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ornery_chemist@mander.xyz ⁨4⁩ ⁨days⁩ ago

I don’t know much about this, but I can’t help but think that “complete” and “consistent” are doing a lot more work in that sentence than my current understanding of the terms would lead me to believe.

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someacnt@sh.itjust.works ⁨4⁩ ⁨days⁩ ago
I am sure there was a typo, it’s Gödel’s incompleteness theorem which proves that consistent systems are incomplete.

Consistency means likely what you expect: it’s that you cannot reach contradiction from very axioms.

The result is insane in my opinion, it means any sensible math system with basic arithmetic has a proposition that you cannot prove. AND you cannot also prove that the system is contradiction-free.

It is completionist’s worst nightmare.

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- exasperation@lemm.ee ⁨3⁩ ⁨days⁩ ago
  
  The result is insane in my opinion, it means any sensible math system with basic arithmetic has a proposition that you cannot prove.
  
  Stated more precisely, it has true propositions that you cannot prove to be true. Obviously it has false propositions that can’t be proven, too, but that’s not interesting.
  
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