Platonism, nominalism and parsimony

Platonist: Platonism is ideologically way more parsimonious than nominalism. For Platonism has one fundamental predicate applying to objects: “instantiates”. Nominalism, on the other hand, has many: “is charged”, “has mass”, “is ____ units away from”, etc.

Nominalist: Platonism also has properties or relations such as charge, mass, or being ____ units away from.

Platonist: Yes, it has these properties among its objects, but there are no fundamental predicates corresponding to them. Platonism has extra fundamental objects, but that’s a question of ontological, not ideological parsimony.

Nominalist: But the Platonist has names for these objects: “charge”, “mass”, etc. And if fundamental predicates count against ideological parsimony, so do names of fundamental entities.

Platonist: If names of fundamental entities count against ideological parsimony, then either we have an objectionably anthropocentric notion of parsimony on which the parsimony of a theory depends on how many fundamental things we have in fact named, or else we are counting nameable fundamental things, and we have to say that a theory on which there are 10⁹⁰ fundamental particles is far less ideologically parsimonious than one on which there are 10⁸⁰ of them, since they’re all nameable. But it seems absurd to decide how many particles we have on grounds of ideological parsimony.

Nominalist: But Platonism has an additional categorial division, between properties (including non-monadic ones, if we want to be charitable and not count relations separately) and non-properties.

Platonist: Yes, but this division is not fundamental, since it can be entirely defined in terms of the Platonist’s one fundamental predicate, and logical and modal operators that nominalists also need: a property is an x such that possibly there are things that instantiate x. (Granted, this requires a sparse Platonism that doesn’t have properties like square circularity.)

Nominalist: But surely there is a difference in kind that explains why some things can be instantiated and others cannot.

Platonist: Sure, but not a difference in fundamental kind. Fundamentally, Platonism should be considered a one-category theory with one predicate, and lots and lots of names.

Goods of instantiation

It's good that there have been someone with Albert Schweitzer's character, or a planet like Saturn. When we talk of the value of there being a thing of a particular sort, we're talking of the value of some property being--say, being a ringed gas giant of such and such appearance--being instantiated. Intuitively, that value of instantiation resides in the instantiated thing: it seems clear that Albert Schweitzer and Saturn have the goods of instantiating Schweitzerlikeness or Saturnlikeness.

But there is a problem with this obvious thing to say. For if the value of Saturnlikeness being instantiated is found in Saturn, then if there were a second planet, Shmaturn, that was Saturnlike then we would have that good twice over, once in each planet. But that misunderstands how goods of instantiation work. It is good that Saturnlikeness be instantiated. It isn't twice as good that it be instantiated twice.

So what do goods of instantiation reside in? One could answer: "Nothing. Goods don't need to have a substrate as a home." But I do have the Aristotelian intuition that goods have something like a metaphysical home, that it is good that p only if that is a good for something that p. Maybe I should abandon that intuition. But let's see what we can say given that intuition.

If Platonism is true, then a very natural answer is that the goods of instantiation are goods for the instantiated properties. This leads to a very interesting idea. Artists do good to the Platonic realm by instantiating it. God benefited kangarooness by creating kangaroos. This seems a bit crazy.

If theism is true, then perhaps goods of instantiation are actually good for God (in a non-internal way that is compatible with divine aseity). God has something supra-Schweitzerlike or supra-Saturnlike about him. It is good for God--it glorifies him--for there to be something Schweitzerlike or Saturnlike. This approach may not actually be that different from the Platonist one if properties are divine ideas.