New Questions About God and Abstract Objects

New Questions About God and Abstract Objects

Are some things merely God's thoughts? If we use numbers does that mean we think they actually exist? Dr. Craig loves this topic!

Transcript New Questions About God and Abstract Objects

KEVIN HARRIS: Dr. Craig, I think we are seeing an increase in questions about abstract objects being that you have done work in that area. So many of our listeners do know about your work in this area, but are there some resources that you can mention?

DR. CRAIG: There are very few published resources. About the only thing book-length would be Paul Gould's book which is called Beyond the Control of God.[1] It is a Six Views book on God and abstract objects. Also on the website,, if you look under the articles on the attributes of God you will find a section on divine aseity where there are some of my articles published.[2] Then of course there are the Cadbury Lectures[3] which are now available both on YouTube and in DVD form along with a C. S. Lewis Society lecture that deal with this topic.

KEVIN HARRIS: If anyone is thinking, “OK, I don't think I'm going to pursue this on abstract objects” the first line of this question, I think, spells out why you should. It says,

Dr. Craig, I want to start off with a sincere thank you for your work in apologetics, theology, and philosophy, as they have helped me form an even greater picture of our maximally great God.

Bill, I found that to be true in my own life for years – in our worship and contemplation of God, and our meditation on him, to come to know him more and more and what he is like. Philosophy, theology, apologetics – all of that does that.

DR. CRAIG: Yes, and this subject certainly redounds to the glory of God as it magnifies his unique status as the creator of everything that exists apart from himself. I think this is what Scripture teaches. The Gospel of John 1:3 says, “All things came into being through him [that is, through Christ] and without him not one thing came into being.” This is an attribute of God that is taught, I think, fairly clearly by Scripture.

KEVIN HARRIS: The writer continues,

In your third Cadbury Lecture you outline both absolute creationism and divine conceptualism and discuss how they both are problematic.

DR. CRAIG: Maybe it would be good to pause and explain what those two views are. Absolute creationism is the view that there are abstract objects like numbers, sets, properties, possible worlds, and so forth, but that these have been created by God. Divine conceptualism is a different view. It says that there are no abstract objects but there are divine thoughts. God has the thought of the number “2,” or of the set of all the natural numbers, or thoughts of possible worlds. So what were normally thought to be abstract objects are in fact thoughts in the mind of God. Those are two attempts to safeguard God's being the sole ultimate reality while being a realist about the existence of mathematical objects like numbers, sets, functions, and so forth.

KEVIN HARRIS: He continues,

The primary argument against absolute creationism was the bootstrapping argument.

DR. CRAIG: Maybe I should say what that is. The bootstrapping objection is a very well-known objection to absolute creationism that is usually thought to be fatal. And that is this – take properties. Absolute creationism would say God has created all properties. But how could God create, for example, the property “being powerful” if God wasn't already powerful? He would have to already have the property of being powerful in order to create the property “being powerful.” So there is a viscous circularity here trying to pull yourself up by your own bootstraps so to speak. This is one of the most well-known objections to absolute creationism. God couldn't have created all properties because he would have to already have properties in order to create them.

KEVIN HARRIS: I was thinking. Would another illustration be: God couldn't create existence because he would have to exist in order to create existence?

DR. CRAIG: Yes, that would be another example, but I didn't use that because many people would deny that existence is a property. They would say that is not a problem because it is not a property. But there are other properties God would have to have.

KEVIN HARRIS: Power is a property.

DR. CRAIG: Yes, being powerful.[4] If not omnipotent, being powerful. But also being conscious. Being concrete. There are a number of properties God would have to have in order to create properties.

