ToKCast
Ep 203: David Deutsch’s ”The Fabric of Reality” Chapter 10 ”The Nature of Mathematics” Part 4
Feb 16, 2024
Discussion on the fallibility of mathematics and the relationship between physics and mathematics. Exploring the nature of mathematics, including the irrationality of the square root of two and the abstract concept of 1. Shifting perspective from seeking ultimate truth to creating explanatory knowledge. The limitations of human knowledge and the importance of seeking knowledge over certainty. The inadequacy of traditional mathematical methods and the limitations of the Turing machine. Exploration of absolute necessary truth in mathematics and the role of proof in establishing mathematical propositions.
01:17:20
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Quick takeaways
- Proof theory is a science that ensures physical processes correctly mirror abstract entities.
- Mathematical knowledge is not more certain than other forms of knowledge, as proofs rely on physical processes and assumptions.
Deep dives
Proof Theory as a Science
Proof theory is not a branch of mathematics, but a science. Proofs are physical processes that depend on the truth of the theory that physical and abstract entities share the appropriate properties. Proof theory is about ensuring that physical processes correctly mirror abstract entities. Proof is a type of computation, and a physical experiment can be regarded as a computation. Proof theory does not confer certainty, as proof is a physical process and knowledge cannot be certain.
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