Joseph Melia’s nominalism and the indexing theory of numbers

According to the Quine-Putnam indispensability argument, we are committed to all the entities that are indispensable to our best scientific theory. John Melia argues contra Quine-Putnam by claiming that even though such entities as numbers are indispensable to our best science, there is reason to deny their existence. In order to defend Melia?s theory from criticism put forth by Mark Colyvan, who demands that Melia provide a nominalistically acceptable paraphrase of our best scientific theory, supporters of this view have argued for the stronger claim that numbers are not indispensable. They all claim that numbers have an indexing role in the scientific explanation. In this article, I will consider some of the arguments for the indexing theory and point out its inadequacies.