Explanatory Indispensability Arguments in Metaethics and Philosophy of Mathematics

This chapter defends explanatory indispensability arguments for the existence of irreducibly evaluative properties from the so-called ‘supervenience objection’. A structurally similar argument and objection are found in the philosophy of mathematics. It is argued that a response to the supervenience objection is available that is structurally similar to a recent response made in the philosophy of mathematics case. The core claim is that reductive realists in metaethics, like nominalists in philosophy of mathematics, have to take what has been called the ‘hard road’. And in metaethics, like in philosophy of mathematics, there are good reasons to think that this road is not navigable.