Can God Create Abstract objects?

In my last post I set out a definition of God’s omnipotence.[1] In this post I want to consider the scope of God’s omnipotence by examining the question, “Can God create abstract objects?”

First, what exactly are abstract objects? Let’s stipulate that objects denoted by the following terms are abstract: ‘property,’ ‘proposition,’ ‘possible world,’ ‘set,’ ‘number,’ and ‘relation.’ Abstract objects are notoriously difficult to define. Most philosophers agree that they are non-essentially spatio-temporal, necessarily existing objects. It is widely held that they are also incapable of entering into causal relationships—they are “causally effete” as some like to say.

Assume abstract objects exist. For the Christian theist, the existence of abstract objects poses a problem. For now there exist infinites of abstract objects that have their being independently of God’s creative activity (since they are incapable of entering into causal relations), an affront to God’s sovereignty. So, the Christian theist is forced to either deny the reality of abstract objects (as William Lane Craig does) or to settle for a kind of non-traditional theism, where God is not supremely sovereign (rather, God is just the creator of the “tiny” physical universe).

Recently, the philosopher Peter van Inwagen argues that traditional theists need not worry about the reality of independently existing abstract objects. God, nor anyone else, can create abstract objects—it is metaphysically impossible (a kind of impossibility more broad that logical impossibility). God is still, according to van Inwagen, the creator of all creatable things—everything visible and invisible (souls, angels, etc.) on heaven and earth and that is enough to affirm the Nicene Creed.

I disagree. I see no reason to think that one of the things God couldn’t do is create abstract objects. There is nothing logically impossible about creating them, although we do need to open up some logical space to see how (that is, while it is assumed by many that (1) “x exists necessarily” entails (2) “x is uncreated” and (3) “x is independent” and (4) “x is eternal” and (5) “x cannot not exist” it is only the (5) that is entailed by (1)). Further, there is nothing, as far as I can tell to show that it is contrary to God’s nature to create abstract objects. Thus, there is no good reason to think that God cannot create abstract objects.

As an omnipotent God, he can. If they exist, he did. And it is much simpler and more satisfying to endorse the claim that God is the creator of ALL distinct reality full stop, not just “all distinct reality…that can enter into causal relations.”

This is no small point. It gets to rock bottom, the most basic distinction in the world—that between creator and creature. There is no “third thing” that stands between the creator and creatures as “uncreated and not God.” To read a full scholarly response to van Inwagen on this topic, see my recently published article in the journal Sophia: Can God Create Abstract Objects? A Reply to Peter van Inwagen.

If you are really interested in this topic, then stay tuned for my forthcoming book Beyond the Control of God? Six Views on the Problem of God and Abstract Objects (Bloomsbury, 2014).