2002/01/30 by Bhupinder Singh Anand, Anand, Bhupinder Singh
Arts and Humanities · Computer Science · Mathematics · Psychology · #03B10 #FOS: Mathematics #General Mathematics (math.GM) #Logic (math.LO) #Logic, programming, and type systems #Philosophy and History of Science #Philosophy and Theoretical Science #math.GM #math.LO #msc:03B10
paper · pdf · doi:10.48550/arxiv.math/0201307
v2: 40 pages. An HTML version of this paper is on the web at http://alixcomsi.com/index01.htm . Preface added, footnotes added, major revisions made
openalex publication_date 2002/01/30 · arxiv created 2002/06/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Goedel's explicit thesis was that his undecidable formula GUS is a well-formed, well-defined formal sentence in any formalisation of Intuitive Arithmetic IA in which the axioms and rules of inference are recursively definable. His implicit thesis was that GUS is not formally inconsistent in any such system. I argue in a constructive, intuitionistically unobjectionable, and recursively definable formalisation PP of IA that GUS is a well-formed formula but an ill-defined formal sentence reflecting the "Liar" paradox in PP. Further, introducing "formal truth" and "provability" values to selected propositions of IA through PP leads to the collapse of Lucas' Goedelian argument.