Saturday, November 30, 2013

Two kinds of Platonism

There are two kinds of Platonism. Both hold that there are properties. But they differ as to the grounding relation that holds between predication and property possession (I will also assume that what goes for properties goes for relations, but sometimes formulate things just in terms of properties for simplicity). Both agree that if there is a property of Fness (there might not be if F is gerrymandered or negative, on sparse Platonisms), then x is F if and only if x instantiates Fness. Deep Platonism further affirms:

  1. If there is a property of Fness, then the fact that x is F is grounded in the fact that x instantiates Fness.
Shallow Platonism denies (1). It is likely to instead affirm:
  1. If there is a property of Fness, then the fact that x is F partly grounds or explains the fact that x instantiates Fness.

Deep Platonism faces two problems. The first is the Regress Problem. For if Deep Platonism is true, then "instantiates" seems non-gerrymandered and positive, and so it should correspond to a Platonic entity, the relation of instantiation. Then, the fact that x instantiates Fness will be grounded in the fact that x and Fness instantiate instantiation. But this leads to a vicious regress where each instantiation relation is grounded in the next.

The second is the Creation Problem. Everything that exists and is distinct from God is created by God. If the properties are all distinct from each other, then at most one is identical with God, and hence all but at most one property are created by God. But explanatorily prior to creating anything, will have multiple properties such as that he is able to do something and that he knows something. But how can he have those properties when there is at most one property at this point in the explanatory story?

Both problems have Deep Platonist solutions. For instance, one might say that "instantiates" is the unique non-gerrymandered and positive predicate that has no Platonic correspondent, or one might say that (1) has an exception in the case of instantiation. And one might say that God has at most one property, say divinity, and he is identical to that property. (But this, too, seems to lead to exceptions for (1), or perhaps an implausible view of what predicates correspond to properties. For there sure seem to be many other non-gerrymandered and positive predicates, like "is wise" and "is powerful", that apply to God.)

But Shallow Platonism has a particularly neat solution to both problems. There either is no regress, or if there is a regress, it is an unproblematic forward regress: because x is F, x and Fness instantiate instantiation, and because of that x, Fness and instantiation instantiate instantiation, and so on. Forward regresses are not at all problematic. And while it may be explanatorily prior to the creation of properties (or of all but one property) that God is wise, it is not explanatorily prior to the creation of properties that God instantiates wisdom.


Mike Almeida said...

The second is the Creation Problem. Everything that exists and is distinct from God is created by God.

Platonists deny that divine ultimacy entails that God creates properties. So, this shouldn't be a problem for them. God creates properties only if his omnipotence extends to doing the impossible: viz., creating necessarily existing objects. But there is no dialectical pressure to extend omnipotence that far. Restrict omnipotence to the metaphysically possible--or something in that ballpark--and you make Platonic properties irrelevant to divine ultimacy. Further, you eliminate this problem for Platonists.

Alexander R Pruss said...

But it's not a question about omnipotence. It's a question about the standard monotheistic doctrine that God created everything other than himself out of nothing.

Sure, you can restrict the quantifiers and say "everything other than himself or abstracta". But that's changing the doctrine. Moreover, you then have to have some sort of an account of abstracta, and that's notoriously problematic.

Mike Almeida said...

It's a question of metaphysical dependence, I understand. Now, whether you move the abstracta into God's mind to secure spme sort of dependence, or you leave the objects on their own, you have objects that are not in any interesting way "created". They are not created in Scotus or Leibniz. Even for Aquinas, they are not created, but in His nature. To get them created, you have to take a radical view of metaphysical dependence. Leftow takes such a view. But Leftow's view, as all such radical views do, is of dubious coherence. I think it's probably not coherent, as I say in a PQ review coming up, but judge for yourself.

Dan Johnson said...


This is really helpful and important, and it parallels the two kinds of Platonism or "erzatsers" about modality that you talk about in your book, the unambitious erzatser and the ambitious erzatser. You are right that the most interesting problems arise mainly for the ambitious sort, or the "deep" Platonist.

Now my question is this: why would you want to be a shallow Platonist? I understand the motivation(s) for deep Platonism. But what good does shallow Platonism do you? Why would you believe that there were such things as Platonic Forms if that wasn't part of the ground or truthmaker of things having properties?

Feels to me like the tradition nominalism/realism debate is a debate over the grounds of ordinary predicative truths, which means Deep Platonism is the only view that really matters. Of course, I would have said that about possible worlds metaphysics, but Plantinga has insisted that he didn't mean to be in the business of identifying grounds for modal truths.

Alexander R Pruss said...

Van Inwagen thinks he can motivate Platonism without any talk of grounding or explanation, and he eschews making any grounding claims (I think he thinks they're nonsense). If so, then his Platonism is Shallow Platonism (of the weaker version that doesn't make the converse explanatory/grounding claim).

For instance, take van Inwagen's argument that there are features spiders and insects have in common, and hence there are features. Nothing about grounding or explanation here.

Heath White said...

I heard PVI give a talk on this once, and the gist was that he didn't really want to be any kind of platonist but felt forced into it by standard Quinean ontological-commitment arguments like the insects/spiders one.