2020/01/21 by Yasha Savelyev, Savelyev, Yasha
Computer Science · Mathematics · #Advanced Topology and Set Theory #Artificial Intelligence (cs.AI) #Computability, Logic, AI Algorithms #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #History and Philosophy of Physics (physics.hist-ph) #Logic (math.LO) #Logic in Computer Science (cs.LO) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2001.07592
openalex publication_date 2020/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We first partly develop a mathematical notion of stable consistency intended to reflect the actual consistency property of human beings. Then we give a generalization of the first and second Gödel incompleteness theorem to stably 1,2-consistent formal systems. Our argument in particular re-proves the original incompleteness theorems from first principles, using Turing machine language to (computably) construct our "Gödel sentence" directly, in particular we do not use the diagonal lemma, nor any meta-logic, with the proof naturally formalizable in set theory. In practice such a stably consistent formal system could be meant to represent the mathematical output of humanity evolving in time, so that the above gives a formalization of a famous disjunction of Gödel, obstructing computability of intelligence.