Some brief notes on nominalism

Nominalism seeks the simplest explanation in ontology.  One of their confusions regarding realism, though, is that they think universals have spatial location.  But as B. Russell pointed out, the universal “being north of” is not spatial.

The austere nominalist is committed to just one ontological category, particulars.  Austere nominalism runs into problems when it gets to the category of abstract particulars, such as “courage is a virtue.”

Metalinguistic Nominalism

Not universals; just linguistic expressions about nonlinguistic objects.  One of the difficulties, though, is it is forced to rely on type/token distinctions, which start to look like universals. It’s not hard to see connections with postmodernism.

Trope Theory

By far the most interesting.  Concrete particulars have colors, etc., but those attributes are just particulars.  So, if two objects have the color “red,” does that mean they share the universal “redness”?  Not necessarily.  Rather, they have the set of resembling trope red.  But isn’t a set a universal?  Not exactly.  Sets have clear-cut identity conditions.  Universals do not.  Sets are identical just in case all members are identical.  Set, α, is identical with set ,β , when the members of each set are identical with one another.

So this appears to give the trope nominalist an edge over the realist, except for one problem.  Take the referents

“Being a unicorn”

And

“Being a griffin.”

Since there are no such things as unicorns or griffins, they must belong to the set, null.  As Loux points out, “given the identity conditions for sets, there is just one null set,” which would mean both propositions are in fact identical.  But this is clearly false (91-92), as any schoolchild knows.

Other problems with trope nominalism (cf Moreland):

  • membership in a set of tropes is arbitrary (Moreland doesn’t expound)
  • Two red balls (A and B) resemble each other because they have red₁ and red₂ constituents.
    • The copula “is” in question is neither of predication or identity, but set membership.
    • Rejoinder:  why red and not green?  Red tropes resemble each other in a different way than green tropes?  Why?
  • If two tropes, Red and Sweet, are in the same location, how are they not identical on the Trope Nominalist view.
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