I’ve heard rumours of a course of five or six lectures Conway did many years ago (before he went to Princeton). The goal is to prove Gödel’s incompleteness theorem but somehow using geometry in some way. I think you need to allow comparing two lines and knowing which is longer (and this foundational thing is hard or maybe impossible) in some sense. I don’t know what is left of eg Gödel numbering or the formal languages stuff because I’ve only heard vague descriptions of this.
I believe the contents of this course were lost to time but I’d like to be surprised.
I saw Conway talk on Gödel’s incompleteness theorems shortly before he went to Princeton, and the proof he gave was the standard one (although very entertainingly and efficiently presented).
Exactly what I was thinking.
This kind of attitude can make people that are less connected to the topics John Conway is talking about, feels much more into it.
My understanding is that it says if anyone anywhere has free will, then so do some elementary particles. It doesn't say anything about if anyone or if any elementary particles actually have free will right? Does it lend support either way to if free will exists?
It shows that to whatever extent an experimenter can behave nondeterministically, so can an elementary particle. So it's useful as a simple way to convince people that quantum mechanical randomness is a true fundamental phenomenon (in particular, that hidden variable theories are all inherently invalid).
I've never seen a coherent definition of "free will", but I don't see how someone whose decision is random has any more or less of it than someone whose decision is nonrandom, so IMO it doesn't really have anything to do with free will one way or another.
Conway distinguishes Free Will from randomness by showing that randomness is just a special case of determinism. The random numbers could have been written down before the big bang and looked up when needed, which is still predetermined.
What makes Free Will free is that it's the selection of some future state independently from the information in a particle's past light cone. Only the particle determines that part of its state. One implication is that our brains, being composed of particles, derive their free will from the sum of the particles' free will. This doesn't imply that particles are conscious or aware, it only means that certain degrees of freedom evolve according to computations performed by the particles independently.
In one of the lectures Conway goes in depth into the philosophy of free will, which he believed in at a time when it was (and still is) almost universally unfashionable.
He notes in the first lecture that he thinks it is impossible to disprove determinism. A determined determinist can always resort to the argument: all of your senses are deceiving you and you are simply experiencing some predetermined script of qualia (he uses the analogy of watching a movie a second time).
I think the invulnerable argument for it is even simpler than that: whatever apparently non-determined behavior we observe may only appear that way because we don’t yet know the rules underlying it.
Any system will appear unsystematic until the precise rules governing it are known.
Since we can’t ever demonstrate that we’ve exhausted all possible theories of a system, the possibility always remains that tomorrow we would discover a perfectly effective one, and from that point the system would be as plainly deterministic as anything else.
In other words: we lack the capability to definitively distinguish between our own lacking knowledge and a system’s (potential) intrinsic non-determinism.
We can perform some measurements [0] which show that spin exists. So, the 101 lemma used in the Kochen-Specker Theorem is related to existing laboratory experiments, and not just thought experiments. But indeed this doesn't say whether people have free will.
We might instead interpret the Free Will Theorem as demolishing a position otherwise claimed: People have free will, but people are special; most other things don't have free will, and certainly particles don't! But the Free Will Theorem explicitly contradicts this position.
In terms of philosophy, there are several nuances to consider. There's Kochen-Specker itself [1], its untestability and its applications. There's free will itself [2], including whether free will is definable, is useful for ethics, and indeed whether free will exists. I think it's interesting that [2] has no mention whatsoever of [1] or the Free Will Theorem more generally.
The HN crowd from my impression wants to deeply think of themselves as being in control of how their life transpired. I'm an outlier and I think free will is an illusion. Not only do I think everything is fated beyond our control but I have the belief that society would function better if people were educated young about understanding the concept of determinism and why we don't have control over how life transpires. Fundamentally we're living in a judgement & punishment system of society because religion adopted the stance of people being in control instead of what we describe as evil being a product of God. I think a society that replaces judgement & punishment with rehabilitation would be fundamentally just. I'm curious if society will evolve or stay unchanging but I think it likely won't be in my lifetime.
> Not only do I think everything is fated beyond our control but I have the belief that society would function better if people were educated young about understanding the concept of determinism and why we don't have control over how life transpires
We can’t really decide to do that because we don’t have the free will for it. Preordained fate has decreed for there to be no such education.
I mean, you argument appears self-defeating to me. Is it not?
"decide" is not incompatible with determinism, it just means the decision will always be the same. We all make decisions every day, they just aren't free.
