Logic in general and mathematical logic in particular ∗

Bertrand Wong

doi:10.48165/

Authors

Bertrand Wong Department of Science and Technology, Eurotech, Singapore Branch, Singapore.

DOI:

https://doi.org/10.48165/

Keywords:

Logical deduction, Gödel’s incompleteness theorems, not provable, valid itY, truths, theorems, axioms, conjectures

Abstract

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 incom pleteness 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 hy pothesis, 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.

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Bertrand Wong

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