#### THE ETERNAL TRUTHS OF MATHEMATICS

David: So this is something that Ard and I were discussing earlier. Are you saying that when I ask you what does two plus two equal, and you say four, it’s always seemed to me the reductionistic argument – when they say, well, consciousness doesn’t exist – is that somehow you come up with the answer four because you were forced to because electrons just got into that state? Whereas I’ve always thought that the reason you say the answer is four is because of the logic of mathematics. So, in other words, it’s the logic of mathematics which is pushing the electrons around, not the other way, where the electrons are forcing you to have a thought.

GE: No, you’re quite right. That’s exactly the way it is.

David: Okay, so he does agree with us. Because we were discussing this earlier, and then we thought, crikey, maybe we’ve both really misunderstood it.

GE: Do you want me to open this up to an even more mind-boggling place?

David: Go on then.

GE: Okay. Where does the logic of mathematics come from?

David: Oh dear.

GE: This is the old question: do we invent mathematics or do we find mathematics? And I’m an unashamed mathematical Platonist: we discover mathematics. Two plus two is four is too simple. Let’s take something more interesting like the fact that the square root of two is irrational. Now the square root of two is irrational no matter whether you’re an Ancient Greek or someone here or someone on Mars. The square root of two is irrational. It’s a timeless, eternal, unchanging mathematical truth. In other words it’s a Platonic kind of statement.

The ontology is the mathematics exists and is there and is unchanging. The fact that the square root of two is irrational is an eternal unchanging truth. What we understand about it is a historically contingent thing, and we didn’t know that 10,000 years ago and we do know it now.

David: But the thing which is true was always true?

GE: The thing which is true is always true and has been true since the beginning of the universe.

David: Right, so in other words it was true when there were only dinosaurs around, and it’s still true.

GE: It was true at the start of the Big Bang. It was true before, when there was just hot gas and nothing else.

Ard: I mean, if you think about it that way, it’s really hard to believe that wouldn’t be the case.

David: Except that if people, physicists, would say look, ‘I’ve got bosons and I’ve got quarks, you know, what is the particle that carries the idea?’ That’s what...

GE: Yeah, but physicists have great trouble telling you this famous question. Why does mathematics underlie physics? The famous thing that Galileo said that the nature of the universe is written in mathematics. And Wigner and Penrose and other people have pondered, why is it that physics can be written in mathematical terms? And that’s a deep philosophical question for which we don’t have a proper answer.

Ard: So the unreasonable effectiveness of mathematics?

GE: The unreasonable effectiveness of mathematics, yes.