Kurt Godel’s Rebuttal of Formalism in Mathematics

Abstract

A major cognitive barrier that Philosophers of Mathematics encounter in the course of unraveling mathematical related ideas of thinkers has been that of rendering the sophisticated crypto-codes associated with the mathematical equations of such ideas into a non-technical form for easy comprehension by both experts and non-experts. The ultimate objective of this research with the title, Kurt Godel’s Rebuttal of Formalism in Mathematics, is to present the incompleteness theorems of Kurt Gödel in a non-technical manner so as to make it equally intelligible to both philosophers and mathematicians. In order to achieve the prime goal stated above, the research will undertake a narrative exposition of some of the attempts to formalize the axioms of mathematics. In the exposition, the contributions of Euclid, Dedekind, Hilbert, Whitehead and Russell in the attempt to build Mathematics into a rigorous formal system that is complete, consistent and decidable would be analyzed. The hallmark of this essay is contained in the discussion of Kurt Gödel’s rebuttal of formalism through the instrumentality of his incompleteness theorems.