Journal Article

Discussion. Applied constructive mathematics: on Hellman's 'mathematical constructivism in spacetime'

H Billinge

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 51, issue 2, pages 299-318
Published in print June 2000 | ISSN: 0007-0882
Published online June 2000 | e-ISSN: 1464-3537 | DOI: http://dx.doi.org/10.1093/bjps/51.2.299
Discussion. Applied constructive mathematics: on Hellman's 'mathematical constructivism in spacetime'

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Hellman ([1998]) 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.

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Subjects: Philosophy of Science ; Science and Mathematics

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