#894 Mathematics and God
June 30, 2024Dear Dr. Craig, my name is Artyom, I am 17 years old and I live in Russia. I have been an ardent atheist since childhood, but about a year ago I began to get involved in philosophy, metaphysics, theology and became a Christian believer. First of all, I want to thank you for what you are doing! You have greatly influenced me and my faith!
I have a question that worries me very much. Are we discovering mathematics or inventing it? I have been studying mathematics since childhood and I am going to become a scientist in the field of pure mathematics (at the moment I am already dealing with some open problems). I am completely convinced that mathematics is objective and is the absolute truth that God invented (I have heard a very beautiful metaphor that mathematics is the language of God). Mathematics is the most beautiful, unusual and fascinating science that I have ever studied.
First, I want to share my thoughts on why I think mathematics is God's thoughts. First of all, this is prompted by the fact that mathematical objects and theories are surprisingly interconnected. Even those who at first glance have nothing in common at all. Secondly, mathematics has a unique beauty and aesthetics that can be felt by anyone who has been interested in it on a serious level. I can go on talking about the beauty of mathematics for a very long time, but I think I'll get right to the point.
I've seen a lot of your speeches where you talked about mathematical realism and anti-realism. I must say right away that the idea of divine conceptualism is very close to me (in my opinion, mathematics is the thoughts of God). In some of your speeches, you have given a counterargument that in this case God must have an infinite number of banal and stupid thoughts, because in mathematics you can come up with countless banal and stupid statements that do not represent any aesthetic and scientific interest. But why not assume that God only thinks about beautiful and important mathematical constructions? I'll give you an example. There are countless different geometries in mathematics. There is the well-known Euclidean geometry, and there are more complex and beautiful geometries. For example, there is Riemannian geometry, there are hyperbolic and spherical geometries (in fact, there are many more of them and many of them are of very serious scientific interest). But at the same time, you can come up with geometry that will not be of any scientific or aesthetic interest (in mathematics there are also concepts that are theoretically possible, but are of no interest). So what prevents us from believing that God's thoughts are only those mathematical objects and statements that really represent some kind of scientific interest and beauty, and consider the rest of the objects and statements to be human fantasies? It seems to me that pure mathematics is doing just that, it studies those mathematical structures that arouse great interest, but the most amazing thing is that these structures turn out to be very closely related to each other. This also suggests that mathematics is not just an invention or a person's thoughts, but something more. And it is interesting that not all areas of mathematics are applied in practice. Pure mathematics has always been studied not for an applied purpose, but for the purpose of learning eternal truths. And it seems to me that we can well assume that beautiful pure mathematics are the thoughts of God, and mathematical and logical concepts that are stupid and meaningless are considered inventions of the human mind. What do you think about this? How would you respond to this argument?
Perhaps my argument is far from the strongest, but as a mathematician I am fully convinced that mathematics is some kind of eternal truth that we are trying to comprehend.
In the end, I want to thank you again for your work!
Sincerely,
Artyom
Russia
Dr. craig’s response
A
It’s wonderful to hear from someone in Russia, Artyom, and particularly of your becoming a Christian and of your interest in mathematics! Your question is closely related to last week’s question #893 “Logic and God.”
I agree that we are discovering mathematical truths and not inventing them. If the truths of mathematics were merely conventional, then we should be able to describe the physical world as we wish, but in fact, we are severely constrained in our scientific theorizing by the need to be mathematically consistent. Indeed, as our Zangmeister video on the applicability of mathematics illustrates, the applicability of mathematics provides evidence of the existence of God. The truths of mathematics are plausibly rooted in the very nature of God as a supremely rational being. As the great physicist Paul Dirac rightly said, “God is a mathematician.”
Now with respect to divine conceptualism, I’m not sure you’ve understood the objection to taking mathematical objects to be God’s thoughts based on the infinite number of banal and stupid thoughts that we should have to ascribe to God. Like last week’s questioner, you seem to be conflating truth and existence. We can agree that mathematical truths are grounded in the nature of God, but does that imply that mathematical objects are thoughts in the mind of God? I don’t think so. Since God is omniscient, he knows only and all truths. If every true proposition is a thought in the mind of God, then God must be thinking an infinite number of thoughts, including many trivial and banal thoughts, like The Taj Mahal is not √2. Indeed, there would also be an infinite number of detestable and unmentionable thoughts. Conceptualism requires more than God’s merely knowing these truths; he must have occurrent (actual) thoughts in his mind identical to each one of these. But that seems incredible. Why would God keep on thinking about such trivial and detestable thoughts rather than put them out of his mind?
We could say that “God only thinks about beautiful and important mathematical constructions,” as well as beautiful or important non-mathematical truths—indeed, I’m inclined to say something like that—, but then we’ve abandoned conceptualism as an ontology for abstract objects because that leaves an infinite number of truths unthought of by God. If you are trying to ground the existence and not just the truth of mathematical propositions, then the conceptualist needs to say that God is actively and constantly thinking about all these things. We can’t dismiss truths which God is not thinking about as merely “human fantasies” because they are truths!
In short, you can hold that “mathematics is some kind of eternal truth that we are trying to comprehend” without going the conceptualist route of thinking of abstract objects, including mathematical truths, as literally thoughts in the mind of God.
- William Lane Craig