KEVIN HARRIS: He continues,

To my knowledge, this argument shows that absolute creationism is circular in asserting that the property “power” was created by God since God himself must first possess said property in order to create. Upon reflection of this lecture, some things came to mind. When we define God as a maximally great being, certain properties come immediately to mind. Omniscience, omnibenevolence, and omnipotence are the big three that come to mind initially. In discussing the Euthyphro Dilemma we see God as not simply possessing the property of goodness, but being the paradigm of goodness itself from which all good flows. Can the absolute creationist elude to such an argument to avoid the bootstrapping objection by stating that God is the paradigm of power – that which all other forms of power are compared to or flows from? Does God exist because the concept of omnipotence exists, or does omnipotence exist because God exists? Neither. God is the paradigm of omnipotence. Why or why not does this argument work in defense of absolute creationism of all things apart from any characteristics of God? All properties of God must naturally be flowing from God in this paradigmatic way, thus not threaten the doctrine of his immutability and thus uncreated.

DR. CRAIG: I think that this is a good solution to the bootstrapping problem for the absolute creationist. He would say that prior to God's creating the property “being powerful” God just is the paradigm of power. It is not that he has the property “being powerful” - he just is the paradigm with power. The problem with that is that it tends to undercut any motivation for being a realist about properties because God doesn't need to have the property of being powerful in order to be powerful. So why be a realist about properties? Why would he then go on to create the property of “being powerful” and then stand in the relationship to it of exemplifying it. This view, I think, is a coherent view. It avoids the bootstrapping objection. But it undercuts any motivation for being a realist about properties. What this answer actually does is to, I think, open the door to anti-realism and to say, “Why just not get rid of properties all together. We don't really need them then.”

KEVIN HARRIS: He then lists some premises:

1. God is immutable (unchanging).

2. God is omnipotent.

3. Therefore the property “power” was not created but found in God himself existing concretely within God.

DR. CRAIG: God just is a powerful being. It is not that he exemplifies some abstract object. He just is powerful. I think that is right, but that is an anti-realist view of properties.


Is it possible that every abstract object apart from God's properties were created by God and every object that God possesses is found in God as the paradigm of that property? This to me doesn't threaten God's aseity since God is immutable and thus is omnibenevolent or omnipotent or any other intrinsic characteristic identified with the maximal great being. If this argument is flawed using the property of omnipotence, how is it not flawed in the property of omnibenevolence when responding to the Euthyphro Dilemma?

DR. CRAIG: It is not flawed. It is a good answer. It avoids a circularity. But, as I say, I think it cuts the nerve of realism. There just isn't any reason then to be a realist about abstract objects like properties anymore.


While you give interesting arguments against the indispensability argument, would not the theist prefer realism? Does, in your opinion, anti-realism downplay characteristics of God? Neutralism seems to avoid metaphysically heavy existent assertions, but isn't that exactly what the theist would want to do with properties concerning God and morality? I know this is an extremely loaded question, and I would like to thank you for your time.

DR. CRAIG: This is a great question. Let's, again, define some terms. The indispensability argument for realism is that if you assert as true statements which involve in them terms that refer to abstract entities (like 2+2=4 involves the terms “2” and “4”) then you are ontologically committed to the reality of those abstract objects.[5] Or if you say that, “There is,” and then you assert an abstract object, that commits you to the reality of that object. So if I say, “There are prime numbers greater than 100,” that commits me to the reality of numbers. The claim of the indispensability argument is we can't get along without such statements. We do assert truths that say there are such things or we use words that refer to such things. Therefore we are stuck with these abstract objects whether we like it or not.

KEVIN HARRIS: They are indispensable when it comes to communication, language, reason.

DR. CRAIG: Yes, that is right. What Neutralism says is that the use of terms to refer to things and saying that there is or are things are not devices of ontological commitment. In ordinary language we use those kind of expressions all the time for things that we don't think exist. For example, I say, “There is a lack of compassion in the world today.” Does that commit me to objects called “lacks” which are out there in the world? There are “lacks” somehow out there? Or if I say, “There is a hole in your shirt” does that commit me to the ontological reality of holes rather than a shirt which is shaped in a certain way? If I say “There are five Fridays in October” does that commit me to the reality of Fridays as objects in the world – mind and language independent things? No, obviously not. We say “There are” or “There is” things all the time without ontologically committing ourselves to those things. Similarly with names. We can talk about the accident that was prevented or Pegasus or Santa Claus and refer to such things without thereby committing ourselves to the reality of those things. So Neutralism would say this indispensability argument for realism fails because it is simply false that singular terms and informal expressions like “There is” or “There are” are ontologically committing for their users. He seems to agree that Neutralism does avoid these metaphysically heavy existence commitments. I think that is what the theist wants to do. He wants to avoid saying that there are uncreated abstract objects that exist independently of God. So I find Neutralism to be very attractive theologically because it preserves divine aseity and enables us to say that God is the sole ultimate reality.

