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barsoap@lemm.ee âš3â© âšweeksâ© agoThatâs computer science alongside with Church/Turing. Maths could have tried to claim it but they doubled down on formalism so they donât deserve it.
That said though incompleteness follows from nothing but logical implication itself so itâs more fundamental than physics (try to imagine a physics without cause and effect) and philosophy (find me a philosopher who wasnât asleep during their logic lectures).
i_love_FFT@lemmy.ml [bot] âš3â© âšweeksâ© ago
Yeah, I meant to say that the incompleteness theorem proves that math cannot be perfectly pure and fundamental. I donât exactly care which field claims it, because I donât like to encourage artificial boundaries between disciplines. Itâs nice to use information theory results in physics :)
barsoap@lemm.ee âš3â© âšweeksâ© ago
The other way around: As long as you accept that cause and effect are a thing, you must accept that there are things that are, fundamentally, uncomputable. And as our universe very much does seem to have cause and effect thatâs a physical law, likewise is complexity theory. Differently put: God canât sort a list with fewer than O(n log n) comparisons.