Publications

This short paper was written after a presentation on the significance of one of Gödel's theorems on intuitionistic arithmetic at the Canadian Society of History and Philosophy of Maths in Vancouver, 2008.

Title:
The Significance of the Kolmogorov-Gödel Embedding
Authors:
Nicolas Fillion
Journal:
Proceedings of the Canadian Society for the History and Philosophy of Mathematics

Additional information

Abstract: The goal of this paper is to evaluate the three classical foundational strategies for arithmetic in light of the Kolmogorov-Gödel embedding of classical arithmetic into intuitionistic arithmetic. Specifically, as far as arithmetic is concerned, it will be shown that: (1) It is possible to characterize the opposition between finitism and intuitionism in a purely formal way, and finitism is strictly more constructive than intuitionism, (2) It is impossible to characterize the opposition between logicism and intuitionism in a purely formal way. It will also be argued that, epistemologically, logicism and intuitionism are simply variations on the same theme.

Download the PDF of the paper.

Cite as:
Fillion, N. (2008). The Significance of the Kolmogorov-Gödel Embedding. Proceeding of the Canadian Society of History and Philosophy of Mathematics, Ed. A. Cupillari, 2008, 77-88.

BibTeX Entry:
@INPROCEEDINGS{Fillion(2008),
author = {Fillion, Nicolas},
editor = {Cupillari, Antonella},
title = {The Significance of the {K}olmogorov-{G}\"odel Embedding},
booktitle = {Proceedings of the Canadian Society for History and Philosophy of Mathematics},
year = {2008}
}