To be clear, any claim that we have mathematical proof that something beyond algorithms is required is unsound, because the argument is not mathematical. It rests on assumptions about human perception of mathematical truth that may or may not be correct. So if that's the point you're making I don't dispute it, although to say an internally consistent alternative viewpoint should be "thrown out into the garbage" on that basis is unwarranted. The objection is just that it doesn't have the status of a mathematical theorem, not that it is necessarily wrong.
If, on the other hand you think that it is impossible for anything more than algorithms to be required, that the idea that the human mind must be equivalent to an algorithm is itself mathematically proven, then you are simply wrong. Any claim that the human mind has to be an algorithm rests on exactly the same kind of validly challengable, philosophical assumptions (specifically the physical Church-Turing thesis) that Penrose' argument does.
Given two competing, internally consistent world-views that have not yet been conclusively separated by evidence, the debate about which is more likely to be true is not one where either "side" can claim absolute victory in the way that so many people seem to want to on this issue, and talk of tossing things in the garbage isn't going to persuade anybody that's leaning in a different direction.
It is unsound because: not only it demands an existence of a physical process that cannot be computed (so far, none found, and not for the lack of searching), but it also demands that such a physical process would conveniently be found to be involved in the functioning of a human brain, and also that it would be vital enough that you can't just replace it with something amenable to computation at a negligible loss of function.
It needs too many unlikely convenient coincidences. The telltale sign of wishful thinking.
At the same time: we have a mounting pile of functions that were once considered "exclusive to human mind" and are now implemented in modern AIs. So the case for "human brain must be doing something Truly Magical" is growing weaker and weaker with each passing day.
This is the usual blurring of lines you see in dismissals of Penrose. You call the argument "unsound" as if it contains some hard error of logic and can be dismissed as a result, but what you state are objections to the assumptions (not the reasoning) based on your qualitative evaluation of various pieces of evidence, none of which are conclusive.
There's nothing wrong with seeing the evidence and reaching your own conclusions, but I see exactly the same evidence and reach very different ones, as we interpret and weight it very differently. On the "existence of a physical process that cannot be computed", I know enough of physics (I have a degree in it, and a couple of decades of continued learning since) to know how little we know. I don't find any argument that boils down to "it isn't among the things we've figured out therefore it doesn't exist" remotely persuasive. On the achievements of AI, I see no evidence of human-like mathematical reasoning in LLMs and don't expect to, IMO demos and excitable tweets notwithstanding. My goalpost there, and it has never moved and never will, is independent, valuable contributions to frontier research maths - and lots of them! I want the crank-the-handle-and-important-new-theorems-come-out machine that people have been trying to build since computers were invented. I expect a machine implementation of human-like mathematical thought to result in that, and I see no sign of it on the horizon. If it appears, I'll change my tune.
I acknowledge that others have different views on these issues and that however strongly I feel I have the right of it, I could still turn out to be wrong. I would enjoy some proper discussion of the relative merits of these positions, but it's not a promising start to talk about throwing things in the garbage right at the outset or, like the person earlier in this thread, call the opposing viewpoint "stupid".
There is no "hard error of logic" in saying "humans were created by God" either. There's just no evidence pointing towards it, and an ever-mounting pile of evidence pointing otherwise.
Now, what does compel someone to go against a pile of evidence this large and prop up an unsupported hypothesis that goes against it not just as "a remote and unlikely possibility, to be revisited if any evidence supporting it emerges", but as THE truth?
Sheer wishful thinking. Humans are stupid dumb fucks.
Most humans have never "contributed to frontier research maths" in their entire lives either. I sure didn't, I'm a dumb fuck myself. If you set the bar of "human level intelligence" at that, then most of humankind is unthinking cattle.
"Advanced mathematical reasoning" is a highly specific skill that most humans wouldn't learn in their entire lives. Is it really a surprise that LLMs have a hard time learning it too? They are further along it than I am already.
I don't know if we're even able to continue with the thread this old, but this is fun so I'll try to respond.
You're correct to point out that defending my viewpoint as merely internally consistent puts me in a position analogous to theists, and I volunteered as much elsewhere in this thread. However, the situation isn't really the same since theists tend to make wildly internally inconsistent claims, and claims that have been directly falsified. When theists reduce their ideas to a core that is internally consistent and has not been falsified they tend to end up either with something that requires surrendering any attempt at establishing the truth of anything ourselves and letting someone else merely tell us what is and is not true (I have very little time for such views), or with something that doesn't look like religion as typically practised at all (and which I have a certain amount of sympathy for).
