Ard: So there are thoughts that are quite constrained, like mathematical thoughts. So I say 1+1=2, but the fact that 1+1=2 is independent of whether or not my brain does those things, right? So the mathematics is true, regardless of whether bosons or fermions exist. Isn’t that right?
AR: Yes. And there, I think, you have the major problem on the research programme of scientism.
AR: The scientistic world view, I think, has very good answers to a huge range of the questions that really trouble human beings when they can’t get to sleep at night, and they’re looking up at the ceiling and wondering about themselves and their place in the universe. The domain in which we have the most trouble is not a domain that most people are interested in: it’s the nature of mathematics and our knowledge of mathematical truths. As you just said, it looks very much like mathematical truths are true, independent of anybody ever having thought them.
Many people are inclined to think that mathematics is just ideas in the head, but it can’t be, for a lot of reasons, and we’ve recognised this ever since Plato. And the one thing that we scientistic philosophers don’t yet have a good account of is how we can have knowledge of mathematics, because we think that knowledge is a causal process that involves an interaction between us and the objects of knowledge. And two, and equals, and prime number, these are abstract objects that do not exist in space and time and that therefore we can’t have a causal connection to. And so our knowledge of mathematics is a deep mystery.
Ard: Doesn’t it trouble you that you need mathematics so much to do science?
Ard: So, it’s not just…
AR: When I said it’s a deep mystery, I meant it’s not just a fly in the ointment. It’s a big project on the agenda of naturalistic philosophy. We need an answer to this question. Now, I’ve been wrapping my head around this problem, a bit. Not as much as the philosophers of mathematics, who are much more deeply steeped in the difficulties of the subject. But the interesting thing is, as often the case in science, what really troubles the people who are at the frontiers of the discipline is so arcane and so alien to the interests of most people that it’s even hard to keep them awake long enough to explain the problem.
Ard: So would you say…?
AR: But it’s a big problem.
Ard: So it’s not just a few clouds on the horizon?
AR: Well, I’m inclined to say that it is a cloud on the horizon – a cloud no bigger than your hand.
AR: But you know how these problems have a tendency to grow, the way the cloud no bigger than your hand ends up being a thunderstorm.
AR: Now I don’t think it’s going to become a thunderstorm.
AR: But it’s a problem.
Ard: It’s a very interesting problem also.
AR: A friend of mine once said that this is a problem on which two millennia of geniuses have laboured with great intensity and made no progress at all.
David: So let’s say when they did wrap their heads round it, they discovered, ‘You know what. It is the way it seemed. There are certain ideas which just exist in the universe, and we somehow can find them…’
AR: Right. So there’s an agen…
David: But that wouldn’t undermine science, would it? I mean, I can’t imagine how it would.
AR: Well, I don’t think it would. There’s an agenda of problems that face the philosophy of science, metaphysics, epistemology, which are generated by the sciences, questions that the sciences, at least not yet, can’t answer. And philosophy is in many ways the guardian of those questions.
Now, there are some philosophers who hold, and some theologians who hold, that these questions will never be answered by the sciences, and therefore they provide good grounds for supposing that science is somehow incomplete and that there are truths of a non-scientific kind that, in competition with scientific truths, somehow may win out. And among these there might well be religious truths.
Now here’s the thing: when I weigh the philosophical puzzles that remain, like the nature of our knowledge of mathematics, against what science has accomplished over the 400 years since Galileo and Newton, when I weigh those in the balance, it seems to me that the balance is so heavily tipped towards science and its accomplishments, by way of explaining and enabling us to understand nature and ourselves, that I cannot take these puzzles seriously.
Now, at the end of the 20th, beginning of the 21st century, there’s still a package of problems that the sciences can’t yet answer, of which I think, as I said, the nature of our knowledge of mathematical truths is one. Do I think that science will never answer them? No, that’s what scientism consists in. It’s the prediction that eventually we’re going to successfully answer these questions.
Ard: So to summarise your argument: what you’re saying is science has shown us so many advances that we should essentially trust it to answer all questions.
AR: The inductive evidence favours that conclusion more strongly than the conclusion that there’s some domain of questions – real questions as opposed to pseudo questions – to which it can give no answer.
David: Why don’t you believe that, then?
Ard: I think that the clouds on the horizon, like mathematics, but I think also moral knowledge is true. I think science’s power derives precisely from its limitations to certain types of questions. I think there are many questions… I think we actually both agree… There are questions…
AR: But you cannot allow the fact that science would give disobliging answers to those questions to rule them as out of bounds for science.