Incompleteness Ex Machina
Logic in Computer Science
2019-09-11 v1 History and Overview
Abstract
In this essay we'll prove G\"odel's incompleteness theorems twice. First, we'll prove them the good old-fashioned way. Then we'll repeat the feat in the setting of computation. In the process we'll discover that G\"odel's work, rightly viewed, needs to be split into two parts: the transport of computation into the arena of arithmetic on the one hand and the actual incompleteness theorems on the other. After we're done there will be cake.
Keywords
Cite
@article{arxiv.1909.04569,
title = {Incompleteness Ex Machina},
author = {Sebastian Oberhoff},
journal= {arXiv preprint arXiv:1909.04569},
year = {2019}
}
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First published on https://www.scottaaronson.com/blog/ on December 30. 2018