Comments on: On Gödel’s Incompleteness Theorem
https://polytropy.com/2018/12/15/on-godels-incompleteness-theorem/
Ἄνδρα μοι ἔννεπε, μοῦσα, πολύτροπον, ὃς μάλα πολλὰ πλάγχθηSun, 13 Oct 2019 15:05:54 +0000
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By: Anthropology of Mathematics « Polytropy
https://polytropy.com/2018/12/15/on-godels-incompleteness-theorem/comment-page-1/#comment-9175
Sun, 13 Oct 2019 15:05:54 +0000http://polytropy.com/?p=5682#comment-9175[…] at issue. In any case, we were considering computer verification of a proof from given axioms. From Gödel, there are theorems about the natural numbers that do not follow from a previously identified list […]
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By: On Being Given to Know « Polytropy
https://polytropy.com/2018/12/15/on-godels-incompleteness-theorem/comment-page-1/#comment-8369
Sat, 24 Aug 2019 14:41:00 +0000http://polytropy.com/?p=5682#comment-8369[…] fantasy for mathematics, as Kaznatcheev reminds us. Versions of the fantasy have been shown, as by Gödel and Turing, to be not just impractical, but […]
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By: On Causation « Polytropy
https://polytropy.com/2018/12/15/on-godels-incompleteness-theorem/comment-page-1/#comment-8341
Tue, 20 Aug 2019 02:10:30 +0000http://polytropy.com/?p=5682#comment-8341[…] Neither is experiment enough: if something happens n − 1 times, we still need a reason to conclude that it will happen an nth time. (I worked with this idea a bit in an essay “On Gödel’s Incompleteness Theorem.”) […]
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By: Anonymous
https://polytropy.com/2018/12/15/on-godels-incompleteness-theorem/comment-page-1/#comment-7587
Thu, 04 Apr 2019 14:30:59 +0000http://polytropy.com/?p=5682#comment-7587Great post. I feel like more technical developments in logic/theoretical computer science/set theory cause people forget about some foundational work such as Goedel’s. I wish all my students read this post.
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By: Piety « Polytropy
https://polytropy.com/2018/12/15/on-godels-incompleteness-theorem/comment-page-1/#comment-7403
Thu, 14 Mar 2019 18:33:55 +0000http://polytropy.com/?p=5682#comment-7403[…] unfitness of her associates and wooers …’ ” (535 C). In writing “On Gödel’s Incompleteness Theorem,” I expressed my dismay over the attitude (and attendant misunderstanding) of one […]
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By: NL XLV: The Germans « Polytropy
https://polytropy.com/2018/12/15/on-godels-incompleteness-theorem/comment-page-1/#comment-7260
Thu, 21 Feb 2019 06:14:26 +0000http://polytropy.com/?p=5682#comment-7260[…] What shall we do? For Collingwood, the arch-barbarists are the Ottoman Turks, when they are at the height of their power (45. 93); but even they “are no exception to the rule which elsewhere, to the best of my knowledge, is unbroken: the rule that barbarists in the end have always been beaten; a rule which I state here merely as the conclusion arrived at by the inductive study of cases” (45. 94). Such an induction is not a proof; to draw the universal conclusion that barbarism always fails, one would have to give a reason—as I suggested in the post “On Gödel’s Incompleteness Theorem.” […]
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By: NL V: “The Ambiguity of Feeling” « Polytropy
https://polytropy.com/2018/12/15/on-godels-incompleteness-theorem/comment-page-1/#comment-7127
Fri, 25 Jan 2019 02:44:47 +0000http://polytropy.com/?p=5682#comment-7127[…] between Collingwood’s work and some of the mathematics of his time. A similar analogy with Gödel’s Incompleteness Theorem (1931) is possible as […]
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By: The Private, Unskilled One « Polytropy
https://polytropy.com/2018/12/15/on-godels-incompleteness-theorem/comment-page-1/#comment-7101
Thu, 17 Jan 2019 13:38:09 +0000http://polytropy.com/?p=5682#comment-7101[…] We know from the work of Kurt Gödel in 1931 that the first-order theory of the natural numbers with addition and multiplication is undecidable. (See “On Gödel’s Incompleteness Theorem.”) […]
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By: Logic of Elliptic Curves « Polytropy
https://polytropy.com/2018/12/15/on-godels-incompleteness-theorem/comment-page-1/#comment-7048
Sun, 06 Jan 2019 17:49:11 +0000http://polytropy.com/?p=5682#comment-7048[…] « On Gödel’s Incompleteness Theorem […]
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