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On Optimism and Opportunism in Applied Mathematics

  • Pages : 121 à 145
  • DOI : 10.1023/B:ERKE.0000005144.7976
  • URL : Lien externe
  • Date de création : 04-01-2011
  • Dernière mise à jour : 04-01-2011

Résumé :


Applied mathematics often operates by way of shakily rationalized expedients that can neither be understood in a deductive-nomological nor in an anti-realist setting.Rather do these complexities, so a recent paper of Mark Wilson argues, indicate some element in our mathematical descriptions that is alien to the physical world. In this vein the “mathematical opportunist ” openly seeks or engineers appropriate conditions for mathematics to get hold on a given problem.Honest “mathematical optimists”, instead, try to liberalize mathematical ontology so as to include all physical solutions. Following John von Neumann, the present paper argues that the axiomatization of a scientific theory can be performed in a rather opportunistic fashion, such that optimism and opportunism appear as two modes of a single strategy whose relative weight is determined by the status of the field to be investigated. Wilson's promising approach may thus be reformulated so as to avoid precarious talk about a physical world that is void of mathematical structure. This also makes the appraisal of the axiomatic method in applied matthematics less dependent upon foundationalist issues.


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