Incompleteness means that maybe it’s actually impossible to prove or disprove the Riemann hypothesis, or whether P=NP. I think that’s a big deal. Maybe the fact that there are meaningful results shown to be unprovable (like axiom of choice) is more satisfying?
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xor@lemmy.dbzer0.com 3 days agothat seems fine for it’s purpose, but the modern interpretation is dumb. Even the way Godell went about proving it is dumb.
how about:
x = 2
2x = 3,000
omg! they’re inconsistent! big whoop….
it just irks me because i saw all these smarty pants talking deep stuff and referencing how the incompleteness theorem changed everything, and it was basically just stoner philosophy, with a rigorous, needlessly convoluted proof.
when i finally read it, being sure it was over my head, it was like cracking a secret code that turned out to say “drink ovaltine”
MBM@lemmings.world 3 days ago
xor@lemmy.dbzer0.com 3 days ago
that’s not a big deal. Some things are unprovable… that’s pretty obvious.
also P≠NP, that’s just dumb.
You can never prove it because you don’t know what new math will be discovered…
exasperation@lemm.ee 3 days ago
Again, Goedel’s theorem was in direct response to Russell and Whitehead spending literally decades trying to axiomize mathematics. Russell’s proof that 1+1=2 was 300 pages long. It was non-trivial to disprove the idea that with enough formality and rigor all of mathematics could be defined and proven. Instead of the back and forth that had already taken place (Russell proposes an axiomatic system, critics show an error or incompleteness in it, Russell comes back and adds some more painstaking formality, critics come back and do it again), Goedel came along and smashed the whole thing by definitively proving that there’s nothing Russell can do to revive the major project he had been working on (which had previously hit a major setback when Russell himself proved Russell’s paradox).
You didn’t define x, the equals sign, the digit 2, 3, or 0, or the convention that a real constant in front of a variable implies multiplication, or define a number base we’re working in. So that statement proves nothing in itself.
And no matter how many examples of incomplete or contradictory systems you come up with, you haven’t proven that all systems are either incomplete or contradictory. No matter how many times you bring out a new white swan, you haven’t actually proven that all swans are white.
And formal logic and set theory may have seemed like masturbatory discipline with limited practical use, but it also laid the foundation for Alan Turing and what would become computer science, which indisputably turned into useful academic disciplines that changed the world.
xor@lemmy.dbzer0.com 3 days ago
you have told me nothing new, and made several incorrect assumptions:…
but hey, i commend your efforts.
match@pawb.social 2 days ago
to be fair, none of us think you understand godel’s incompleteness theorem
xor@lemmy.dbzer0.com 2 days ago
to be fair, i don’t think you speak for “all of us”, i also don’t think you’ve actually read it.
underwire212@lemm.ee 2 days ago
I’m not sure who hurt you, but I hope you get better soon.
xor@lemmy.dbzer0.com 2 days ago
creative trolling tactic, at least