God and Abstract Objects
Dr. Craig discusses a decade of work he's done on this important theological issue.
God and Abstract Objects
Kevin Harris: Dr. Craig, you have been buried in a lot of work on God and abstract objects. I want to get some definitions out in just a moment. We have done some things on this. People can go to reasonablefaith.org, as well as refer to your written work on this. A little background, what led you to this particular study?
Dr. Craig: Well, back in the early 1980s as a young philosopher recently out of graduate school, I attended a conference of the Society of Christian Philosophers in Milwaukee, at which Thomas Morris, who was then at the University of Notre Dame, spoke. Morris presented a paper called “Absolute Creationism” and in this paper he pointed out that, in contradiction to the Orthodox Christian doctrine of creatio ex nihilo, which states that God has created everything other than himself, that there are objects that seem to be uncreated and even uncreatable. And what he had in mind were so called abstract objects - things like numbers and sets and propositions and properties. Now, many of us who had been weaned on the work of Alvin Plantinga believed that there are such entities as propositions, properties, possible worlds, and mathematical objects, and yet Morris was arguing that these things, if they exist, exist necessarily and would seem to be incapable of being created. The argument that he gave there has come to be called the bootstrapping argument. What he argues is that the person who thinks God created these objects is caught in a sort of vicious circle trying to pull himself up by his own bootstraps which is impossible because consider: take the property of being powerful. This is certainly a property that God has because he is omnipotent. If God created the property of being powerful, then prior to his creating it logically didn’t God have to have some power? Well, of course he had to be powerful in order to create the property of being powerful. So, he already had the property of being powerful, so how could he create it? You can see the vicious circle that exists there. Some of these objects do not simply exists necessarily but they seem to be uncreatable by their very nature. Although Morris attempted to answer this objection, his answer was so obviously ineffective and unconvincing that I left that conference with a very deep sense of trouble for theism. This was an objection to theism that struck at the very heart of theism, and I had no idea how to answer it. So, I simply put it on the back burner for many years and then a little over 10 years ago decided to take it off the shelf and begin to work on it because this question is related to the doctrine of God’s aseity which is God’s property of being self-existent. And the claim is that there are other things besides God that are self-existent and uncreated, namely these abstract objects. So, as part of my long range research program of doing a philosophical analysis of the principal attributes of God, I decided it was high time for me to tackle aseity and to meet head on the challenge posed by these abstract objects. So, that is what I have been embroiled in as my major research project for more than a decade now.
Kevin Harris: What material do you go to to read on this?
Dr. Craig: Principally, it’s philosophy of mathematics, Kevin, because the most important philosophical issue, I think, raised among philosophers of mathematics is the ontological status of these objects. That is to say, do you think that the number 2 actually exists? Now, certainly there are two apples say, or two glasses on the table, but apart from the glasses or the apples does the number 2 itself exist?
Kevin Harris: And if you were to write it on a chalkboard, that would be a representation of the number 2.
Dr. Craig: Yes, that would be a numeral not a number. There are different numerals. For example, Arabic numerals we use, but then there are Roman numerals that look very different than our Arabic numerals. But these, as you say, are representations of the number 2 which, if it exists, is not any kind of a physical thing. It would be an abstract object that would apparently exist beyond time and space.
Kevin Harris: We learn from elementary school that there is a distinction between abstract and concrete, that these seem to be the two big things that stand in opposition and that need to be distinguished.
Dr. Craig: Well, you are certainly right in saying that this is a major bifurcation of reality that metaphysicians point to. Peter van Inwagen, who is a very prominent Christian philosopher and metaphysician, has said that the difference between abstract objects and concrete objects is so great that even the difference between God and creatures pales by comparison to the difference between abstract and concrete objects. So, that this would be a major dividing line in reality, in one’s ontology of what exists.
Kevin Harris: Stanford University says it is widely agreed that the distinction between abstract and concrete is of fundamental importance, and yet, there is no standard account of how it should be drawn. I keep thinking of similar things, that it is difficult to perhaps define what is abstract.
