  Maddy willingly concedes that philosophical doctrines such as definabilism or realism are important inspirations for mathematical development even if they fall short of justifications (1997, 192). And she accepts that “theories of mathematical truth or existence or knowledge do in fact appear in most mathematical debates over proper methods, alongside more typically mathematical considerations” (2007, 348). But she maintains that such theories have not in the end played an ‘instrumental role’ (2007, 359), and that they have racked up a ‘track record of irrelevance’ (2007, 366) in the development of mathematics.