Applied constructive mathematics: On Hellman's 'mathematical constructivism in spacetime'

claims that constructive mathematics is inadequate for spacetime physics and hence that constructive mathematics cannot be considered as an alternative to classical mathematics. He also argues that the contructivist must be guilty of a form of a priorism unless she adopts a strong form of anti-realism for science. Here I want to dispute both claims. First, even if there are non-constructive results in physics this does not show that adequate constructive alternatives could not be formulated. Secondly, the constructivist adopts a 'philosophy first' approach that Hellman rejects. This deep difference means that the viability of constructive mathematics cannot yet be decided by determining whether current scientific theories require classical mathematics. We need to decide which approach is most appropriate before we can even determine how we should go about deciding whether we should be constructive or classical mathematicians.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1093/bjps/51.2.299
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 31,385
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles
On the Scope and Force of Indispensability Arguments.Geoffrey Hellman - 1992 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:456-464.
Can Constructive Mathematics Be Applied in Physics?Douglas S. Bridges - 1999 - Journal of Philosophical Logic 28 (5):439-453.
Did Bishop Have a Philosophy of Mathematics?Helen Billinge - 2003 - Philosophia Mathematica 11 (2):176-194.
Varieties of Constructive Mathematics.D. S. Bridges - 1987 - Cambridge University Press.
Mathematical Constructivism in Spacetime.Geoffrey Hellman - 1998 - British Journal for the Philosophy of Science 49 (3):425-450.
Added to PP index

Total downloads
50 ( #116,968 of 2,225,984 )

Recent downloads (6 months)
2 ( #251,215 of 2,225,984 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature