  To illustrate this problem, suppose, as many philosophers maintain, that the general principle of ontological economy—posit as few entities as possible—is a scientific standard. Suppose also, as Penelope Maddy maintains, that a set-theoretic version of ontological profligacy—posit as many sets as possible—is a mathematical standard (this is one way of cashing out the set-theoretic maxim Maddy calls MAXIMIZE). These two standards clash, as Maddy recognises (1997, 131). Thus given these assumptions a predicativist set theory which posits a relatively small number of sets, say of the kind developed in Hermann Weyl's Das Kontinuum, might be scientifically superior to ZFC, which posits more sets. Yet ZFC is generally thought to be mathematically superior to a predicativist set theory. Perhaps the right diagnosis is that the clash is only superficial, since the correct scientific version of ontological economy is ‘posit as few concrete entities as possible’ and the correct mathematical version of ontological profligacy is ‘posit as many abstract entities as possible’. However that may be in this instance, the mathematical-cum-scientific naturalist has to come up with a general policy for dealing with potential clashes, or argue that no such clashes are possible.