Questions about God and Abstract Objects

By William Lane Craig Feb. 26, 2016 9:00 a.m. Apologetics, Philosophy

This is the weekly Q & A blog post by our Research Professor in Philosophy, Dr. William Lane Craig.



Hello, my name is Lana, and I took a course at Purdue called "Metaphysics." I saw you at your debate with Alex Rosenberg. Anyways, And I'm glad I took the course, but I didn't take nominalism, or as you dub it, anti-realism, very seriously. I came out of it being a very strict platonist, but then I re read the gospel of John and I realized I was in huge trouble, I came to all the same conclusions about platonism as you did, I was a platonist, until now. So I floundered about wondering what the truth could be. I didn't take divine conceptualism very seriously at first because it was introduced to me initially by Berkleyianists, and I really do loathe idealism. I don't think it's compatible with Christianity. But I gave it another look and realized divine conceptualism can work with a worldview rejecting Berkley and his type. I don't remember the course too well so if I make a mistake that's why, and maybe I don't understand the same jargon but you did answer my question somewhere out there, I need some guidance.

So I read some of your articles on what you had to say and you convinced me to take nominalism very seriously. And I am rooting for you because I really want you to be right, I think it works so well with all the questions over the years I've had. But I have some questions and criticism I need to get out of the way first. First off, you mention figuralism and fictionalism, but not the trope theory, why is that? It's so popular as I understand it, although I remember my instructor telling me that tropes are almost just universals in disguise. I don't know, but here's my questions/criticisms. It was my big argument against nominalism back in the day, and it convinced me to be a Platonist,

How do you deal with token vs type in nominalism/anti-realism? What do you think types are? A lot of people seem to say either universals or tropes, but what alternatives are there? I asked one friend, and I remember they told me they understood the type of a let's say circle, is simply a description of a physical characteristic an object can take. Types are an easy way of categorizing the world around us, as it really appears.

I never had the time to delve deep enough into the token vs type distinction to really know if this is defensible, but it really sounds like your explanations of fictionalism and figuralism.

So maybe I missed this in your discussions, but how do you explain how there are identical shapes, called circles, around. How are they all identical in this regard? My reply used to be, well there are universals, this is why, they are all exemplified by the same source. Divine conceptualism also has an easy answer to this, it comes from an idea in god's mind. But what about in the other theories you advocate for?

But at the same time, do I need a single source besides God, to explain this? It is an assumption. But it's not a bad one either.

Also one more question, you said that the idea of God creating universals is a "pulling yourself by your bootstraps" issue, I totally agree, but I have trouble understanding how this is different from divine conceptualism. So in the latter theory, God is wise, and because God is wise, he has the idea of wisdom? Then particulars besides God exemplify wisdom? Am I getting this right? I don't know. In nominalism, God is simply wise, the end of story, much simpler, I love it.

If you don't have time for this reply I understand, but a prayer to Jesus Christ in faith will suffice.

Anyways God bless!!


United States


Dr. William Lane Craig’s Response

I have to be alert to the fact, Lana, that although you and I are interested in God and abstract objects, most of my readers are probably not, and so I have to resist taking many questions on this topic. But the tone of your letter was so sweet that I just couldn’t resist. So here goes!

Your first question is why I don’t mention trope theory. The reason is simply because it’s too narrow a solution to be applicable to the wide variety of abstract objects. Tropes are meant to be concrete substitutes for abstract properties. But even if we replace abstract properties with concrete tropes, that won’t help us with mathematical objects like numbers, sets, and so on. I do mention in my book versions of concrete realism about mathematical objects which take them to be physical realities; but this strikes me, along with the vast majority of philosophers, as quite implausible and, I think, inferior to conceptualist versions of concrete realism, which take such objects to be mental states or events, most plausibly in God’s mind.

You next ask, “How do you deal with token vs type in nominalism/anti-realism?” I don’t deal with it because types, if they exist, are not the sort of abstract object that threatens divine aseity and is of concern to me. Some abstract objects, if they exist, are plausibly created and contingent entities, such as the Equator, the center of mass of the solar system, fictional characters, musical and literary works, and so on. Sentence types seem to fall into this category. As linguistic entities (in contrast to propositions), sentence types seem to be the byproducts of human language and so contingent and non-eternal. Such abstracta do not pose a challenge to divine aseity and so are of no concern to me. I’m not inclined to believe in such things, but I have no bone to pick with those who do. Sentence types are postulated in order to explain, e.g., how it is that you and I utter the same sentence, when different noises come out of your mouth than out of mine. I suspect that sentence types are just make-believe entities that we imagine to exist because it is very useful to do so. But I have no axe to grind here; it’s a matter of indifference to me whether sentence types exist.

As for shapes, check out my dialogue with Peter van Inwagen on this score, recently published in Philosophia Christi.[1] As for the question of why things have the same shape, this is a version of the old problem of the One over the Many. It seems to me that resemblance is not the real issue here, but rather why a particular object is, e.g., spherical. If you can give an account of why a particular object is spherical and why another object is spherical, then there just is nothing more to explain. It certainly won’t explain anything to say that they are spherical because they stand in a primitive relation to some causally unconnected abstract object the sphere. Such an assertion seems to me explanatorily vacuous, rather like postulating “dormative powers” to explain why some drug makes you sleepy.

Finally, I think that divine conceptualism can avoid the bootstrapping problem that attends absolute creationism if the conceptualist rejects the Platonist’s ontological assay of things, that is, denies that things are ontologically composed of properties and something else. The conceptualist can adopt the old view of abstract objects as abstractions: they are formed by the mind’s abstracting away from a thing everything but, say, its shape. On this view, even though God is, say, omnipotent, the property omnipotence doesn’t exist until God thinks it. So logically prior to His thinking it, omnipotence does not exist, even though an omnipotent God does. No vicious circularity here!

The question is whether the absolute creationist couldn’t say something similar: logically prior to His creating it, omnipotence does not exist, even though an omnipotent God does. I have come to think that the absolute creationist could coherently say such a thing. In fact, van Inwagen is a Platonist who does reject the Platonist’s typical ontological assay of things. On his view God is not composed of properties plus something else, nor do properties serve to explain why things are as they are. So a Platonist of van Inwagen’s stripe could embrace absolute creationism without vicious circularity.

Once one rejects the Platonist ontological assay of things, however, then the nerve of realism, whether creationist or conceptualist, about properties seems to have been cut. Simpler, as you say, to be an anti-realist and do without them—but then one must answer the argument that we cannot dispense with such abstracta because we refer to them and quantify over them in sentences we accept as true, which is the burden of my book.


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[1] Peter van Inwagen, “Did God Create Shapes?” and William Lane Craig, “Response to Bridges and Van Inwagen,” Philosophia Christi 17/2 (2015): 285-298.

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