About the Chasm Separating the Goals of Hilbert's Consistency Program\n from the Second Incompletess Theorem

2018/07/12 by Dan E. Willard, Willard, Dan E.
Computer Science · Mathematics · Physics and Astronomy · #03B52 #03F25 #03F45 #03H13 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Logic, programming, and type systems #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications

paper · pdf · doi:10.48550/arxiv.1807.04717

openalex publication_date 2018/07/12 · openalex created_date 2022/09/12 · openalex updated_date 2026/07/28

Abstract

We have published several articles about generalizations and boundary-case\nexceptions to the Second Incompleteness Theorem during the last 25 years. The\ncurrent paper will review some of our prior results and also introduce an\n`enriched' refinement of semantic tableaux deduction. While the Second\nIncompleteness Theorem is a strong result, we will emphasize its boundary-case\nexceptions are germane to Global Warming's threat because our systems can own a\nsimultaneous knowledge about their own consistency, together with an\nunderstanding of the \Π₁ implications of Peano Arithmetic.\n

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