Mathematical Pluralism and Indispensability

Abstract

Pluralist mathematical realism, the view that there exists more than one mathematical universe, has become an influential position in the philosophy of mathematics. I argue that, if mathematical pluralism is true (and we have good reason to believe that it is), then mathematical realism cannot (easily) be justified by arguments from the indispensability of mathematics to science. This is because any justificatory chain of inferences from mathematical applications in science to the total body of mathematical theorems can cover at most one mathematical universe. Indispensability arguments may thus lose their central role in the debate about mathematical ontology.

Mathematical pluralism

“…Balaguer has to abandon the idea of de re truth conditions and de re knowledge of mathematical claims. Jonas (2023) (§4.2.2) notes that such a result leaves it unclear as to “which one of the countless copies of the numbers 13 and 17 are involved in scientific explanation”.…”