Goedel's Incompleteness Theorem

7 Dec 2021  ·  Serafim Batzoglou ·

I present the proof of Goedel's First Incompleteness theorem in an intuitive manner, while covering all technically challenging steps. I present generalizations of Goedel's fixed point lemma to two-sentence and multi-sentence versions, which allow proof of incompleteness through circular versions of the liar's paradox. I discuss the relation of Goedel's First and Second Incompletneness theorems to Goedel's Completeness theorems, and conclude with remarks on implications of these results for mathematics, computation, theory of mind and AI.

PDF Abstract
No code implementations yet. Submit your code now


  Add Datasets introduced or used in this paper

Results from the Paper

  Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.


No methods listed for this paper. Add relevant methods here