Truth, Beauty and Goodness

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?

RP: Yes.

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…

Ard: Fitness.

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.

A SPACE TO BE DISCOVERED

Ard: So that kind of raises another really interesting question, because there are these abstract truths, like the truths of mathematics, the world of ideas. Where do those come from?

David: You said where this time.

Ard: This time I said where. Where do they come from? I didn’t say, ‘where are they?’ But, ‘what is their cause?’

GE: What is the cause of those mathematical logical truths?

Ard: Yes, exactly.

GE: It’s the nature of logic is all I can say. That is the way it is.

David: You see, for you, it’s God.

Ard: I think it comes from God.

GE: God? Okay, well I’m prepared to say that that is one possibility. There’s an alternative possibility, which is that God has to obey…

Ard: Obey the law of logic.

David: God is one of the ideas in your realm of ideas.

Ard: Well no, there’s a long argument among theologians and philosophers…

GE: I’m sure there’s a long argument with theologians.

Ard: …whether the laws of mathematics are created by God, or whether God, in fact, has to obey the laws of mathematics. So, for example, you might say, even God can’t make a square circle because it’s a non-logical. It’s law of non-contradiction. But the interesting point is that here we have these abstract, non-physical realities that have causal powers in our world. We think of God as a non-physical, abstract entity who has causal impact on the world, so there’s some analogy there. And once you hold that there’s one kind of non-physical reality, then it’s not so strange to think there might be another kind.

GE: That’s this kind of theology which I avoid.

Ard: You avoid theology?

GE: Yeah, I avoid theology.

GE: From my view point, existence isn’t just physical existence: there’s these abstract existences. So then you should ask me in philosophical terms how do I justify the word existence? And I’ve got a very simple answer to that. I take the existence of physical entities, like we’re seeing in this room, as being real – that’s my starting point – and I take the hierarchy of this to be real. So, in other words, this thing is made up of a metal ball, which is made up of atoms, which is made up of quarks. I believe that the ball is real, as well as the atoms are real.

I think just because it’s made of atoms doesn’t mean that it isn’t a real ball. So that physical hierarchy is real. Then I say that anything else which has a demonstrable causal effect on here must also be real.

David: Ah, so your ideas?

GE: Otherwise you have uncaused entities in the world.

David: Right.

GE: I’ve got in my hand a pair of spectacles. Now, how did they come into existence? Someone had the idea of a pair of spectacles and then created these by a machine, and so on. If they hadn’t had that idea, this wouldn’t exist. So that idea has to be real too, even though it’s not a physical entity.

The generic way to think about this, the deep structure of cosmology, is possibility spaces. Now, physicists like to talk about physical laws, but you can talk about the laws, or you can talk about what is possible given those laws. And actually, in many ways, it’s better to talk about what’s called a phase space, or a Hilbert space.

Once you start the line of argument I’ve been giving, there’s a mathematical possibility space. It’s a space of possible logical arguments and outcomes. If you now keep pursuing this line of argument, we can only think a thought because it is possible to think the thought. That sounds like a meaningless tautology, but actually what it means is the following: there is a set of possible thoughts which is up there in some Platonic space. You can’t think a thought unless it’s one of the thoughts which can be thought because it’s a logical possible thought.

David: So that realm of ideas your talking about, you would say that came into existence in the Big Bang along with… along with the…?

GE: I wouldn’t necessarily say it came into existence. I think it might in some sense pre-exist the big bang.

David: Oh, okay. Pre-exist. But it exists, so then what natural selection is doing was creating more and more complicated minds, or brains, rather, and at some point they can access this realm?

GE: That is correct, and so that space of abstract stuff was sitting there waiting to be discovered, and eventually minds reached a sufficient complexity that they could discover it. But that space doesn’t need minds to exist, it’s there.

David: It’s there already.

GE: Yeah. There’s a wonderful book out of this by Paul Churchland called Plato’s Camera.

David: Yes, I’ve read it.

