Six Views on God and Abstract Objects

Readers interested in the argument for God from logic will want to check out a forthcoming book: Beyond the Control of God? Six Views on the Problem of God and Abstract Objects, edited by Paul Gould, Bloomsbury Academic, 2014.

From the publisher’s website:

The question of God’s relationship to abstract objects touches on a number of perennial concerns related to the nature of God. God is typically thought to be an independent and self-sufficient being. Further, God is typically thought to be supremely sovereign such that all reality distinct from God is dependent on God’s creative and sustaining activity. However, the view that there are abstract objects seems to be a repudiation of this traditional understanding of God. Abstract objects are typically thought to exist necessarily and it is natural to think that if something exists necessarily, it does so because it is its nature to exist. Thus, abstract objects exist independently of God, which is a repudiation of the traditional understanding of God. Philosophers have called this the problem of God and abstract objects.

In this book, six contemporary solutions to the problem are set out and defended against objections. It will be valuable for all students or scholars who are interested in the concept and nature of God.

One of the contributors is my good friend Greg Welty, who defends theistic conceptual realism, the view that abstract objects such as propositions really exist, but as ideas within God’s mind (as opposed to entities that exist eternally alongside of God and perhaps also independently of God). I’ve seen his essays for the volume, and he does a great job of defending TCR against some formidable opponents (and all within quite oppressive word limits). His positive case for TCR and his rebuttals of various criticisms are obviously important for defending the argument for God from logic.

Here’s the table of contents for the book, showing the six views featured:

  1. Introduction to the Problem of God and Abstract Objects, Paul Gould
  2. God and Propositions, Keith Yandell
  3. Modified Theistic Activism, Paul Gould and Richard Brian Davis
  4. Theistic Conceptual Realism, Greg Welty
  5. Anti-Platonism, William Lane Craig
  6. God with or without Abstract Objects, Scott Shalkowski
  7. Abstract Objects? Who Cares!, Graham Oppy

All of the contributors, apart from Oppy, are Christian theists.

Welty’s contribution to the book is basically a boiled-down version of his DPhil dissertation at the University of Oxford. I’ve been prodding Greg for years to get the full version published so that it can be more easily accessed. If you agree with me that he’s committing a heinous act of injustice by not making it more widely available, please message him on Twitter (@gregwelty) and make your outrage known. (Sorry, Greg!)

12 thoughts on “Six Views on God and Abstract Objects”

  1. I just read your tweet. Man, I need to check Twitter earlier than this :-)

    Thanks for the post!

  2. James-

    Since this book won’t be out until next year and Greg’s publication May or may not happen, where could I go to get some good information on your position as it relates to abstract objects? Your paper is very helpful, but Bill Craig is really pushing his perspective and offers quite a number of arguments, though most of what I’ve heard from him has been in podcasts, lectures, etc.

    Either way, I’m just curious…if anti-Platonism is true, would this refute your argument?

    1. Mike,

      Check out Greg’s MPhil thesis, which serves as a preview of his DPhil dissertation.

      Would anti-Platonism refute our argument? It depends what “anti-Platonism” involves! If you mean nominalism, the view that abstract objects have no real existence, then yes — that would be inconsistent with our position. But note that our argument for God from logic includes an argument for realism (and thus against nominalism) with respect to propositions. So the question is whether the arguments Craig gives for nominalism are stronger than our arguments for realism. That’s one of the main issues debated in the Six Views book.

  3. I listened to Craig’s recent podcast on this book, and I must be honest I am having a hard time understanding what his position is. Maybe, I am not smart enough, but it seems to me that there is way to much work to do to justify nominalism. At least that is my humble opinion.

  4. Well, imagine that you regard realism about abstract objects to posit an infinite realm of objects that eternally and necessarily exist, alongside God. You might regard that as a double-threat to theological orthodoxy, since there is now an ontological realm over which God has no control (vs. divine sovereignty), and a realm that doesn’t depend upon God for its existence and yet God must be in contact with it in order to be omniscient (vs. divine aseity). That might motivate you as a theist to be quite energetic in getting around the arguments for realism about abstract objects, so that you can adopt nominalism or fictionalism instead. What’s a little complication when the doctrine of God is at stake? :-) So I think I understand a bit where he’s coming from. (It also helps if opposing realism might dispose of a particular objection to the kalam argument, namely, that actual infinites *do* exist after all, in the form of Platonic realism about numbers, etc.)

  5. How close is Dr. Welty’s theistic conceptual realism to Gordon Clark’s “theistic-Platonic realism”?

    1. Haha. I was hoping you would just know his position and any significant differences. :-P

      It’s been a while since I read him (and I should note I only dabble in philosophy), but the post rang bells of recollection in my head.

      Here’s a summary by a Clark fan:

      Nothing exists outside of the mind of God. That is the meaning of the words “omniscient” and “omnipresent.” If man is going to know the truth, he must come to know the eternal propositions in the mind of God.

      Here’s a potentially relevant quote from Clark himself:

      The solution [to the problem of “unity in multiplicity” in the Trinity] the following pages defend is the philosophy of Realism, often called Platonism. Strictly, it is not Platonism, but rather the theory of ideas as transformed by Philo. The term Realism, as opposed to empirical and nominalistic epistemology, denotes any theory insisting that we know the real object, and not merely a sensory image or representation of it. Plato called these real objects Ideas. The argument is this: Suppose we have a lot of dice of various sizes. They all have the same shape. Now, this shape is something real. Even though the shape comes in different sizes, it is the same identical shape. If sensory objects alone were real, there could be no idea of similarity or identity, for none of the individual dice is itself similarity. Nor is any one of the dice cube. If one of the dice were the cube, and if only sense objects are real, then no other die could be cube. Hence, there is a real object of knowledge, the cube. It is not a sense object, not only for the preceding reason, but also because this cube exists in many places at once, as no sense object can. Similarly, Plato united all men under the Idea Man, all horses under the Horse, and all beautiful things under real Beauty. With other arguments also Plato asserted the reality of knowable intellectual objects.

      1. Well, with Plato (and, apparently, Clark) I also hold to “the reality of knowable intellectual objects.” It’s not clear from the second quote how this view is Philonic rather than Platonic.

        As for the first quote, “Nothing exists outside of the mind of God.” Really? No people, for instance? :-)

  6. Dr. Welty,

    Thanks for the reply. I understand why Craig appeals to nominalism to avoid the problem of the Platonic menagerie. What puzzles me is why he is willing to accept nominalism but will not accept divine simplicity. Whatever way we can get around the aseity issue is good, but it seems to me that nominalism leads to more problems than simplicity. I must confess I have classical Thomistics/reformed scholastic leanings on issues like simplicity. I may be a little biased. :) I look forward to reading the book!

  7. Probably because, on his view, at least nominalism doesn’t require us to say that a person can be a property, or that omniscience is goodness, or saddles us with Morris’s ‘problem of modal uniformity’ (such that modal discriminations cannot be made with respect to God), and so on. These are *alleged* implications of simplicity that don’t attach to nominalism.

    Interestingly enough, in their seminal article ‘Absolute Creation,’ Morris and Menzel consider the simplicity and nominalist routes and reject both in favor of a theistic activism in which God creates his nature. Go figure :-)

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