  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 that mathematical explanations need not have a true explanans and consequently the objects posited by such explanations need not exist (see now also Leng 2010, chapter 9).  By focusing on inference to the best explanation, Saatsi 2007 also resists the implication that scientific realism forces a commitment to mathematical Platonism. Another challenge has been raised by Bangu 2008, who claims that mathematical language is essential to the formulation of the question to be answered (“why is the life cycle period prime?”) and thus that the argument begs the question against the nominalist. The existence of numbers and properties of numbers is already assumed in the acceptance of the statement “the life cycle period is prime”. A similar objection to any attempt to use mathematical explanations in physics for inferring the existence of the mathematical entities involved in the explanation had already been raised in 1978b by Steiner, who had discarded such arguments with the observation that what needed explanation could not even be described without use of the mathematical language. Thus, the existence of mathematical explanations of empirical phenomena could not be used to infer the existence of mathematical entities, for this very existence was presupposed in the description of the fact to be explained. Indeed, he endorsed a line of argument originating from Quine and Goodman according to which “we cannot say what the world would be like without numbers, because describing any thinkable experience (except for utter emptiness) presupposes their existence.” (1978b, 20)