GE: And Plato’s Camera talks about, in detail, how the structuring of the mind as a neural network enables us to recognise Platonic patterns, and they then get incorporated into electronic patterns in the brain, and then they can go down and effect what happens in the real world. So I see this causal link from Platonic spaces into intelligent minds, into electrons. It’s a downward causation, and then into causing effects in the real world.

For instance Pythagoras’ theorem is used by surveyors and architects. Or the number Pi is discovered, and it’s then used by engineers and it changes what happens in the real world because it’s used in engineering design.

David: So ideas have some kind of existence in our universe. It’s just it’s not a, sort of, physical existence like wood or steel.

GE: Yes, that’s right.

MATHEMATICS, GOODNESS AND GOD

David: Do you think mathematics… I mean, you are a mathematician… is it something we are making up?

MN: I believe…

David: Or something we are discovering?

Ard: Or do you think evolution created mathematics?

MN: I think mathematicians unveil eternal truth, you know, that exists independent of evolution. So you have something like prime numbers, numbers, they are just principles that exist. So, for me, the material world is an instantiation of fundamental principles.

David: Right. But if I’ve got those, then surely I don’t need God. I mean, in other words, there are these truths and they are the things which make the world the way it is, and they’re there before I thought about them, so I’m discovering them…

MN: But those fundamental principles, these eternal fundamental principles, for me, that is God.

David: Ah, okay.

Ard: Okay, here’s a question: if someone says to you, ‘Well mathematics is really science,’ what would you say?

MN: No. Mathematicians can make statements that are independent of any particular universe.

Ard: So give me an example.

MN: Well, some properties of prime numbers.

Ard: Okay.

MN: There are infinitely many prime numbers.

Ard: And so these are true, they don’t need scientific experiments to…

MN: Yeah, they don’t need any particular universe to be instantiated to make them true.

Ard: And do you think there’s a parallel between these mathematical truths, which don’t need scientific proof, and theological truths or philosophical truths?

MN: Yes, very much, philosophical ways…

Ard: Or theological truths.

MN: So, for me, philosophy and theology, that’s very close, and the most convincing way to think about theology is always the philosophical one.

Ard: And so do you think that if something, just like mathematics, is true independent of scientific experiments, something like that could be true for philosophical truths or theological truths?

MN: Yes…

David: Or moral truths.

Ard: Or moral truths.

MN: Yes, definitely. So, for example, when Andrew Wiles proved Fermat’s last theorem, then it doesn’t need a scientific experiment to confirm it: it was just, this is now true.

Ard: Yeah. And could there also be, then, moral truths, for example, or other theological truths that are true the way Fermat’s last theorem is true?

MN: Yeah, again, you have to ask yourself, what is the meaning of goodness and where does goodness come from? And I would agree with Plato, that goodness is a form – is the highest form: it’s the form that illuminates all other forms, because all other forms that exist, it’s good that they exist.

Ard: And so goodness is something that exists independent of us?

MN: As the highest form, yes.

Ard: As the highest form. That’s really interesting.

David: If you see these truths as being out there, then when we think of them, the way a lot of people think is that, ‘I’m making this up,’ or ‘I’ve grasped it.’ If they’re there, then it’s more of an encounter, isn’t it? That you’re encountering something.

MN: So Socrates and Plato, they asked themselves, what is learning? And they came to the conclusion that all learning is only remembering.

David: In the sense that there is something there that was waiting for you.

MN: Yeah, in some sense. And also Augustine asks the question, actually, how do these concepts that you understand enter your brain? So if he understands the sense of touch, the sense of smell, the sense of seeing, of hearing, and there’s a certain concept, you know.

David: Okay.

MN: And he then says, for that concept, maybe love, maybe goodness, it doesn’t come to you through any of those senses.

David: And where does it come from Martin?

MN: From God.

Ard: From God.

MN: From the fundamental principles. It’s like from the fundamental principles.

Ard: Martin and I agree.

David: Yeah, I know, I’m feeling in the minority. I don’t think I got mine from God, but I don’t know.

Ard: I think.. I think you did.

David: I know you do.