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.
Highlights
Philosophy of mathematics is characterized by the distinction between the foundational and anti-foundational positions in the field
This paper focuses on the nominalist and platonist arguments, since they provide the most viable versions of the third and fourth characteristics of the debate which I mentioned earlier
(3) I have pointed out that regardless of whether Leng shows that mathematical statements in our best scientific theories can be treated as akin to fictions, the primary problem with her account is that fictions require a realist ontology
Summary
Philosophy of mathematics is characterized by the distinction between the foundational and anti-foundational positions in the field. Adopting the semantic view of theories, in this context, allows the distinction between ontological and truth-value MR∕MAR since it allows one to determine the objectivity of a mathematical statement by positing that there is a model which gives it a true interpretation. In this scenario, the truth of AX is separated from empirical matters since the truth of AX is utterly dependent on the operations and relations allowed between the members of U. Filosofia Unisinos – Unisinos Journal of Philosophy – 20(3):268277, sep/dec 2019
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