 Modified versions of the indispensability argument stressing the importance of the indispensability of mathematics for explanations in science were considered, before Baker, by the nominalist Field as a challenge to the platonist use of such arguments. Field (1989, 14–20) accepts the cogency of this type of inference to the best explanation but he argued (Field 1980) that platonist mathematics could be replaced by a nominalistically acceptable theory that was sufficient for the development of classical mechanics. In addition, the nominalistic replacement would also have the virtue of providing ‘intrinsic’ explanations of the physical phenomena (for a probing discussion of ‘intrinsic explanation’ see Marcus 2013). That led to much discussion as to how far Field’s program could be pushed. Malament 1982 had objected that the obstacles to the nominalization of phase-space theories in Hamiltonian mechanics seemed insuperable. Lyon and Colyvan (2008) go beyond Malament’s claim by arguing that even if a nominalistic reconstruction of phase-space theories were available, the nominalist would still have to show that such reconstruction can yield the explanations yielded by the non-nominalistic version(s). They believe that the nominalist will fail in this task and make a plausible case for their thesis by providing a case study of a physical system known as the Hénon-Heiles system (incidentally, this same case study is used by Molinini 2011 to test the theories of mathematical explanation offered by Steiner, Kitcher and van Fraassen). The system describes the motion of a star around a galactic center. Their claim is that the phase-space analysis of the system provides explanations that cannot be provided by any nominalist reconstruction. At the end of their article, Lyon and Colyvan also review a few possible moves the nominalist can make in response. One such move would deny that mathematical explanations have any bearing on physical explanations and that some bridge principles linking the mathematics to the physical system, are required. They reply: