 Whereas the issues treated in section 3.1 affect mainly the methodology of science, a different set of issues has emerged in connection to the nominalism-platonism debate in philosophy of mathematics. Colyvan 2010 (and the earlier Colyvan 2006) contrasts hard road and easy road nominalism. While the hard road nominalist offers non-mathematical versions of our best scientific theories, the easy road nominalist simply retains the original, mathematical versions of the theories, and qualifies our acceptance of them so as to exclude a commitment to abstract entities. Colyvan argues that easy road nominalists such as Azzouni, Melia and Yablo are unable to account for the explanatory role of mathematics in science, for example, the explanation of the absence of asteroids in the Kirkwood gaps. He claims that any account of how such explanations are possible that avoids mathematical commitments would require hard road nominalism, that is, showing how one can eliminate reference to mathematical entities. Replies include Bueno 2012, Yablo 2012, Leng 2012, and the rejoinder Colyvan 2012a. Bueno claims that the mathematics used in scientific explanations only plays a descriptive role and not an explanatory role. Yablo distinguishes three degrees of mathematical involvement in physical explanation, the third of which entails the existence of mathematical entities but, he claims, it is hard to establish whether it ever obtains.  Leng defends the possibility of accounting for mathematical explanations nominalistically and emphasizes the importance of structural explanations, which according to her do not commit us to mathematical objects but only to physical objects that instantiate a mathematical structure. Much of the discussion in this area, which addresses whether the mathematics present in the formulation of scientific theories or mathematical explanations offered in science is eliminable, is deeply related to so-called indispensability arguments. 