It all comes down to the status of abstractions. In what way do they exist? As the most real sort of thing? Or only as concepts, or names for classes of things?
Theory of Forms - Wikipedia, the free encyclopedia

It would be helpful if you devoted at least a couple of minutes to sketching out what you did understand so far, and what you think you missed, and why you feel your metaphysics professor wasn't thorough. It is a big topic and this might provide an entry point.

A universal is a kind of umbrella under which we put groups of individual things who share an essential quality or qualities. For example, all triangles have the feature of triangularity (three angles adding up to two right angles, etc.). So the question becomes, does this "triangularity" have any ontological status, such that it is an actual feature of reality, or is it just a name we give to a group of similar objects?

The realist position regarding Universals says that Universals themselves exist, in some substantial way. What that means is that a universal, say the form of a triangle or the color red, actually exists as a universal thing. Two examples of this position have been 1) Plato, whose theory of forms put forward the idea that Pure objects (triangularity, redness) exist separate from the particular instances of those objects (e.g.this triangle, or a red shirt). Plato's theory was understandably rather primitive, and few still hold the position in exactly the way he put it forward. 2) Bertrand Russell is an example of a modern realist re: universals. He puts forth arguments supporting the idea that universals subsist independently of the spatialtemporal instances of them.

Nominalism states that universal entities of this kind (triangularity, redness) don't actually exist, but that they are only our classifications for a multiplicity of similarities, which we abstractly group together. This is more of an Aristotelian position (though not exactly), but the position is as ancient as philosophy itself. The modern analytic literature has all kinds of dumb names, like 'tropes' and things. But for good nominalist approaches one ought to look for Continental philosophers.

I prefer the Platonist explanation, even though I know it is very difficult to prove. However I think there is an argument emerging for it from the anthropic principle. There are a few key ratios and constants which have very specific characteristics and without which, life and the universe would not exist. These could be interpreted as a type of Platonic law or real universal. Now, do these 'exist'? Well, no, they don't 'exist'. They can only be inferred or measured. You can't point at anything in the universe and say, look, there is the gravitational constant (or whatever it is). But on the other hand, if it weren't real, nothing would exist.

I think this is the way that Plato's universals exist - actually, not 'exist', but this is the way in which they are real - and that the Nominalists are barbarians.:bigsmile: