David Deutsch: evaluation

Transcript context

…How do you think about the various paradoxes of self-reference that arguably underlie number theory, set theory — right? There’s also Gödel’s theorem. Any other results? I’m sure you know them better than I do. I think Gödel’s theorem, for example, with its roots in self-reference paradoxes, shows us that even within pure mathematics, there is no such thing as a solid foundation for all our knowledge. And therefore there’s no such thing as fully comprehending everything. We might think that we’re pretty sure what the laws of arithmetic are. We’re pretty sure that we can see that three times seven is the same as seven times three by just laying out beads on the table. But we can’t ever lay out beads on the table to tell us that x times y is the same as y times x regardless of what x and y are — and yet we can know that. The way we know that is by proving it, and we prove it from the axioms using rules of inference. How do we know the rules of inference are true? We don’t. They are conjectures. They have exactly the same status as laws of physics that we conjecture. We never know anything for certain. We might be mistaken about anything. On the other hand, we can have knowledge. I think we also really do know that x times y equals y times x, even though we have no solid foundation for that. What, in your opinion, is the best test of the many-worlds interpretation?…

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