KEVIN HARRIS: Another question on a similar topic.

Dr. Craig, after sharing your lectures on abstract objects with friends, I've noticed that I frequently encounter the same objection to your attempts at avoiding ontological commitment [which we just talked about]. Consider the following sentence. “2 is less than 3.” You and I agree that this sentence can be taken as literally true without committing one to the existence of “2.”

DR. CRAIG: OK. That means he takes a Neutralist view of the use of singular terms. You can say “2 is less than 3” and the truth of that statement doesn't commit you to the existence of the number “2.” So he has adopted a Neutralist view.

KEVIN HARRIS: He continues:

The objection I often here is that if you say that it is true that 2 is less than 3 then you are affirming that 2 has a certain property, namely that it is less than 3. However, if 2 doesn't exist then how can it possess properties?

DR. CRAIG: OK. Great question! There are actually two different anti-realist views about this subject. Alexius Meinong was an Austrian philosopher around the beginning of the 20th century who believed that there are non-existent objects. Things like the round square, the golden mountain.

KEVIN HARRIS: He believed that there are non-existent objects?

DR. CRAIG: Yes. Centaurs. Unicorns. Things of that sort.[6] So he would say that something can possess properties even though it is non-existent. The round square has the property of being round and being square. So Meinong would adopt the view that even though 2 doesn't exist, it has the property of being less than 3 and being an even prime number and so forth. Most (by far) anti-realists reject Meinong's view. They would agree that non-existent things can't have properties. But what they would just do is adopt an anti-realist view of properties. They would say that affirming that 2 is less than 3 doesn't commit you to the existence of a property any more than it commits you to the existence of the number 2. So you don't need to affirm that the number 2 in a literal sense exemplifies this abstract object which is the property of being less than 3.

One way to put it is to say that not every predicate implies a property. Just because there is a true predication (like 2 is less than 3) doesn't mean that there is a property as an abstract object “being less than 3.” I think that it is very clear that not every predication implies a property. For example, consider properties like this: Kevin Harris has the property of being such that Indira Gandhi was assassinated when she was the Prime Minister of India. That is a true statement – a predication – but do you really have that property? Does Kevin Harris have the property of being such that 2+2=4 or being such that Alvin Plantinga taught at the University of Notre Dame until he retired to Grand Rapids? Those aren't properties that Kevin Harris possesses. It is simply not true that true predications are sufficient for the ascription of properties. The Neutralist or anti-realist will simply say that properties don't exist, but nevertheless these predications are true.

KEVIN HARRIS: I've heard it put this way: “I believe Pegasus exists but Pegasus is not extended into space.”

DR. CRAIG: That sounds more like the divine conceptualist view that we talked about where Pegasus is an idea in the mind of God. Some might say it is an idea in the mind of human persons. I don't hold to that view myself. I would prefer the Neutralist view which just says that the use of names and expressions like “There is” or “There are” are not ontologically committing and therefore you can have true sentences involving such terms like “Pegasus is a mythological winged horse.” That is true, but that doesn't commit you to the reality of Pegasus.[7]

[1] Paul Gould, Beyond the Control of God?: Six Views on The Problem of God and Abstract Objects (Bloomsbury Academic, 2014).

[2] See (accessed April 25, 2016).

[3] See (accessed April 25, 2016).

[4] 5:00

[5] 10:22

[6] 15:00

[7] Total Running Time: 18:25 (Copyright © 2016 William Lane Craig)