The Applicability of Mathematics and the Indispensability Arguments
DOI :
https://doi.org/10.20416/lsrsps.v3i1.313Mots-clés :
Philosophy of Mathematics, Indispensability Argument, Mathematical Explanation, Applicability of Mathematics, Metaphysics, Mathematical RealismRésumé
In this paper I will take into examination the relevance of the main indispensability arguments (Quine’s and Colyvan’s, Putnam’s, and explanatory indispensability argument) for the comprehension of the applicability of mathematics. I will conclude not only that none of these indispensability arguments are of any help for understanding mathematical applicability, but also that these arguments rather require a preliminary analysis of the problems raised by the applicability of mathematics in order to avoid some tricky difficulties in their formulations. As a consequence, we cannot any longer consider the applicability problems as subordinate to ontological ones: no ontological stance on mathematical entities (or truths) can offer an easy road to the comprehension of the applicability of mathematics.
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