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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.