So in this case, it has all been determined that we do not have the education currently, but that says nothing of what the future is determined to be.
I am certainly not holding my breath for society to bite the bullet and accept this. The only way I could see any kind of transformation happening (in the US, at least) is if the sitting president were to physically say "Free will is not a thing, and because of that I'm implementing these reformations". I think that would be enough to get _a_ percentage of the populace at least talking/thinking about it (if not a large percentage).
If free will is an illusion, why not the rest of the world (a la Descartes' Evil demon thought experiment)? Why do you trust your senses at all?
I am compelled by the notion of free will described by Schopenhauer (expanding on Kant). Namely, that 'one can do as he wills but not will as he wills'. Lived experience leads us to infer an indeterminate/inseparable energy/force/Will that we perceive with our senses and organize through the concepts of time/space/causality. However, we, being on the 'inside' of one particular object, are in a peculiar state: we are free to accept or reject this Will.
If I ask you to think of a number between 0 and 10, a number may pop up in your head (seemingly out of nowhere, though clearly through some process affected by genetics/neurochemistry). Despite this, you (whatever 'you' is) are still free to accept or reject this proposition.
In this sense, people can still be punished for accepting propositions of murder in some coherent way. You are affected by, but not the sum total of, your genetics and neurochemistry. Nevertheless, the latter might play a large role that we shouldn't discount.
> Despite this, you (whatever 'you' is) are still free to accept or reject this proposition.
The outcome happens from all the previous moments you lived. Randomness doesn't make a person have free will and randomness may just be an illusion from our lack of understanding when it comes to what's resulting in the outcome we appear as random.
We're the sum total of genetics, environmental factors and all the external forces upon us since birth. That means if we're being punished it was outside the realm of it could have been different.
Probably no more dangerous than free will beliefs because as with some determinist beliefs, it's moderated by thinking life is dictated by a greater order, see Calvinism or the many determinsts who aren't "dangerous" as well as those of us who think deterministic belief leads us to more nuanced and moderate views on societal events, that something begets something begets something, ad infinitum which can lead to better prevention and help mechanisms. I'm certainly not a danger other than to cheesecake or endangered anymore than anyone else who believes the will is free of physical influence and that at its core it's random, or a god or something fueling the RNG or whatever.
I agree with most of your reply but imposing a contentious philosophy upon others wouldn't go well nor would I want to condone it. I'm not very determined to believe in determinism but I do and it doesn't change my views on punishment very much as I'm still determined to have a sense of self and societal protection in that I'd prefer "bad" people kept from society until reformed although I am less judgemental as a result from thinking about it more over the years.
Just because we can't determine why something happens doesn't mean its not predetermined. Every RNG gets its seed somehow, I don't see how we can be so sure that there is absolutely _zero_ cause for a given effect.
True, but I think this isn't a good response to the idea that determinism means you don't have control over your life. Reality having randomness doesn't give us more control over our lives. (If anything, I'd think that fact alone would mean we have less, because it means there's probably entropy getting in the way of whatever our true decision processes are.)
I really love the way this article puts the issue: https://www.lesswrong.com/posts/NEeW7eSXThPz7o4Ne/thou-art-p.... The idea that determinism takes away free will from us is inherently based on the idea that we're something outside of physics, and that physics is exclusively deciding the future instead of us. However, if you make the common assumption that our brain is a material object running within physics and producing our decisions, then there is no contradiction between deterministic physics and whatever is meant by free will.
Another way I like to think about it: If you made an AI and ran it in some closed simulation, would you expect it to care whether the simulation was completely deterministic (with all probabilistic events operating from a pre-chosen seed and a strong RNG) or had some kind of randomness? The question won't directly affect the AI's life inside the simulation either way. Wouldn't you find it weird if it did actually care and had a preference about that detail of its world, or if it thought it wasn't a true free AI if there was no randomness in its simulation? If the AI thought the world had randomness or not, and then learned the opposite, you'd find it weird if the AI restructured everything it knew about itself and the world directly based on that. If you the operator happened to toggle whether the simulation had randomness several times over its run while working on its code, and at some later point the AI was let out of the simulation, you wouldn't expect the AI to take offense at this change. There's nothing about its quality of life, decision-making abilities, or life circumstances that would be affected by the answer. It's just an implementation detail of its world that's not directly relevant to an intelligence, except in matters of modeling how the world works.
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I believe the contents of this course were lost to time but I’d like to be surprised.
