Comments on S Kauffman's paper arxiv:0907.2492
Elemer E Rosinger
TL;DR
This paper critiques Kauffman's approach to scientific theories, proposes a method to develop mathematical theories beyond Gödel's limitations, and integrates recent work on inconsistent and self-referential mathematics.
Contribution
It introduces a novel approach combining inconsistent and self-referential mathematics to construct theories beyond Gödel's incompleteness.
Findings
Identifies deficiencies in Kauffman's proposal
Suggests a new framework using inconsistent mathematics
Proposes theories that surpass Gödel's limitations
Abstract
Deficiencies in Kauffman's proposal regarding a new way for building scientific theories are pointed out. A suggestion to overcome them, and in fact, independently construct mathematical theories which are beyond the reach of Goedel's incompleteness theorem is presented. This suggestion is based on bringing together recent developments in literature regarding inconsistent mathematics and self-referential mathematics.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Quantum Computing Algorithms and Architecture · Quantum Mechanics and Applications