
Ep 14: Ch 8, Part 2: "A Window on Infinity"
ToKCast
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A Mathematical Proposition Is True or False
There is no such thing as abstractly proving something. Mathematical truth is absolutely necessary and transcendent. But all knowledge is generated by physical processes, and its scope and limitations are conditioned by the laws of nature. A mathematical theory of proofs has no bearing on which truths can or cannot be proved in real life. The whole motivation for seeking a perfectly secure foundation for mathematics was mistaken. It was a form of justification ism. So contrary to what most mathematicians since antiquity have believed, and believed to this day, proof theory can never be made into a branch of mathematics. Proof theory is a science. Specifically, it is computer science.
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