I think you would have to tell me something about how that would change the world. For example, perhaps if choices are non-deterministic, we can reduce crime rates by studying psychology, whereas if choices are deterministic, crime rates will never go down no matter how much psychology we as a civilization learn. Therefore, in the first world, it’s useful to study psychology, while in the second world it is not. I don’t believe that is the case, though. But that’s the kind of argument that would get me to care one way or the other.
You do mention something about the world being doomed/not necessarily doomed, but again, I don’t think that actually is a matter of determinism or not. At some point in the future, the world will either be doomed or not doomed, and our actions will decide which is the case. We should therefore take actions to avoid the doomed world, and our brains are configured to follow this precept in either world. Adding true randomness back in just makes it so that there is now aleatoric uncertainty about the future, not simply epistemic uncertainty.
But you seem to be arguing for something more than just “a brain which uses a truly random source of entropy to run a random algorithm”. I don’t want to comment on it, because clearly I don’t understand.
I don’t believe in your 2, and never said anything along those lines.
Sorry.
An inward firing account of choice, the brain mechanisms that enable it, does not answer all the questions, because some of them are outward firing questions about how people interact and societies work
I feel like these are separate areas that can be solved individually. The first area is a question of modelling the brain: How does the brain learn? How does it map information to better than random actions? The second area is a question of social responsibility: As a society, when should we hold people responsibility so that we can accomplish X? What system of rewards and punishments helps us develop a healthy society?
The first area is about psychology, neuroscience, and AI. The second area is about ethics, economics, and game theory. It’s true that answers in the first area can inform us about answers in the second area, but I don’t see the case for the other direction.
It is of course both. You have no moral responsibility alone on a desert island; but also none if you live in a society but don’t have the appropriate brain functions
I disagree. I think it is not both. Who we choose to hold responsible and for what actions is solely a social problem, though of course we should use material facts and mathematical laws to inform us of how to do that well.
Yes, but you can also have a richer model as well.
Richer than what? I haven’t proposed any model of social responsibility.
Potentially, yes, because an interpreter can include a sandbox , that prevents the code from doing what it thinks it’s doing.
This is an interesting perspective. I personally take the perspective that two things are identical if you can’t distinguish between them, so code running in a sandbox is just as real to the program as when it is not in a sandbox, as long as the sandbox faithfully simulates interacting with the outside world. Nevertheless, to an outside observer, these situations do not look identical, so there is a sense in which the program running in the sandbox is less real to the outside observer. But I think this stretches the meanings of “real” and “unreal” beyond their typical use-case of distinguishing between ideas and the material world or between truth and fabrication. It’s probably more useful to coin a new term like “root” or “base” to distinguish between a simulated universe and a universe not running in a simulation.
I actually believe in empiricism.
I wasn’t trying to say you don’t believe in empiricism! I was trying to argue that it would be more pragmatic to simply describe the world instead of worrying about whether the label “real” or “unreal” applies.
But I don’t have a fully equipped neurology lab, so I can’t test my testable model of free will.
You mentioned libertarian free will, which according to Google says that human beings can make choices undetermined by prior causes, physical laws, or divine predetermination. Would brains taking advantage of true randomness in the universe count, provided it exists? Or does there need to be some special substance which is only used in choice-making? Or am I just completely missing the mark?
I don’t really find the distinction between “a brain uses a random algorithm which takes advantage of true randomness” and “a brain uses a random algorithm which uses chaos for its ‘entropy’” very important for understanding how choice-making works.
I would be very interested in hearing a test you could perform to validate/invalidate your model of free will. I’m still not really sure what you mean by free will, see, and I think that would help a lot.
I assume you’re in the same position.
Pretty much.
What were you expecting me to do, that I’m in a position to do, and yet not doing? And, are you doing it yourself?
Right now I would mostly appreciate you explaining what your model of free will is.
No, I mean “each choice is not a choice, it’s just following the configuration”. “learning” is across time, and is about changes in configuration. But at each choice-point, there is no actual choice.
That depends on what you mean by “actual choice”. From a mechanistic definition of choice, there is a choice: An action was output based on input information. I don’t know what a sensible definition of a choice looks like other than this. I also don’t understand what keeps this from being an “actual” choice. Is it that you feel like it’s not really you making the choice, if it’s just your brain running an algorithm? But you are that algorithm running on that brain. It is you who is making the choice.
Well, no. You can program it to use pseudorandom data in an algorithm, or even “hardware-random”, which isn’t necessarily random, just unpredictable by humans. ―Dagon
Compare what you said with what I said:
It is, though, an interesting question whether true randomness exists, or whether everything that appears random is just chaos. ―joseph_c
I am not claiming that true randomness necessarily exists, just that I can program a computer to use a random algorithm, so nondeterminism isn’t a mysterious question: Just supply true randomness to a random algorithm.
it just does what it’s configured to do
Yes. It does what it’s configured to do, and nothing special beyond that. What it’s configured to do is learning and choosing.
that feels like a choice to the qualia-experiencer
I think when people talk about the qualia of choice-making, they are talking about the experience of making a certain kind of high-level choice, which involves consciously gathering information, such as by looking around or dredging up memories, and then committing to an action. But notice that this involves several lower level choices in the process: What information do you pay attention to? Which memories do you recollect? What self-modifications does committing to an action involve? These lower-level choices may lack qualia, because you are not consciously aware you are making those choices. They could be just instinctual or trained like muscle memory.
I imagine the qualia of such a high-level choice to be similar to the qualia of running, a combination of smaller experiences of actions like legs extending, arms pumping, lungs breathing, muscles aching, and so on. But other people may focus on just the experience of committing to a course of action, and call that the point at which a choice is made. However, in my opinion, the qualia you get there is actually the qualia of carrying out an action, the action of self-modifying to keep a commitment, not the qualia of making the low-level choice itself for that commitment.
