Mathematics and the God Hypothesis – Discovery Institute

Image credit: Tom Brown, via Flickr (cropped).

In arecent post,atheist biologistJerry Coynetakes issue with a commenter who asserts that God exists in the same sort of way mathematics exists. Heres the analogy the commenter offered,as quoted by Coyne:

Think of numbers for example, or mathematical equations, these are metaphysical things, that have not been created, however were discovered. The number 7 was the number 7 before anything at all came into existence. This is also true concerning the nature of God. He is not some material being that has come into existence, he is like a number that has always existed, (and by the way nobody will deny this logic with the number, however when someone mentions God a problem occurs).

Coyne who as you might guess is unimpressed by this approach to demonstrating Gods existence, replies:

The problem is that we can manipulate numbers and use them to arrive at truths, while we cant do the same with our conception of God, which remains a Platonic ideal. The only way to manipulate this Platonic God is to answer detractors that demand evidence by saying, Give me evidence that the number 7 actually exists as an empirical entity.

Although its clear that this kind of god does not correspond in any way to the theistic God believed by many faiths, including Abrahamic ones, its a conception of God thats been confected simply to avoid the questions What was there before God? and Who created God? It finesses the question by assertion that God is like the number 7 to mathematical realists. But in fact it does make an assertion about God: that he has an objective reality, which is why he resembles numbers to mathematical realists. Just as mathematical realists cant prove that numbers are actual entities existing out there, so Defender cant prove that God is an actual entity existing somewhere.

The commenter did not intend to prove Gods existence using mathematics. He merely pointed out that Gods existence is analogous, in limited ways, to the existence of numbers they, like God, are immaterial, real, and eternal. Which, of course, is true. And Coyne will have none of it.

There is, in fact, a classical proof of Gods existence that uses universal concepts such as mathematics, proposed most prominently by St. Augustine(354430 CE) of Hippo in the 4thcentury AD. Its sometime called theAugustinian Proof. I find it quite compelling and it goes like this:

Two kinds of things exist in the natural world: particulars and universals. Particulars are specific material things we know by our senses a rock, a tree, my neighbor Joe, etc. Universals are abstract concepts that we know in the sense that we can contemplate them 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 counting numbers 1, 2, 3, 4 and so on. There has been some 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 have no existence at all in other words, are they are merely words?). This is a profound question, but the view that natural numbers (and other universals) do exist in reality in some fashion 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 any human mind to count the suns. But it is surely just as true that our solar system had one sun a billion years ago as it is true now. So the number1really exists in some fashion independent of the human mind. The same could be said of any number. For example, we know the ratios of many physical constants of the universe that have existed since the Big Bang, and because these ratios are real (we can measure them) then the numbers the ratios represent are real.

So how could numbers exist in reality, independent of the human mind?Platoproposed a realm of Forms in which universals exist, and in which our concepts participate. There are notorious problems with Platos concept of the realm of Forms (philosopherEdward Feserhas agood discussionof this). But it seems undeniable that universals (such as numbers) do really exist in some real sense.

The solution proposed by Augustine (and many other philosophers and theologians, most notablyGottfried Wilhelm Leibniz) is calledscholastic realism.Scholastic realism posits thatGods Mindis 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.

Whats remarkable about the reality of universals as proof for Gods existence is that it points in a simple and clear way to some of Gods attributes, such as infinity, eternity, and omnipotence.

Read the rest at Mind Matters News, published by Discovery Institutes Bradley Center for Natural and Artificial Intelligence.

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Mathematics and the God Hypothesis - Discovery Institute