Dr. Craig: Yes, that is very true, and so, what philosophers typically do is point to paradigm examples that everybody agrees would be abstract if they exist: numbers, proposition, things of that sort, but even also, works of art or novels or musical compositions. Beethoven's 5th symphony is not identical with any series of ink marks on paper.
Kevin Harris: Or wavelengths from the violin?
Dr. Craig: Not even that. That’s right, because otherwise it would cease to exist when the orchestra is no longer playing if it was just the wavelengths. And if the manuscript were burnt up then Beethoven's 5th symphony would cease to exist, but obviously, that is not the case. So again, these things like a musical score or a performance are taken to be just tokens or instances of this abstract entity which is Beethoven's 5th symphony which is not identical with any of it’s tokens, at least for those who believe in abstract entities. So, as I say, there is not a universally agreed upon definition, but there is pretty much universal agreement on many of these paradigm cases. Now, I think that abstract objects are definable in terms of their causal effeteness. That is to say, what distinguishes an abstract from a concrete object is that concrete objects have causal powers whereas abstract objects have no causal powers. They are utterly impotent and effete and cannot be causes of anything.
Kevin Harris: The number 7 cannot cause anything.
Dr. Craig: Right, it has no effects.
Kevin Harris: But a rock can fall on your head and cause a bruise. I just have to say, as a layman, that has really helped me, that distinction.
Dr. Craig: And that is widely agreed upon by philosophers. Not universally, but I think very, very widely shared.
Kevin Harris: I’m googling Stanford Encyclopedia here, Bill, and it says, “Some of these paradigm examples,” in other words if we can get some clear cut examples that will help, some paradigm examples of concrete things are like rocks, and trees, and human beings, magnetic fields, protons, and stars, but some clear cases of abstractions or abstracta are, “classes, propositions, concepts, the letter a, the number 2, and Dante's Inferno.”
Dr. Craig: Oh, see there was a literary work. The Inferno is not identical with any particular paper token of it. These could all be burned up, and yet, that would not mean that there was no such thing as Dante’s Inferno anymore. Maybe it could be preserved on a computer instead of in a paper book. So yes, again that would be an example of where someone looks at a literary work as being an abstract object.
Kevin Harris: Our good friend, J. P. Moreland, has a bumper sticker on his car that says, “I brake for universals” and so, in other words, he does believe in the existence of things like universals, that they actually exist but they are not extended in space. I know that the two of you need to have a long conversation on that some time. That is a funny bumper sticker.
Dr. Craig: It is, because if universals exist at least on Platonism, they don’t exist in the physical concrete world. They would be abstract objects that would not exist in space. And universals, for those that are not familiar with the terminology, would be things that can be multiply instantiated. For example, the property red can be exemplified by many different things. There is a red fire truck, a red dress, red flower, and the property of being red would be this abstract object which is exemplified by all of these particular red colored things. So, the idea there is that redness is a universal which exists in multiple places.
Kevin Harris: Tell me, Bill, where immateriality plays into this. If something is immaterial, I mean obviously, an abstract object would not be a material object.
Dr. Craig: Right, because you see, if it were material you could bump into it. It would have causal power. So, an abstract object, if it is causally effete, can not be a material thing.
Kevin Harris: And God is not an abstract object, but he is immaterial.
Dr. Craig: Good point. So, immateriality would be a necessary but not a sufficient condition of being abstract. There are concrete objects that are immaterial. Now, that may sound a little paradoxical to some people. Concrete sounds like material, but in this case, by concrete one does not mean physical or material, one means that it is something that is not abstract, it has causal powers. So, souls, angels, God, would all be examples of concrete objects that are immaterial.
Kevin Harris: So, the first thing that you mentioned about how God and abstract objects, some of the problems are that power would be something that God has, but yet, he creates power. So, that is one of the problems. What are some more problems as far as God and abstract objects? By the way, clarify that again for me.
