Matheism?

Is Materialism a necessary precondition for mathematics? What about empiricism? Is there anything about mathematics that requires physical testing? What about falsification?

These are the sort of questions that come to mind when considering the premise that Platonism should be disregarded when it comes to mathematics. This is a somewhat obscure principle when stated in that way, but it is easier to visualize if stated thus:

Is mathematics invented, or is it discovered?

Why is this important to the field of mathematics? Well, it’s not, really. It is important to a subset of mathematicians, as we’ll see.

The issue is broached in an article written for the Newsletter for the European Mathematical Society, June, 2007, by British mathematician E.B. Davies, of King’s College, London, UK. The article is titled, “Let Platonism Die”. He defines Platonist mathematics as follows:

”Mathematical Platonism comes in many flavours, but two particular elements are usually present. One is the assertion that there exists a mathematical realm outside the confines of space and time in which ideal forms of mathematical entities exist. This should be taken literally – the realm is independent of human society and would exist even if humans had never evolved. Theorems are statements about the properties of these mathematical entities, so their truth does not depend on whether anyone has a proof or even of (sic) whether there could be a proof….

and,

”The other aspect of Platonism is that it involved a definite claim about the way the human brain functions. Platonists believe that our understanding of mathematics involves a type of perception of the Platonic realm, and that our brains therefore have the capacity to reach beyond the confines of the physical world as currently understood, albeit after a long period of intense concentration. If one does not believe this then the existence of the Platonic realm has literally no significance. This type of claim has more in common with mystical religions than with modern science.”

and again,

”…scientifically testable claims are not settled by taking a poll of the opinions of people who have never done any experiments to verify them…. It seems to have escaped the notice of the Platonists that scientific investigations into the mental processes underlying mathematical understanding are just now being carried out.”

According to Davies, mathematical entities are capable of being empirically tested just as the functioning of the brain might be tested. The idea of abstraction is not feasible. So the entire premise is one of philosophical materialism, where nothing can possibly exist beyond the tangible.

While this seems somewhat understandable for novice empiricists who have not yet differentiated between philosophical and functional materialism, it seems rather odd coming from a mathematician.

Shall we test this premise for logic? Just how physical are mathematical concepts? What is the mass of an integral? Or the volume of a straight line? Or the weight of Boolean algebra? Or for that matter, Pi? Can I serve Pi on a truth table? Maybe with a cup of hot logarithms?

The idea that mathematics is material is fatuous; it is derived from a need – the need for a completely material universe including all of the things composed of nothing but concepts or those things that cannot be physically grasped for measurement. The need is philosophical materialism, which is to say, atheism. The need for there not to be anything else drives the conclusion that there is, in fact, nothing else – despite inability to prove such a thing.

So I refer to this principle, that mathematics is material, as Matheism. It is not a necessary precept for mathematics to be pursued. It is not material in itself. Matheism disproves itself in the same way that all other material philosophies do: the proposition of materialism is not material; ergo it is a paradox and is false.

And the charge of “mystical religion”? A red Herring used to distract from the obvious religious aspect of belief in philosophical materialism.

The article fails to produce any evidence for materialism. There is little question that mathematical relationships exist, even if they are not yet discovered. So in a sense, mathematics does resemble science in that it reveals relationships that exist, using terms that are understandable to man. Just as Newton didn't invent gravity, neither did he invent the relationship between velocity and acceleration. What he did was to invent a mnemonic method of revealing those preexisting truths. And the mnemonic is not material.

Contrary to Davies' opinion, the principles of mathematics are abstract, non-material, and do in fact exist outside the space-time, mass-energy realm of our universe. The principles of mathematics are not invented by men, they are revealed as true relationships, by men.

Davies' tract is a thinly coated attempt to justify atheism. It doesn't pass the test of logic.