|An Inventory of Ontological Views About Universals|
Let's expand our inventory of possible views a little. Possible views include (more or less in order of increasing ontological commitment):
Nominalism. (Quine links this with formalism in the philosophy of mathematics.) There are only particular things; there are no universals. But wait: if there are no universals, then what are we doing when we group objects by their shared properties? Answers include:
Class Nominalism. Classes are abstract, but they aren't universals. (I think.) Any bunch of particulars can be grouped into a set. To say that an object is red (for example) is only to say that it is an element of a particular set of objects.
Resemblance Nominalism. To say that an object is red is to say that it is at least as similar to certain paradigm objects as they are to each other.
Conceptualism. (Quine links this with intuitionism in the philosophy of mathematics.) There are universals, but they are mind-dependent. They are constructed by us (they are concepts or ideas), and exist only in our minds.
Realism. (Quine links this with logicism in the philosophy of mathematics.) There are universals, and they aren't mind-dependent. No, they really, honest-to-gosh exist. --But how many universals are there? Where are they located? Must they have instances?
Universalia in rebus. There are universals, but only where they are instantiated (that is, only where their instances exist). (So they can be entirely in several places at once. But since universals are only where their instances are, there can be no universals without instances.)
Universalia ante rem. There are universals, and they are not located in space and time at all. "Where are they?" is a bad question, since "where" asks for a location; locations are positions in space and time; and universals don't have such positions. But the idea that they exist, but do not exist anywhere in space and time, leads naturally to the Platonic view that there is a sort of separate world of Forms.