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Full Length Article
Volume 0 - 2019 , Issue I - Vol 0, PP: 21-26 , 2019

Title

A short remark on Gödel incompleteness theorem and its self-referential paradox from Neutrosophic Logic perspective

Authors Names :   V. Christianto   1 *     F. Smarandache   2  

1  Affiliation :  Satyabhakti Advanced School of Theology – Jakarta Chapter, INDONESIA

    Email :  victorchristianto@gmail.com


2  Affiliation :  Dept. Mathematics & Sciences, University of New Mexico, Gallup, USA

    Email :  smarand@unm.edu



Doi   :  10.5281/zenodo.3908371

Received: January 17, 2019 Revised: April 04, 2019 Accepted: May 29, 2019

Abstract :

It is known from history of mathematics, that Gödel submitted his two incompleteness theorems, which can be considered as one of hallmarks of modern mathematics in 20th century. Here we argue that Gödel incompleteness theorem and its self-referential paradox have not only put Hilbert’s axiomatic program into question, but he also opened up the problem deep inside the then popular Aristotelian Logic. Although there were some attempts to go beyond Aristotelian binary logic, including by Lukasiewicz’s three-valued logic, here we argue that the problem of self-referential paradox can be seen as reconcilable and solvable from Neutrosophic Logic perspective. Motivation of this paper: These authors are motivated to re-describe the self-referential paradox inherent in Godel incompleteness theorem. Contribution: This paper will show how Neutrosophic Logic offers a unique perspective and solution to Godel incompleteness theorem.

Keywords :

Gödel incompleteness theorem , unprovability , undecidability , Neutrosophic Logic , Aristotelian Logic 

References :

[1] K. Gödel. UBER FORMAL UNENTSCHEIDBARE S¨ATZE DER “PRINCIPIA MATHEMATICA” UND VERWANDTER SYSTEME I, aus: “Monatshefte fur Mathematik und Physik” 38 (1931), 173-198.

[2] Rebecca Goldstein. Incompleteness: The Proof and Paradox of Kurt Gödel. New York: Atlas Books, 2005, pp. 156.

[3] Jason W. Steinmetz. An Intuitively Complete Analysis of Gödel’s Incompleteness. arXiv: 1512.03667

[4] Uri Ben-Ya’acov.  Gödel’s incompleteness theorem and Universal physical theories. 2019 J. Phys.: Conf. Ser. 1391 012067. doi:10.1088/1742-6596/1391/1/012067

[5] Peter Smith. An introduction to Gödel’s theorems. Second edition. Cambridge: Cambridge University Press, 2013.

[6] Janice Padula. The logical heart of a classic proof revisited: A guide to Gödel’s ‘incompleteness’ theorems. Australian Senior Mathematics Journal 25 (1) 2011.

[7] V. Christianto & F. Smarandache. Lost in Mathematics: The Perils of Post-Empirical Science & Their Resolution.  In press

[8] F. Smarandache. A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability", American Research Press, Rehoboth, NM, 1999.