As far as our debate is concerned, I think we've agreed that it is about being persuaded by evidence rather than considering one view to to have been proven or disproven in a mathematical sense. You could consider it mere semantics, but you used the word "unsound" and that word has a particular meaning to me. It was worth establishing that you weren't using it that way.
When it comes to the evidence, as I said I interpret and weight it differently than you. Merely asserting that the evidence is overwhelmingly against me is not an effective form of debate, especially when it includes calling the other position "stupid" (as has happened twice now in this thread) and especially not when the phrase "dumb fuck" is employed. I know I come across as comically formal when writing about this stuff, but I'm trying to be precise and to honestly acknowledge which parts of my world view I feel I have the right to assert firmly and which parts are mere beliefs-on-the-basis-of-evidence-I-personally-find-persuasive. When I do that, it just tends to end up sounding formal. I don't often see the same degree of honesty among those I debate this with here, but that is likely to be a near-universal feature HN rather than a failing of just the strong AI proponents here. At any rate "stupid dumb fucks" comes across as argument-by-ridicule to me. I don't think I've done anything to deserve it and it's certainly not likely to change my mind about anything.
You've raised one concrete point about the evidence, which I'll respond to: you've said that the ability
to contribute to frontier research maths is posessed only by a tiny number of humans and that a "bar" of "human level" intelligence set there would exclude everyone else.
I don't consider research mathematicians to possess qualitatively different abilities to the rest of the population. They think in human ways, with human minds. I think the abilities that are special to human mathematicians relative to machine mathematicians are (qualitatively) the same abilities that are special to human lawyers, social workers or doctors relative to machine ones. What's special about the case of frontier maths, I claim, is that we can pin it down. We have an unambiguous way of determining whether the goal I decided to look for (decades ago) has actually been achieved. An important-new-theorem-machine would revolutionise maths overnight, and if and when one is produced (and it's a computer) I will have no choice but to change my entire world view.
For other human tasks, it's not so easy. Either the task can't be boiled down to text generation at all or we have no unambiguous way to set a criterion for what "human-like insight" putatively adds. Maths research is at a sweet spot: it can be viewed as pure text generation and the sort of insight I'm looking for is objectively verifiable there. The need for it to be research maths is not because I only consider research mathematicians to be intelligent, but because a ground-breaking new theorem (preferably a stream of them, each building on the last) is the only example I can think of where human-like insight would be absolutely required, and where the test can be done right now (and it is, and LLMs have failed it so far).
I dispute your "level" framing, BTW. I often see people with your viewpoint assuming that the road to recreating human intelligence will be incremental, and that there's some threshold at which success can be claimed. When debating with someone who sees the world as I do, assuming that model is begging the question. I see something qualitative that separates the mechanism of human minds from all computers, not a level of "something" beyond which I think things are worthy of being called intelligent. My research maths "goal" isn't an attempt to delineate a feat that would impress me in some way, while all lesser feats leave me cold. (I am already hugely impressed by LLMs.) My "goal" is rather an attempt to identify a practically-achievable piece of evidence that would be sufficient for me to change my world view. And that, if it ever happens, will be a massive personal upheaval, so strong evidence is needed - certainly stronger than "HN commenter thinks I'm a dumb fuck".
To be clear, any claim that we have mathematical proof that something beyond algorithms is required is unsound, because the argument is not mathematical. It rests on assumptions about human perception of mathematical truth that may or may not be correct. So if that's the point you're making I don't dispute it, although to say an internally consistent alternative viewpoint should be "thrown out into the garbage" on that basis is unwarranted. The objection is just that it doesn't have the status of a mathematical theorem, not that it is necessarily wrong.
If, on the other hand you think that it is impossible for anything more than algorithms to be required, that the idea that the human mind must be equivalent to an algorithm is itself mathematically proven, then you are simply wrong. Any claim that the human mind has to be an algorithm rests on exactly the same kind of validly challengable, philosophical assumptions (specifically the physical Church-Turing thesis) that Penrose' argument does.
Given two competing, internally consistent world-views that have not yet been conclusively separated by evidence, the debate about which is more likely to be true is not one where either "side" can claim absolute victory in the way that so many people seem to want to on this issue, and talk of tossing things in the garbage isn't going to persuade anybody that's leaning in a different direction.