A Theory That Proves Its Own Inconsistency · Yan Sheng's site
I recently read this mind-bending blog post by Joel David Hamkins that proves this result: there is a Turing machine program P P such that for any function f:N→N f:N→N—possibly uncomputable!—there is a model of Peano arithmetic (PA) in which P P computes f f on the standard natural numbers. If this statement doesn’t surprise you, I’m not sure what else would (except maybe those who work in logic or set theory; I’m convinced that these people routinely believe as many as six impossible things before breakfast).
A Theory That Proves Its Own Inconsistency · Yan Sheng's site Welcome to my site! © 2019. All rights reserved. Yan Sheng's site A math blog A Theory That Proves Its Own Inconsistency 06 Dec 2018 logic I recently read this mind-bending blog post by Joel David Hamkins that proves this result: there is a Turing machine program $P$ such that for any function $f:\bb N\to\bb N$—possibly uncomputable!—there is a model of Peano arithmetic (PA) in which $P$ computes $f$ on the standard natural numbers. If this statement doesn’t surprise you, I’m not sure what else would (except maybe those
Explore this link on the map →saved by
related reading
- Gödel's incompleteness theorems - Wikipediaen.wikipedia.org
- Gödel’s Incompleteness Theorems (Stanford Encyclopedia of Philosophy)plato.stanford.edu
- Philosophy of Mathematics (Stanford Encyclopedia of Philosophy)plato.stanford.edu
- How Gödel’s Proof Works | Quanta Magazinequantamagazine.org
- Consistency - Wikipediaen.wikipedia.org
- Inconsistent Mathematics (Stanford Encyclopedia of Philosophy)plato.stanford.edu
- What Gödel Discoveredstopa.io
- Intuitionistic logic - Wikipediaen.wikipedia.org
- Arithmetical hierarchy - Wikipediaen.wikipedia.org
- Eat. Sleep. Math.eatsleepmath.tumblr.com
- How Many Numbers Exist? Infinity Proof Moves Math Closer to an Answer. | Quanta Magazinequantamagazine.org
- Peano axioms - Wikipediaen.wikipedia.org