Abstract
This paper argues that, insofar as we doubt the bivalence of the Continuum Hypothesis or the truth of the Axiom of Choice, we should also doubt the consistency of third-order arithmetic, both the classical and intuitionistic versions.
Underlying this argument is the following philosophical view. Mathematical belief springs from certain intuitions, each of which can be either accepted or doubted in its entirety, but not half-accepted. Therefore, our beliefs about reality, bivalence, choice and consistency should all be aligned.
Underlying this argument is the following philosophical view. Mathematical belief springs from certain intuitions, each of which can be either accepted or doubted in its entirety, but not half-accepted. Therefore, our beliefs about reality, bivalence, choice and consistency should all be aligned.
| Original language | English |
|---|---|
| Article number | nkac011 |
| Pages (from-to) | 283-305 |
| Number of pages | 23 |
| Journal | Philosophia Mathematica |
| Volume | 30 |
| Issue number | 3 |
| Early online date | 30 Jun 2022 |
| DOIs | |
| Publication status | Published - Oct 2022 |
Bibliographical note
The article was published in advance in June 2022. The issue appeared in October 2022.Keywords
- Scepticism
- Axiom of Choice
- Continuum Hypothesis
- Consistency
- Quantification
- Bivalence
ASJC Scopus subject areas
- Logic
- Philosophy