Research Article

Exploring the Foundational Significance of Gödelʼs Incompleteness Theorems

Yong Cheng [PDF]

Article information
Vol 2, No 1
RAP0012 – Research Article
Recieved: November 19, 2021
Accepted: June 21, 2022
Online Published: July 13, 2022
DOI: 10.18494/SAM.RAP.2022.0012
Cite this article
[APA]
Cheng, Y. (2022). Exploring the Foundational Significance of Gödelʼs Incompleteness Theorems. The Review of Analytic Philosophy, 2(1), 1-30. Japan: MYU. https://doi.org/10.18494/SAM.RAP.2022.0012

Abstract

Gödelʼs incompleteness theorems, published in 1931, are important and
profound results in the foundations and philosophy of mathematics. On the
basis of new advances in research on incompleteness in the literature, we
discuss the correct interpretations of Gödelʼs incompleteness theorems, their
influence on various fields, and the limit of their applicability. The motivation
of this paper is threefold: to explore the foundational and philosophical
significance of new advances in research on incompleteness since Gödel, to
introduce new advances in research on incompleteness to the general philosophy
community, and to commemorate the 90th anniversary of the publication of
Gödelʼs incompleteness theorems.

Keywords

The first incompleteness theorem, The second incompleteness theorem, The
limit of incompleteness, The intensional problem, Interpretation

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