On 3 April 2015 at 19:30, Matt Oliveri <[email protected]> wrote: > > Your story is only partially right. The part that all math gets > reduced to natural numbers isn't right. (Or at best, it's misleading.) > Only the syntax is typically reduced to natural numbers. The semantics > usually stops at set theory. Specifically ZFC, which is waaaaay > stronger than Peano arithmetic.
On this specific point, I disagree. ZFC is not stronger that Peano arithmetic. I will try an paraphrase prof Harper's argument: Lets assume the consistency of Peano arithmetic can be proved or disproved in set theory. What happens if ZFC proves Peano arithmetic inconsistent? Which theory are you going to get rid of? Natrual arithmetic of ZFC? The answer is clear, every mathematician intuitively understands arithmetic, you would of course throw ZFC away. Keean.
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