The amazing thing about brains is that we can break up high level decisions down into smaller pieces which involve decisions themselves, and this process doesn’t really seem to have a limit for how high-level the decisions can go. How that works is a question for psychology, neuroscience, and AI.
it’s a mystery how a physical process (your brain) can have nondeterministic outputs.
I can program a computer to use a random algorithm. There is nothing mysterious about nondeterministic outputs. It is, though, an interesting question whether true randomness exists, or whether everything that appears random is just chaos.
Before I begin my response, I would like to point out that I really don’t appreciate your commenting style. I spent a while working on my post, and you didn’t even bother to engage with my first paragraph, where I say that capacity to choose otherwise is asking the wrong question. If you think it is the right question to be talking about, you should argue for that, not just assume it is something we can agree on.
When I talk about choosing, I am talking about modelling the world, not some magical and mysterious capacity that non-choosers lack. A chooser is defined simply to be an entity that takes in information and outputs actions. Choosers are a useful abstraction because such things exist: Many entities perform more optimal actions by using information they possess. But there is no need to hypothesize an elan volonté for how this all works.
Now, to talk a bit more about the content of your comment...
But do you know that? Surely establishing how the capacity for choice actually works requires empirical investigation.
You claim that there is some “capacity to choose”, but whence comes this idea of a capacity to choose? I fear that you just have an intuition that “you make your own choices”, and then you take this intuition too far, saying that no choice can be “real” if it has a causal or physical link to the rest of reality.
I say that choice-making is the process of converting information into actions. You are the one who says it requires some special capacity to choose. You are the one who claims there is anything to talk about there, at all.
Undetermined choices are more momentous… it is nothing special… you are nothing special… only the BB [Big Bang] is special...
Libertarian free will… [not] merely caused… doom [not] inevitable… [sense of control] determinism robs them of.It doesn’t matter if an undetermined choice is more “momentous”; that doesn’t make it more true. I don’t even grant that undetermined choices are more momentous than determined choices. Our future depends on our choices, whether they are deterministic or not.
I do grant, though, that it would be more important to study choice-making if choice-making was more momentous.
It’s like the difference between a car and a train. The train goes somewhere but it can’t jump off the tracks
And both are controlled by people.
I agree that there are varying levels of ownership we can assign to entities that make choices. The self-tuned PID controller has more ownership over its choices than the human-tuned PID controller, but less than a human has over his/her own choices. The error you are making is in only accepting two extremes: (1) Choices are completely deterministic, owned completely by the universe as a whole, and (2) choices follow from “free will”, owned completely by the agent with free will.
Also, I think it is important to distinguish modelling the world from social responsibility. Whether someone is to be held responsible for their choices is a social problem, not a fact of the universe. We can model a computer as making choices without holding it responsible, and instead holding its programmer responsible.
a simulated universe might seem just like a real universe...but it isnt real.
When you run a computer program, is it less “real” if it is written in an interpreted language than if it is written in a compiled language? (An interpreted language works by simulating a virtual computer which executes higher level instructions using the base computer, while a compiled language directly outputs instructions to be used on the base machine. This is, of course, a great simplification of how interpreters work.) Does “real” to you just mean that you have reached the limit of your understanding? I wonder what you think a physicist would say if you asked him whether an electron is “real”. He, after all, understands that an electron is a theoretical model, not a hard fact of existence.
Instead of seeking to apply labels like “real” or “unreal”, I think you would be better served by looking at what is actually happening.
I make choices, between different possible actions (or, to be more specific, my brain does).
How would you respond to my reply to Dagon?
I think I would need you to explain what you mean by free will for me to be able to answer that.
Yep! That’s why I’m trying to explain choice-making without this “free will” concept.
I didn’t want to include this in the main post, because I wanted to keep it concise and on-topic, but I don’t think determinism is relevant. If you were given the options of receiving a million dollars or of receiving death, you would try damn well to make your choice as deterministic as possible. That doesn’t stop it from being a choice you make. Likewise, a computer can be given a source of entropy and run a random algorithm; computers need not be deterministic. Stochasticity doesn’t magically give you any more “real” choices than you had before.
I think people get the idea into their head about stochasticity being necessary for choosing because they consider a real choice to require the possibility to choose otherwise. So, they imagine a choice function like a brain split in two, sometimes choosing one way and sometimes choosing another:
However, I think this is the wrong model to have for the possibility of choosing otherwise. Instead, you should imagine that a different choice function in your place might choose a different action:
This solves the problem of capacity to choose otherwise without requiring stochasticity. That a choice is made is just a way of pointing out there is some choice function, a chooser, and that there exists a different chooser that would result in a different action. That it is one chooser and not another determining the action is the whole point of saying that that chooser, and not the other made the choice. In how I view choosing, choices are still made even if the universe is deterministic, it’s just that the choosers are determined beforehand in what places they will be. But that doesn’t make the concept of a chooser or a choice useless, no less than abstracting away a clump of particles as a rock is useless. We abstract clumps of particles as rocks because we can model rocks more simply than modelling all the particles one by one. We abstract away choosers because there are choosers, entities such as humans that take actions based on information they gather.
On the other hand, the question of whether someone is to be held responsible for their choices is a social problem.
In my essay, I was using volition mostly as just a synonym for choice-making. So, it makes choices on which direction to push the pendulum. But maybe you are asking whether the PID controller “owns” the choices it makes? I would say it owns them more than a PID controller tuned by a human owns its choices, but less than a human owns his/her own choices. The human, after all, can modify how he/she goes about learning in the first place, while the PID controller you have described cannot modify its tuning algorithm.
I kind of agree, but for what it’s worth, I thought it was amusing.