Nominalism, Ideological Parsimony, and Property Pythagoreanism

Dan Marshall (Lingnan University)

Abstract: The ideological (or qualitative) parsimony of a theory is roughly how many fundamental aspects of reality there are according to the theory. It is widely held that ideological parsimony is an important theoretical virtue. It is also widely held that the best realist theories about abstract objects are more ideologically parsimonious than the best nominalist (or anti-realist) theories, and that this is a good reason to be a realist about abstract objects.

This paper first discusses how we should understand ideological parsimony. It then discusses one important argument for realism about abstract objects being more ideologically parsimonious that nominalism. The argument appeals to property pythagoreanism, which is a realist view that endorses metaphysical analyses such as (1) and (2), where p is the property of being unit positively charged and r is the property of being 1 metre away from.

(1)  For it to be the case that x is unit positively charged is for it to be the case

that x instantiates p

(2)  For it to be the case that x is 1 metre away from y is for it to be the case

that x stands in r to y.

The argument is that, since property pythagoreanism is the best realist theory, and since property pythagoreanism is more ideologically parsimonious than the best nominalist theories, the best realist theories are more ideologically parsimonious than the best nominalist theories. I will argue that this argument fails.