(1) Nominalism states that there aren't strings, formulas, numbers, sets, sequences, functions, groups, etc.This is not some containable inconsistency, say to do with idealization, or frictionless planes, etc. Nominalism states that there are no physical quantities. Nominalism states that Peano arithmetic doesn't exist. Nominalism states that an SU(3) gauge theory like QCD is false because there are no groups. Etc. But science states that there are quantities; that Peano arithmetic does exist, and is not finitely axiomatizable; that the gluons are associated with an SU(3) gauge symmetry; etc.
(2) Science (e.g., physics, linguistics) states that there are strings, formulas, numbers, sets, sequences, functions, groups, etc.
Therefore, nominalism is inconsistent with science.
The premises (1) and (2) are justified as follows. The first (1) is how nominalists describe their view. And (2) is justified by looking at a physics textbook.