Thank you to the UD News desk for putting up From Closer To Truth: Is Mathematics Invented Or Discovered? In this video public intellectual Robert Lawrence Kuhn interviews mathematicians and philosophers regarding the titular question.
The most profound statement in the video does not address the question. It addresses the current cultural constraints on the approach to answering this — indeed all – questions. Kuhn is interviewing mathematician Gregory Chaitin. At about 13:25 Chaitin tentatively expresses that he would like to believe that mathematics expresses a fundamental reality that is independent of the physical world. The following exchange ensues:
Chaitin: It’s a separate reality, and I don’t know where it is. Don’t ask me where the positive integers live, but they don’t live here I don’t think. You know it’s like a religion in a way. It’s like a subject that is stuck in the middle ages. I mean in a way I would say, to be provocative, they are thoughts in the mind of God. I mean where are these . . . where is the subject? It’s not here. So you believe in some invisible world, better than ours, purer. This is beginning to sound a little religious, isn’t it, in some, it’s a strange form of religious, but it’s . . .
Kuhn: Does that upset you? That it sounds religious?
Chaitin: No.
Kuhn: You sound defensive [UD Editor: Kuhn is spot on here!]
Chaitin: Well, given the current situation one has to sound defensive.
Wow. Think about what Chaitin says here. He is advancing a proposition [Platonism] that has a provenance dating back thousands of years. He appears inclined to believe this proposition is true in that it accurately reflects reality. In other words, he appears to believe that the answer to the question is that mathematics has an independent existence that is discovered, that it is not something merely contrived or invented. Yet he appears to be afraid to state his belief plainly and without reservation.
Why should that be? We all know the answer to that question. He is afraid of the bureaucrats at the Ministry of Truth. And he is right to be afraid of those bureaucrats, because they have the power to cancel him, to literally destroy his career. And he knows that while those bureaucrats may tolerate advancing Platonism as an interesting speculation so long as one qualifies it enough with such phrases as “stuck in the middle ages,” they would never tolerate a public intellectual who affirmatively and vigorously asserts and defends the truth claim that Platonism accurately describes reality. This is what he means by “the current situation.”
It should be profoundly disturbing to every lover of truth that the physicalists at the Ministry of Truth have such an iron grip on intellectual discourse that some of the most famous intellectuals in the world are literally terrified to express without qualification certain thoughts they believe to be true.
From Closer to Truth: Is mathematics invented or discovered? – Uncommon Descent