I think we'll find godel's most pungent critiques of modern logic & mathmatics to be the maddening limits of LLMs.

Why? His incompleteness work explains why software and math suck so he would already expect them to; they're rhetorical and can never fully be a closed loop body of knowledge as we can never with rhetoric concretely observe/define the far future or far past; merely simulate rhetorically

Ergo all defined axiomatic systems have sentences about the far past and future that cannot be defined in those languages with certainty. Most do not make the connection to physics. Gödel did and would 100% aware the limits exist and will always exist

Scaling laws aren't just for computers; humans cultures do not scale infinitely through time, just approximately 2-3 generations

As I understand immutable physical truth like this played a huge role in his early research and ultimately were the forcing function that led him to incompleteness

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kevin42 a day ago | parent [-]

"all defined axiomatic systems have sentences about the far past and future that cannot be defined in those languages with certainty."

This is often misunderstood or misstated to mean that there are some things that are unknowable or unable to be solved. (I'm not saying that's what you were implying, I am referring to the common way I see his theorem being represented)

But what he really proved is that no single sufficiently powerful, consistent, effectively specified formal system can prove every arithmetic truth.

He didn't prove that there are mathematical truths that are unsolvable through any possible extension or alternative framework. It's just that one framework isn't enough to solve all problems.

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LdBaringSwallow a day ago | parent [-]

You're just restating Gödel verbatim without considering what that would entail physically; they're implicitly unsolvable as it would take forever to solve them all; the universe would experience heat death before they're all solved.

Scaling issues do not just matter when making bridges and when hosting LLMs.

Back in Gödel's day physicists were like rockstars and all Gödel's output was 100% influenced by Einstein and the rest. Given the group's expertise in the domain the implicitly forever incomplete/never computed did not need to be spelled out explicitly.

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rcxdude 7 hours ago | parent [-]

This part is already true without Gödel: combinatorics means there is mindbogglingly more that could be expressed in the universe than ever will be. The shocking aspect of incompleteness was how it made mathematics closer to physics (or perhaps, from some points of view, to philosophy), not what it implied about what was knowable in physics.

	▲	LdBaringSwallow 4 hours ago \| parent [-]
		I think you're conflating abstraction like E=mc^2 and concrete ground truth of every moment ever everywhere in the observable/non-observable (observable has to come from somewhere) universe. Yeah we can and have formed general conclusions from what has been observed. But Gödel was talking to the limits of usefulness of abstraction like E=mc^2 when it comes to determining past and future physical truth to a high precision. E=mc^2 is, to conjure an absurd simile to invoke a reaction of how insane the effort would feel, like saying there's a rock on a hill. Gives us nothing about the shape, color, mass... any sentences describing the concrete properties cannot be proven without observation. Technically we cannot empirically know if E=mc^2 was true 700 billion years ago. Our trusted abstraction are only relatively true.