David: If you're willing, as both of you do, say, look there's some kind of ideas, truths, in this case mathematical ones, which are woven into the fabric of the universe, could there be other kinds of truths? Like moral truths or aesthetic truths?
RP: Other kinds of truths? Well there certainly could be, yes, I'm not saying that mathematical truth is the whole of truth. That would be too arrogant a statement to make. We don't know of any other area which is so successful in describing the physical world. Now you see...
David: But could there be different truths altogether?
RP: Well, you see, there could be.
David: What's your feeling about that? Do you think the only truths that are in the world are maths?
RP: I think the trouble is the word truth. You can have things that people have a greater respect for. They might be great works of music, of architecture or painting, all sorts of things which have a value of their own, which you can't say you could reduce to mathematics, and I wouldn't necessarily want to do that.
Ard: Could there be other kinds of truths that you in effect discover rather than create?
RP: Well you might say... You see, I'm not against, I mean we're going to get sort of Platonism in some form. You see, the Platonic ideals, truth is only one of them, and you would say truth, beauty, if you like, and morality.
Ard: And goodness?
RP: The true, the good and the beautiful. Now I would be quite happy to give some kind of reality to all these things. Now the only thing that mathematics has to say in a clear way, I suppose, is the truth part, and it's talking about necessary truths. Well it's not talking contingent truths. We're not talking about something which might be here or might be there. We're talking about things which by their very nature are true or false.
It's also clear that there are inter-relations between, in particular, beauty and mathematics, and people very often talk in terms of a beautiful result. And it's certainly the case that if you have two alternatives where you worry about which is true, it's a better bet to think that the one which is more beautiful is more likely to be true. But this is always a very subtle issue. You might find there's a deeper reason that you hadn't realised before which makes the other one actually beautiful in a deep sense that you hadn't appreciated before.
Ard: So beauty is a guide to truth?
RP: I think beauty is a clear guide to truth.
Ard: But sometimes beauty… it's hard to be sure you've perceived it correctly.
RP: Yes, and beauty is, of course, a very personal thing, and people may have different views.
David: Has it been a guide for you in your work?
RP: Yes, certainly. I am definitely sympathetic to all three of the Platonic ideals. The truth one, which I'm taking as the pure, necessary truth, I think that's an absolute thing. And when it comes to beauty, well, you see, I would say there is a great subjectivity to beauty, and there's no doubt about that. But I would say there's a kernel of truth to all that which is independent of people. And I really sort of argue that great music can be great in itself, not just because people appreciate it.
David: And the moral?
RP: And then the moral, I would see even more so, probably. But, you see, this is an interesting question, because one of the things I spent a lot of time worrying about has been the issue of consciousness. And so I have these three worlds in a sense: you have the mathematical world, and then the physical world here. And the laws of physics seemed to be governed by mathematics, but it's only a part of the mathematical world, as far as we know, which governs the laws of physics. And it's only a part of the physical world, as far as we know, which has conscious experiences.
But if you are worrying about the other Platonic values, you see, do they have absolute existence as well? And the moral one seems to depend ‒ I'm not sure I think that this is entirely so ‒ but it seems to depend on the existence of consciousness. I mean, if there were no conscious beings around, the notion of morality somehow seems to evaporate. It has to do with conscious beings.
So I would say that truth and beauty are tied up together, and it's certainly a good guide to truth. In mathematics it's certainly true. And I would say also that the issue of consciousness is connected with this, because in order to understand what's going on in the mathematical world, I would argue that you need consciousness.
Ard: In some sense what you're saying is consciousness is needed to probe mathematical truth?
Ard: But conscious may also needed to probe goodness or moral truth?
RP: Well it’s all tied up with moral truth, because morality is tied up with consciousness.
Ard: Do you think these things like cruelty being wrong is something that we discover is true… like mathematical… like 1+1=2 is true?
RP: Yes, well I guess, in a sense, I am trying to take a view like that. It's a Platonic kind of view, but I think you have to be jolly careful with these things because there are always many different sides, and there is a danger, you know, if you're setting yourself up as saying this is the truth. Not just this is the truth, but this is right; this is what people should do.
Ard: But you might say, well, okay, some kinds of truths are…we know that they're there, but they're hard to access in a way that we're sure about, so we're more careful about them. Whereas if somebody comes around and says 1+1 does not equal 2, we can be fairly authoritarian and tell them that they're wrong.
David: I certainly wouldn't cross the bridge that they built.
Ard: That's right, that's a good point. Whereas I think the point is people worry about morals…that we're going to start imposing in the same way that when I mark an exam somebody doesn't get what 1+1 equals and says 1+1=3, I'll say it's wrong. They worry that if I think that moral truths are also there to be discovered that I'm going to do the same thing to them. But the fact is that morals, like beauty, there's a kernel there. There's definitely something about it which is much harder to put your finger on, but I think it's important to say it's more than just something that we can't quite put our finger on; it’s something that’s actually out there.
RP: Yes, I think would say that.
David: Why do you say that? I mean is it important to you? Why would you be led to think those ideas, to think those things?
RP: Very hard to know why one thinks something.
David: Because a lot of people might listen to you and say, well, look, wait a minute, I thought he was a mathematician and a scientist, and now he's veering off into these other things?
RP: That’s why I don’t like to talk about them. I think the danger there is it's much easier to get it wrong. You see in mathematics, that’s the whole beauty of the subject, if you like, that you can see who's right and who's wrong. And that is a big, important thing. Now that doesn't spread much into other areas, I mean it does to a degree. You can in physics, or in the real world, or in geography, you could say, okay, there's a continent over there, and you can go and find it, or not. You see that's… I mean there are...
David: But then why do you…? Since it is dangerous to have these ideas, where does this feeling or intuition come from? Do you think for you, such that you think, well, yes I just, I do think that there could be a moral...?
RP: It is true ‒ I don't think it is just a question of what works best in society. I mean you certainly get the view with people, often, that right and wrong is just a question of what makes society work.
David: It's a matter of fashion almost.
RP: It's a matter of fashion or a matter of…
RP: Convenience. It's a society that goes with…chugs away in a nicely oiled fashion.
David: But do you have a feeling it's...
RP: There is something much deeper.
David ...that some kernel of it is woven...?
RP: Yes, I do, yes.
David: But do you, how...?
RP: Without being religious, you see, I suppose that's what's a bit unusual, because you get people who would have a religion, and which they strongly believe in, and which they would argue is why they hold these beliefs.
David: But that's not the case for you?
RP: That's not what I would say, no. But if you… I mean, do you say Platonism is a religion of some sort? I don't.