Ep: 108 Steven Pinker’s ”Rationality”Chapter 3 ”Logic and Critical Thinking” - reflections and analysis.
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The Ultimate Arbiter of All of Mathematics
It was once thought that no matter what area of mathematics, ultimately it could be broken down to its basic logical constituents. This is known as hilbert's programme after the mathematician who proposed work be done to find that ultimate foundation of mathematics. But kurt girdle showed that this can never actually be achieved. There cannot be a single set of axioms forming the basis of all mathematics from which everything that is true or valid in some system would have a proof. Instead, forget anything more complicated, like all of mathematics, just the few axioms under pinning simple arithmetic are such that even in simple arithmetic, there can be valid claims made for which no one would ever
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