Graduate studies at Western
British Journal for the Philosophy of Science 51 (2):299-318 (2000)
|Abstract||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)|
|Through your library||Configure|
Similar books and articles
Geoffrey Hellman (1992). On the Scope and Force of Indispensability Arguments. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:456 - 464.
D. S. Bridges (1987). Varieties of Constructive Mathematics. Cambridge University Press.
Helen Billinge (2003). Did Bishop Have a Philosophy of Mathematics? Philosophia Mathematica 11 (2):176-194.
Douglas S. Bridges (1995). Constructive Mathematics and Unbounded Operators — a Reply to Hellman. Journal of Philosophical Logic 24 (5):549 - 561.
Douglas S. Bridges (1999). Can Constructive Mathematics Be Applied in Physics? Journal of Philosophical Logic 28 (5):439-453.
Geoffrey Hellman (1997). Quantum Mechanical Unbounded Operators and Constructive Mathematics – a Rejoinder to Bridges. Journal of Philosophical Logic 26 (2):121-127.
E. B. Davies (2005). A Defence of Mathematical Pluralism. Philosophia Mathematica 13 (3):252-276.
Solomon Feferman, Relationships Between Constructive, Predicative and Classical Systems of Analysis.
Geoffrey Hellman (1998). Mathematical Constructivism in Spacetime. British Journal for the Philosophy of Science 49 (3):425-450.
Added to index2009-01-28
Total downloads10 ( #114,517 of 739,079 )
Recent downloads (6 months)1 ( #61,778 of 739,079 )
How can I increase my downloads?