Dr. Craig: Well, the idea there is that according to the Bible and Christian tradition, God is the creator of everything other than himself. John 1:3 says of the Logos, who is Christ, “All things came into being through him and without him, nothing has come into being.” So, that verse teaches the universal scope of God’s creation. Everything other than God and his own Logos, his mind, has been created by God. So, if a person believes there are abstract objects, he must say, I think theologically, that these things are created by God. But, as I explained, it seems that it is impossible for some of these things to be created because you get into a vicious circle. In order to create the property of being powerful you already have to have the property of being powerful.
Kevin Harris: So, what does this bring up? Something would be co-eternal with God?
Dr. Craig: They would be co-eternal with God, which is another problem because the Scriptures say that everything other than God is created by God, and therefore, the created order had a beginning. There is a state of affairs in the actual world which consists of God and God alone. Yet, on this view, if there are these abstract objects they are co-eternal with God. Indeed, God is just an infinitesimal part of reality, he is surrounded by infinities of infinities of infinities of beings that are uncreated by him and are co-eternal with him. His creation of the physical universe is an infinitesimal triviality compared to the realms of uncreated being.
Kevin Harris: If, in fact, these abstract objects are real. Could we say that God is somehow ontologically prior than these abstract objects even though they seem to be co-eternal?
Dr. Craig: Well, that is what the absolutist Creationist wants to say - that God has created these things. But that is difficult, as I say, because it gets you into a vicious circle. In that ontologically prior state, was God powerful or wasn’t he? Well, if he wasn’t, then how could he create the property of being powerful? But if he was powerful already, then didn’t he already have the property of being powerful? If you say, no he didn’t, but he was powerful anyway, well then why create the property of being powerful? It seems to become obtuse then.
Kevin Harris: I tried to get around it, but I couldn’t. I’m thinking of what God may be logically prior to.
Dr. Craig: Well, obviously the priority that we are talking about here is not chronological priority. We are talking about explanatory priority or logical priority, and it is precisely then that you run into this bootstrapping problem.
Kevin Harris: What about simultaneous? Would that just be a euphemism for co-eternal.
Dr. Craig: That wouldn’t help, because again we are talking about explanatory priority that is not related to time.
Kevin Harris: Well, if you were to kind of tick off some of the problems in theology and philosophy that this brings up, we have looked at maybe two, can you spell out some more?
Dr. Craig: No, I think that this is a the main one. This is huge.
Kevin Harris: Oh, yeah, it is big enough, believe me. Yeah, it is huge.
Dr. Craig: Well, actually I guess there is another one that perhaps is equally huge that is related to this. Let’s suppose that there are these properties like omnipotence, omniscience, omnipresence, and eternity that God has by his very nature. What that means is, God is who He is in virtue of his nature, but if these properties that constitute God’s nature are uncreated by him then that means that God depends on these properties for being God. He is God because he has these properties which exist independently of him. So, that this would mean that God is in fact not a self-existent beings. He is dependent upon these independently existing abstract objects.
Kevin Harris: Wow! Does Swinburne believe something like this?
Dr. Craig: No, Swinburne solves the problem by denying that abstract objects exist.
Kevin Harris: Ah, as I understand Swinburne does not believe that God is a necessary being. I wonder how that played into it.
Dr. Craig: Well, that would be more of the view of Keith Yandell, who believes both that God is a contingent being like Swinburne, but then unlike Swinburne, also believes that there are these necessarily existing abstract objects. Yandell is a Christian philosopher from the University of Wisconsin.
Kevin Harris: Let’s talk about the book that you are participating in, Bill, but first of all can you get us off the hook here and solve this problem?
Dr. Craig: Well, that is the problematic of the book. Paul Gould is editing a book on God and abstract objects in which he has assembled a team of six philosophers to engage this question and try to come to different perspectives on the problems.
Kevin Harris: It’s a concrete book with concrete philosophers, and you are one of them.
Dr. Craig: That’s right. I am one of several that are participating in this view Six Views on God and Abstract Objects.
Kevin Harris: Have you had a chance to review the other views?
Dr. Craig: Oh, yes. The book consists of six chapters written by each of us - our position papers. And then each person responds to the other five chapters and then finally you are given a chance to respond to your five critiques.
Kevin Harris: Give us a thumbnail of some of the other views represented.
