In a recent post, atheist biologist jerry coyne disputes a commentator who asserts that God exists in the same way that mathematics exists. Here is the analogy offered by the commentator, quoted by Coyne:

Think of numbers for example, or mathematical equations, these are metaphysical things, which have not been created, but which have been discovered. The number 7 was the number 7 before anything existed. This is also true regarding the nature of God. He is not a material being that has come into existence, he is like a number that has always existed (and besides, no one will deny this logic with the number, but when someone mentions God, a problem arises).

jerry coyne“A new conception of God: He is real in the sense of mathematics” at Why evolution is true (July 20, 2022)

Coyne, who – as you might guess – is unimpressed with this approach to demonstrating the existence of God, replies:

The problem is that we can manipulate numbers and use them to arrive at truths, while we cannot do the same with our conception of God, which remains a Platonic ideal. The only way to manipulate this Platonic God is to respond to critics who demand proof by saying, “Give me proof that the number 7 actually exists as an empirical entity.”

While it is clear that this type of god does not correspond in any way to the theistic God believed by many religions, including the Abrahamic ones, it is a conception of God that has been crafted simply to avoid the questions “What had he before God?” and “Who created God?” He refines the question by asserting that God is like the number 7 for mathematical realists. But in fact, he makes a claim about God: that he has an objective reality, which is why he resembles numbers to mathematical realists. Just as mathematical realists cannot prove that numbers are real entities existing there, “Defender” cannot prove that God is a real entity existing somewhere.

jerry coyne“A new conception of God: He is real in the sense of mathematics” at Why evolution is true (July 20, 2022)

The commentator did not intend to prove the existence of God using mathematics. He simply pointed out that the existence of God is analogous, in a limited way, to the existence of numbers – they, like God, are immaterial, real and eternal. Which, of course, is true. And Coyne won’t.

There is, in fact, a classic proof of the existence of God which uses universal concepts such as mathematics, proposed above all by St. Augustine (354-430 CE) from Hippo in the 4^e century of our era. It is sometimes called the Augustinian proof*. I find it quite convincing and it goes like this:

Two kinds of things exist in the natural world: particulars and universals. Particulars are specific material things that we know through our senses – a rock, a tree, my neighbor Joe, etc. Universals are abstract concepts that we know in the sense that we can contemplate and talk about them – geology, botany, humanity, etc. But we cannot know any of these abstractions by our senses alone. We know abstractions by our intellect, which is our capacity for abstract thought.

Mathematics is an archetype of universals – take for example the set of natural numbers. It includes all counted numbers – 1, 2, 3, 4 and so on. There has been a debate among philosophers and mathematicians about the reality of numbers (i.e. do they exist in a separate Platonic realm, or only in the human mind, or do they not exist du everything – in other words, are they just words?). This is a deep question, but the idea that natural numbers (and other universals) actually exist in a certain way is very hard to deny.

For example, consider the formation of our solar system. It formed around one sun, not two or three or a million suns – and it formed before there was a human mind to count the suns. But surely it’s just as true that our solar system had a sun a billion years ago as it is now. So the number 1 actually exists independently of the human mind. The same could be said of any number. For example, we know the ratios of many physical constants in the universe that have existed since the Big Bang, and because those ratios are real (we can measure them), then the numbers that the ratios represent are real.

So how could numbers exist in reality, independent of the human mind? Plato proposed a realm of Forms in which universals exist, and in which our concepts participate. There are notorious problems with Plato’s concept of the realm of Forms (philosopher Edward Feser has a good talk of this). But it seems undeniable that universals (like numbers) do exist in a real sense.

The solution proposed by Augustine (and many other philosophers and theologians, notably Gottfried Wilhelm Leibniz) is called school realism. Scholastic realism postulates that The Spirit of God is the Platonic realm of Forms. Augustine proposed that universals such as numbers, mathematics in general, propositions, logic, necessities and possibilities exist in the Divine Intellect, which is infinite and eternal.

What is remarkable about the reality of universals as proof of the existence of God is that they indicate in a simple and clear way some of the attributes of God, such as infinity, eternity and omnipotence. To see how, consider again the set of natural numbers, which is infinite. Therefore:

– The Spirit that contains them must be itself infinite.

– Because the Spirit in which the natural numbers exist is infinite, it is also omnipotent. The limitations of power are finite and incompatible with an infinite Spirit.

— Because numbers exist independently of the material universe, they are eternal (for example, the truth that 1+1=2 is independent of time) and therefore the Spirit that contains them is eternal.

I find the Augustinian proof of the existence of God via the reality of universals in the divine mind compelling proof. This is a very satisfying and even beautiful concept – our abstract thoughts have a real existence in the mind of our Creator, and we, who are created in his image, participate in his thoughts.

So while the analogy drawn by the commentator on Coyne’s blog between God and mathematics does not in itself demonstrate the existence of God (as the commentator acknowledges), the very existence of mathematics and other concepts abstracts points quite directly to an infinite, omnipotent world, and eternal divine intellect.

Thus, mathematics itself is proof of the existence of God. As I have observed elsewhere, God is everywhere, if you know how to look for him.

To note: *Philosopher Edward Feser has a very nice discussion of this proof in his superb book Five proofs of the existence of God (2017). I highly recommend it.

You can also read: The argument of the Hidden Divine against the existence of God = nonsense. God in himself is infinitely greater than us, and he transcends all human knowledge. A God with whom we do not struggle – who is not hidden from us in any substantial and painful way – is not God, but a mere figment of our imagination. (Michael Egnor)