  On its first reading, ontological naturalism in the philosophy of mathematics is a straightforward consequence of methodological scientific naturalism. It states that the ontology of mathematics is the mathematical ontology of our best natural science. Scientific platonists claim, following Quine and Putnam, that this ontology is platonist, as do mathematical-cum-scientific platonists (e.g., Burgess and Rosen (1997)). Resistance to scientific platonism and the associated indispensability argument has been mounted on several fronts (e.g., Field 1980, Sober 1993, Maddy 1997, ch. II.6, Paseau 2007). Consult Colyvan (2011) for a detailed discussion.