Dr. Craig: Well, Paul Gould, the editor of the book, and Rich Davis have written one chapter which is a sort of modified absolute creationism. They hold that God creates many abstract objects except for the properties that make up his own nature, and there they seem willing to embrace Platonism. Platonism is the view that abstract objects exists. I regard it as a kind of compromise position, where they will try to defend the view that God creates most of these but not the properties that make up his own nature.
Keith Yandell, whom I’ve already mentioned, is the Platonist in the group. He believes that abstract objects exist; that they are uncreated by God, and he even thinks that God is not necessary in his existence. So, Yandell has a very radical view, I think, thoroughly Platonistic, and he just sees no theological problem at all. He is quite blasé about the problem posed by abstract objects to divine aseity or creation.
Also in the book would be Greg Welty, who I believe did his doctoral dissertation on this subject under Swinburne, and Welty feels keenly the theological problem posed to divine aseity by the reality of these objects. So, he adopts a view called divine conceptualism, and he identifies what we normally refer to as abstract objects, things like numbers, propositions, properties, as the contents of God’s mind. So, he takes a view that is, really, a classical Augustinian view, that what we thought were abstract objects were actually ideas in the mind of God, or thoughts in God’s mind.
I take the view that a defensible position for the Christian theist is that there are no abstract objects. These things are just useful fictions; they do not, in fact, exist. I deal with the most important argument that Platonists offer on behalf of their existence and attempt to show that this argument doesn’t go through, and that therefore, a perfectly defensible view is that there are no abstract objects, and therefore, everything is concrete and is created by God.
The next participant is Scott Shalkowski, and he takes a view that is rather similar to mine I am pleased to say. We are fairly closely aligned in our views in this book. He also would say, I think, that abstract objects don’t exist, but he also doesn’t think it is theologically problematic if they do. So he, like Yandell, is oddly blasé about this problem, but in fact, he doesn’t think they exists. He doesn't say they are useful fictions, instead Shalkowski’s view seems to be that talk about abstract objects is just a sort of figurative language. We can express truths by using figures of speech that are not literally true. For example, if I said it’s raining cats and dogs, that could be a true statement even though there are no animals falling from the sky. It’s a figure of speech to say it is raining cats and dogs, which means it is raining very hard. Similarly, he would say when we say things like two is the number of men that entered the bar, what we really mean is that two men entered the bar. We don’t really mean to postulate an entity two in existence to the men. It’s just the men that went into the bar, and it is just a way of speaking to say two is the number of the men that went into the bar. So, he sees abstract talk as not literal but more figurative.
Then the final participant is the atheist philosopher, Graham Oppy from Australia. Oppy’s view is that the existence of abstract objects has no implications for either naturalism or theism, but the reason he says that is because he holds or speaks of a very thin or attenuated sort of naturalism or theism. Normally, the naturalist is a physicalist who believes that only material objects exists, and so, the naturalist would normally be very disturbed by thinking that there are these abstract objects that are real and are out there. But Oppy’s naturalism is very attenuated. It just amounts to denying that God exists or something of that sort. And as for theism, again, Oppy’s theism that he entertains would just be that there is a sort of being that is the creator of the world, and is good and is worshiped, but he doesn’t need to be the creator of literally everything that exists. So, Oppy is also very indifferent to this question. He thinks that it is of no significance for either theism or for naturalism.
Kevin Harris: Well, Bill, would a more orthodox view or perhaps a biblical view of God just somehow anchor abstract objects in God; in God’s mind?
Dr. Craig: Well, that’s what the conceptualist like Welty would say. That abstract objects are ideas in the mind of God and certainly that is probably the mainstream, theistic position that was defended by Augustine, and I think Aquinas would hold to something similar, and the ancient Jewish philosopher, Philo of Alexandria, thought this. So, divine conceptualism is for me, a kind of fall back position. If my view doesn't work out, I am prepared to fall back on divine conceptualism, but as I began to study this issue it seemed to be that even divine conceptualism concedes too much to the Platonist in thinking that there has to be reference of things like the word two or propositions or other mathematical objects, and therefore, like Shalkowski, I’m very suspicious that we are being deceived by our language. That we are reifying linguistic terms into entities and thinking that our language is a sort of mirror of reality. This is sometimes called the picture theory of meaning, that every word pictures something in reality and I think that’s clearly false, Kevin. For example, when I say, “The whereabouts of the Prime Minister are unknown” I don’t mean that there is some object in the world called whereabouts that actually exists. So, it’s not true that every noun or noun phrase that we use in our truth sentences refers to some object that actually exists in the world.
