An argument that presupposes what it seeks to prove against an opponent begs the question against that opponent

The argument has not gone unchallenged. Indeed, Leng 2005 tries to resist the conclusion by blocking premise b). She accepts a) but questions the claim that the role of mathematics in such explanations commits us to the real existence (as opposed to a fictional one) of the posits. This, she argues, will be granted when one realizes that both Colyvan and Baker infer illegitimately from the existence of the mathematical explanation that the statements grounding the explanation are true. She claims