An article by Assistant Professor of Philosophy Russell Marcus was published in the philosophy of mathematics journal Philosophia Mathematica. In “How Not to Enhance the Indispensability Argument,” he presented considerations against the new enhanced or explanatory version of the indispensability argument.
The indispensability argument says that our mathematical beliefs are justified by the uses of mathematics in science (e.g. real numbers for measurement and sets for functions). The new explanatory argument says that our mathematical beliefs are justified by their appearances in scientific explanations. This argument differs from the standard indispensability argument which focuses on the uses of mathematics in scientific theories.
Marcus argued that “the new argument depends for its plausibility on an equivocation between two senses of explanation. On one sense, the new argument is an oblique restatement of the standard argument. On the other sense, it is vulnerable to an instrumentalist response. Either way, the explanatory indispensability argument is no improvement on the standard one.”