Essential Incompleteness of Arithmetic Verified by Coq — mentioned by auggierose

Wed, 11 Oct 2017 21:35:19 GMT

I don't think working with Coq has ever or will ever be particularly pleasant :-) O'Connor gave a nice talk at TPHol's which I attended: https://arxiv.org/abs/cs/0505034 Keeping up with Coq shouldn't have been too difficult for him.

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Essential Incompleteness of Arithmetic Verified by Coq — mentioned by jplasmeier

Thu, 13 Oct 2016 15:51:01 GMT

I find this argument to be an unsatisfactory against "algorithmic consciousness". There have been automated proofs of Godel's theorem for a long while [0]. I don't mean this to be evidence on the contrary, but Penrose seems to ignore the fact that a computer can realize multiple axiomatic systems, and use them to make statements like Godel's Theorem(s). Godel's Theorem(s) are often taken out of context for philosophical purposes, for better or for worse, and it's important to remember that Godel's Theorem(s) relies on a meta-language (ZFC) to make statements about PA. For a much more…

Paper and discussion history. A mention is not an endorsement.

Essential Incompleteness of Arithmetic Verified by Coq · HackerPapers discussions

Essential Incompleteness of Arithmetic Verified by Coq — mentioned by auggierose

Essential Incompleteness of Arithmetic Verified by Coq — mentioned by jplasmeier