Kevin Harris: When you say reified, does that mean to make something real?
Dr. Craig: Yes.
Kevin Harris: A mistake we often make, philosophers make, and physicists often make, is reifying nothing.
Dr. Craig: That is a perfect example. If you say the universe was created from nothing, then because nothing is a noun in that sentence - right? it is the object of the preposition - someone might be tempted to reify it, and turn nothing into a thing. So, as to say “It was created from nothing,” well how was that done? What properties does nothing have? This leads to endless confusion. I think we have talked about this before. If I said I had nothing for lunch today, it would be obtuse for you to say “well how did it taste?” or “was it filling?” It would be absurd, and that would be an example of reifying linguistic terms and thinking they refer to objects or realities.
Kevin Harris: When you say that these things are just useful fictions, it almost sounds like they are concepts, but you wouldn’t consider your position conceptualism?
Dr. Craig: I don’t think it’s conceptualism because I’m not saying that the number 2 is an idea that exists in the mind of God. I certainly think God does have an idea of the number 2, but so do I and so do you. Now, think about this, Kevin. If the number 2 is literally in God’s mind, then what is it that you are thinking about when you think about the number 2? It’s gotta be something else cause it’s in your mind. You are not in the mind of God. So, I think that conceptualism leads to some really problematic sorts of conclusions of this sort if you say that literally these objects are these thoughts in the mind of God. Since I don’t have those that would mean I don’t have any thought of 2 or proposition or something. So, I think, it is preferable to just say that there are no such objects, but we can have ideas of things that aren't real.
Kevin Harris: If they are outside of the human mind that means we discover abstract objects. If they are somehow anchored in God’s mind (the conceptualist, the Divine mind), then we discover them just as part of creation. We don’t determine...
Dr. Craig: Well, they wouldn’t be part of creation.
Kevin Harris: Oh yeah, that’s right. They would be co-eternal.
Dr. Craig: But you are right about discovering them.
Kevin Harris: You don’t determine what is abstract...
Dr. Craig: You find it. Yeah, this leads to interesting questions. For example, you talked about Dante’s Inferno. Well, who created the poem Dante’s Inferno or Beethoven's 5th? If it is an abstract object then maybe Beethoven and Dante didn’t really do it; they just discovered it. Which means that their not really as great creators and artists as we might think.
Kevin Harris: Yeah, I don’t see how Beethoven's 5th could have just been discovered by Beethoven. I see how it could be created and arranged.
Dr. Craig: And in all fairness, some Platonist who think that literary works and musical works are abstract will also endorse that these are products of human creation. But it is difficult to see why that would be the case if they are abstract objects. Why wouldn’t they just always be there and Beethoven and Dante just happened to hit upon them? Which for anyone who has a deep appreciation of art and aesthetics is a very unpalatable view.
Kevin Harris: And it really sends me into a tizzy there even thinking about it. You could have Beethoven's 5th with one note that would be different. Yeah, and that’s a different abstract object. Wow! Well, Bill, you have really been doing some work.
Dr. Craig: Yeah, this is very, very heavy metaphysics and very challenging because this is a question, obviously as I say, that is of interest to non-theist as well. Philosophers of mathematics and philosophers of language wrestle with these questions wholly independently of their theological significance. In fact, I think that many of them would be quite surprised to hear that philosophers of religion are interested in these debates and are participating in them. So, I will be interested to see their reaction to this book that Gould is editing because it will probably show applications of their work theologically that they would never have anticipated.
Kevin Harris: Let’s definitely visit this topic again, especially after the book comes out.