[0] https://ncatlab.org/nlab/show/Lawvere's+fixed+point+theorem
[1] http://tac.mta.ca/tac/reprints/articles/15/tr15.pdf
[2] https://arxiv.org/abs/math/0305282
I've never seen a coherent definition of "free will", but I don't see how someone whose decision is random has any more or less of it than someone whose decision is nonrandom, so IMO it doesn't really have anything to do with free will one way or another.
In one of the lectures Conway goes in depth into the philosophy of free will, which he believed in at a time when it was (and still is) almost universally unfashionable.
Any system will appear unsystematic until the precise rules governing it are known.
Since we can’t ever demonstrate that we’ve exhausted all possible theories of a system, the possibility always remains that tomorrow we would discover a perfectly effective one, and from that point the system would be as plainly deterministic as anything else.
In other words: we lack the capability to definitively distinguish between our own lacking knowledge and a system’s (potential) intrinsic non-determinism.
We might instead interpret the Free Will Theorem as demolishing a position otherwise claimed: People have free will, but people are special; most other things don't have free will, and certainly particles don't! But the Free Will Theorem explicitly contradicts this position.
In terms of philosophy, there are several nuances to consider. There's Kochen-Specker itself [1], its untestability and its applications. There's free will itself [2], including whether free will is definable, is useful for ethics, and indeed whether free will exists. I think it's interesting that [2] has no mention whatsoever of [1] or the Free Will Theorem more generally.
[0] https://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experime...
[1] https://plato.stanford.edu/entries/kochen-specker/
[2] https://plato.stanford.edu/entries/freewill/
We can’t really decide to do that because we don’t have the free will for it. Preordained fate has decreed for there to be no such education.
I mean, you argument appears self-defeating to me. Is it not?
So in this case, it has all been determined that we do not have the education currently, but that says nothing of what the future is determined to be.
HN says i'm posting too fast so I cannot reply to other comments. I can only edit this comment.
I am compelled by the notion of free will described by Schopenhauer (expanding on Kant). Namely, that 'one can do as he wills but not will as he wills'. Lived experience leads us to infer an indeterminate/inseparable energy/force/Will that we perceive with our senses and organize through the concepts of time/space/causality. However, we, being on the 'inside' of one particular object, are in a peculiar state: we are free to accept or reject this Will.
If I ask you to think of a number between 0 and 10, a number may pop up in your head (seemingly out of nowhere, though clearly through some process affected by genetics/neurochemistry). Despite this, you (whatever 'you' is) are still free to accept or reject this proposition.
In this sense, people can still be punished for accepting propositions of murder in some coherent way. You are affected by, but not the sum total of, your genetics and neurochemistry. Nevertheless, the latter might play a large role that we shouldn't discount.
The outcome happens from all the previous moments you lived. Randomness doesn't make a person have free will and randomness may just be an illusion from our lack of understanding when it comes to what's resulting in the outcome we appear as random.
We're the sum total of genetics, environmental factors and all the external forces upon us since birth. That means if we're being punished it was outside the realm of it could have been different.
My life got better after I rid myself from those thoughts. I firmly believe, they are dangerous.
What is your reasoning?
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[1] https://arxiv.org/pdf/quant-ph/0604079v1.pdf
I really love the way this article puts the issue: https://www.lesswrong.com/posts/NEeW7eSXThPz7o4Ne/thou-art-p.... The idea that determinism takes away free will from us is inherently based on the idea that we're something outside of physics, and that physics is exclusively deciding the future instead of us. However, if you make the common assumption that our brain is a material object running within physics and producing our decisions, then there is no contradiction between deterministic physics and whatever is meant by free will.
Another way I like to think about it: If you made an AI and ran it in some closed simulation, would you expect it to care whether the simulation was completely deterministic (with all probabilistic events operating from a pre-chosen seed and a strong RNG) or had some kind of randomness? The question won't directly affect the AI's life inside the simulation either way. Wouldn't you find it weird if it did actually care and had a preference about that detail of its world, or if it thought it wasn't a true free AI if there was no randomness in its simulation? If the AI thought the world had randomness or not, and then learned the opposite, you'd find it weird if the AI restructured everything it knew about itself and the world directly based on that. If you the operator happened to toggle whether the simulation had randomness several times over its run while working on its code, and at some later point the AI was let out of the simulation, you wouldn't expect the AI to take offense at this change. There's nothing about its quality of life, decision-making abilities, or life circumstances that would be affected by the answer. It's just an implementation detail of its world that's not directly relevant to an intelligence, except in matters of modeling how the world works.