##plugins.themes.academic_pro.article.sidebar##

Download
pdf
Statistic
Read Counter : 68 Download : 79

##plugins.themes.academic_pro.article.main##

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.

Keywords

Formalism Godel Incompleteness Paradox

##plugins.themes.academic_pro.article.details##

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite
Christopher Alexander Udofia PhD. (2022). Kurt Godel’s Rebuttal of Formalism in Mathematics. Zien Journal of Social Sciences and Humanities, 8, 31–39. Retrieved from https://zienjournals.com/index.php/zjssh/article/view/1592

References

  1. Berto, Francesco. There is Something about Godel: the Complete Guide to the Incompleteness Theorem. London: Blackwell, 2009.
  2. Hempel, Carl G. “What makes Mathematical Truth Indelible?” History and Philosophy of Science for Undergraduates. Helen Lauer Ed. Ibadan: Hope 464, 2003
  3. Chaitin, Gregory. Thinking about Godel and Turing: Essays on Complexity, 1970-2007 World Scientific publishing, 2007.
  4. Dedekind, Richard. “was Sind und was sollendie Zahlen”(“On what Numbers ought to be”) From Kant to Hilbert: A Source Book in the Foundations Mathematics.Vol.11.Ed.William Ewald. New York: Oxford, 1996.
  5. “ Continuity and Irrational Numbers.” From Kant to Hilbert: A Source Book in the Foundations Mathematics. Vol. 11. Ed. William Ewald New York: Oxford University press 1996.
  6. Feferman, Solomon. In the Light of logic. New York: Oxford, 1998.
  7. Ferrieros, Jose. Labyrinth of Thought: A History of Set Theory and it's Role in Modern Mathematics. Germany: Birkhauser Berkshire Again. 2007.
  8. Frege, Gottlob. “ Letter to Russell.” From Frege to Godel: A Source Book in Mathematical Logic, 1879-1931. London: Harvard University press, 1975.
  9. “Bezriffsschrift.” From Frege to Godel: A Source Book in Mathematical
  10. Logic: 1879-1931. Ed. Jean Van Heijenoort. London: Harvard press, 1967
  11. “LettertoRussell.”FromFregetoGodel:ASourceBookinMathematicalLogic,1879-1931.London:HarvardUniversitypress,1975.
  12. Franzen, Torkel. Godel’s Theorem: An Incomplete Guide to its Use and Abuse. Sweden: A.K. Peters, 2005.
  13. Fraenkel, Abraham A. et al. Foundation of Set Theory. vol. 67. Amsterdam: Elsevier, 2001.
  14. Godel, Kurt “On Undecidable Sentences.”Kurt Godel Collected Works vol. III: Unpublished Essays and Lectures. Feferman, Solomon et al., Eds. New York: Oxford University Press, 1995.
  15. "On Formally Undecidable Propositions of Principal Mathematica." Kurt Fidelity Collected Works, volume 1: Publications 1929-1936. German, Solomon etal. New York: Oxford University Press, 1986.
  16. Goldstein, R. Incompleteness: The Proof and Paradox of Kurt Gödel. Atlas Books/Norton; 2005.
  17. Hilbert, David. “On the infinite.” From Frege to Godel: A Source Book in Mathematical Logic, 1879-1931. London: Harvard University press, 1975.
  18. “Mathematische Probleme.” Bulletin of the American Mathematical Society.Vol. 8(1902)437-479.
  19. Kneebone, G. (135-136) (Mathematical Logic and the Foundations Mathematics: An Introductory Survey.London: D. Van Nostrand, 1963)
  20. Nagel, Ernest and Newman, R. James. Godel’s Proof. New York: 2001.
  21. Odifreddi, Piergiorgio. The Mathematical Century: The 30 Greatest Problems of the last 100 years. United kingdom: Princeton University press, 2004.
  22. Russell, Bertrand. Principles of Mathematics. London: Routledge, 2010.
  23. “Letter to Frege.” From Frege to Godel: A Source Book in Mathematical Logic, 1879-1931. London: Harvard University press, 1975.
  24. Russell, Bertand and Whitehead, Alfred North. Principia Mathematica. Cambridge: Cambridge University press, 1997.
  25. Peano, Guiseppe “The Principles of Arithmetic Presented by a new Method”. From Frege to Godel: a Source Book in Mathematical logic, 1879-1931 Jean Van Heijenroot ed. London: Oxford press, 1967.