Thoughts on theistic Platonism

Platonists hold that properties exist independently of their instances. Heavy-weight Platonists add the further thesis that the characterization of objects is grounded in or explained by the instantiation of a property, at least in fundamental cases. Thus, a blade of grass is green because the blade of grass instantiates greenness (at least assuming greenness is one of the fundamental properties).

Heavy-weight Platonism has a significant attraction. After all, according to Platonism (and assuming greenness is a property),

1. Necessarily (i) an object is green if and only if (ii) it instantiates greenness.

The necessary connection between (i) and (ii) shouldn’t just be a coincidence. Heavy-weight Platonism explains this connection by making (ii) explain or ground (i). Light-weight Platonism, which makes no claims about an explanatory connection between (i) and (ii), makes it seem like the connection is a coincidence.

Still, I think it’s worth thinking about some other ways one could explain the coincidence (1). There are three obvious formal options:

2. (ii) explains (i)
3. (i) explains (ii)
4. Something else explains both (i) and (ii).

Option (2) is heavy-weight Platonism. But what about (2) and (3)? It’s worth noting that there are available theories of both sorts.

Here’s a base theory that can lead to any one of (2)–(4). Properties are conceptions in the mind of God. Furthermore, instantiation is divine classification: x’s instantiating a property P just is God classifying x under conception P. It is natural, given this base theory, to affirm (3): x’s instantiating greenness just is God’s classifying x under greenness, and God classifies x under greenness because x is green. Thus, x instantiates greenness because x is green.

But, interestingly, this base theory can give other explanatory directions. For instance, Thomists think that God’s knowledge is the cause of creation. This suggests a view like this: God’s classifying x under greenness (which on the base theory just is x’s instantiating greenness) causes x to be green. On this view, x is green because x instantiates greenness. If the “because” here involves grounding, and not just causation, this is heavy-weight Platonism, with a Thomistic underpinning. Either way, we get (2).

And here is a third option. God wills x to be green. God’s willing x to be green explains both x’s being green and God’s classifying x as green. The latter comes from God’s willing as an instance of what Anscombe calls intentional knowledge. This yields (4).

So, interestingly, a theistic conceptual Platonism can yield any one of the three options (2)–(4). I think the version that yields (3)—interestingly, not the Thomistic one—is the one that best fits with divine simplicity.