MATHEMATICS IS A CIRCULAR REASONING
Abstract
This paper elucidates the fundamental limitations of mathematical logic revealed by Gödel's incompleteness theorems and the epistemological circular structure inherent in mathematical reasoning. We propose reinterpreting this circularity as a Bayesian belief updating process, where consistency is treated as a probabilistic belief updated based on empirical data.
Fields of Study & Subjects
History and Theory of Mathematics
Logic
Reasoning
and Knowledge
Computability
AI Algorithms
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 25 February 2026
- Language
- EN
- Document type
- Preprint