The Operator Theory of Instantiation

Abstract

Armstrong holds the Supervenience Theory of instantiation, namely that the instantiation of universals by particulars supervenes upon what particulars and what universals there are, where supervenience is stipulated to be explanatory or dependent supervenience. I begin by rejecting the Supervenience Theory of instantiation. Having done so it is then tempting to take instantiation as primitive. This has, however, an awkward consequence, undermining one of the main advantages universals have over tropes. So I examine another account hinted at by Armstrong. This is the Operator Theory of instantiation, by which I mean the theory that universals are operators, and that a particular instantiates a monadic universal because the universal operates on the particular, resulting in the state of affairs. On this theory the state of affairs supervenes on the instantiation rather than vice versa. In the second part of the paper I develop this theory of universals as operators, including an account of structural universals, which are useful for accounts of modality and of mathematics.