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Bulletin of Pure and Applied Sciences- Math& Stat. (Started in 1982)
eISSN: 2320-3226
pISSN: 0970-6577
Impact Factor: 4.895 (2017)
DOI: 10.5958/2320-3226
Editor-in-Chief:  Prof. Dr. Lalit Mohan Upadhyaya
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Article Details

Bulletin of Pure and Applied Sciences- Math& Stat. (Started in 1982)
Year : 2021, Volume & Issue : BPAS-Maths & Stat 40E(2), JUL-DEC 2021
Page No. : 172-176, Article Type : Original Aticle
Article DOI : 10.5958/2320-3226.2021.00020.5 (Communicated, edited and typeset in Latex by Lalit Mohan Upadhyaya (Editor-in-Chief). Received May 10, 2020 / Revised July 21, 2021 / Accepted August 18, 2021. Online First Published on December 17, 2021)

Logic in general and mathematical logic in particular

Bertrand Wong1
Author’s Affiliation : 1 Department of Science and Technology, Eurotech, Singapore Branch, Singapore. 1. E-mail: [email protected]

Corresponding Author : Bertrand Wong,
E-Mail:-[email protected]


This paper brings up some important points about logic, e.g., mathematical logic, and also an inconsistence in logic as per Gödel’s incompleteness theorems which state that there are mathematical truths that are not decidable or provable. These incompleteness theorems have shaken the solid foundation of mathematics where innumerable proofs and theorems have a place of pride. The great mathematician David Hilbert had been much disturbed by them. There are much long unsolved famous conjectures in mathematics, e.g., the twin primes conjecture, the Goldbach conjecture, the Riemann hypothesis, etc. Perhaps, by Gödel’s incompleteness theorems the proofs for these famous conjectures will not be possible and the numerous mathematicians attempting to find the solutions for these conjectures are simply banging their heads against the metaphorical wall. Besides mathematics, Gödel’s incompleteness theorems will have ramifications in other areas involving logic. This paper looks at the ramifications of the incompleteness theorems, which pose the serious problem of inconsistency, and offers a solution to this dilemma. The paper also looks into the apparent inconsistence of the axiomatic method in mathematics. 

2020 Mathematics Subject Classification : 03A05, 03A10, 03AA99, 03F40, 03F99.


Logical deduction, Gödels incompleteness theorems, not provable, validity, truths, theorems, axioms, conjectures.
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