Fictionalism and mathematical explanations

Pamela Ann Jose Boongaling

Abstract


In this paper, I place Mary Leng’s version of mathematical instrumentalism within the context of the debate in mathematical realism/anti-realism as well as within the context of the platonism/nominalism debate. I maintain that although her position is able to show how the conjunction of Quinean naturalism and confirmational holism does not necessarily lead to the conclusion that mathematical objects must necessarily exist for they are indispensable in our best scientific theories; her usage of both theses still leads to platonism. Such is the case for her characterization of scientific theories as akin to a set-theory that accommodates fictitious objects and statements within it is untenable due to the dependence of fictions on a realist ontology.

Keywords: fictionalism, mathematical instrumentalism, indispensability argument, Mary Leng, platonism, nominalism.



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