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Löb’s Theorem

TagLast edit: 11 Mar 2023 7:49 UTC by Yoav Ravid

Löb’s Theorem is theorem proved by Martin Hugo Löb which states:

If PA proves “If Peano arithmetic proves ‘X’, then X”, then Peano arithmetic proves X

Which has consequences for reflective reasoning.

The Car­toon Guide to Löb’s Theorem

Eliezer Yudkowsky17 Aug 2008 20:35 UTC
36 points
103 comments1 min readLW link

Open tech­ni­cal prob­lem: A Quinean proof of Löb’s the­o­rem, for an eas­ier car­toon guide

Andrew_Critch24 Nov 2022 21:16 UTC
58 points
35 comments3 min readLW link1 review

Prob­a­bil­is­tic Payor Lemma?

abramdemski19 Mar 2023 17:57 UTC
69 points
7 comments4 min readLW link

A Proof of Löb’s The­o­rem us­ing Com­putabil­ity Theory

jessicata16 Aug 2023 18:57 UTC
71 points
0 comments17 min readLW link
(unstableontology.com)

A sim­ple model of the Löbstacle

orthonormal11 Jun 2015 16:23 UTC
2 points
0 comments2 min readLW link

Over­com­ing the Loe­bian ob­sta­cle us­ing ev­i­dence logic

Squark14 Mar 2014 18:34 UTC
22 points
17 comments6 min readLW link

Some con­struc­tions for proof-based co­op­er­a­tion with­out Löb

James Payor21 Mar 2023 16:12 UTC
43 points
3 comments4 min readLW link

Löb’s the­o­rem sim­ply shows that Peano ar­ith­metic can­not prove its own soundness

Adrià Garriga-alonso22 Apr 2021 9:17 UTC
5 points
15 comments1 min readLW link

A proof of Löb’s the­o­rem in Haskell

cousin_it19 Sep 2014 13:01 UTC
52 points
8 comments3 min readLW link

Med­i­ta­tions on Löb’s the­o­rem and prob­a­bil­is­tic logic [LINK]

Quinn10 Aug 2014 21:41 UTC
17 points
0 comments1 min readLW link

A proof of in­ner Löb’s theorem

James Payor21 Feb 2023 21:11 UTC
13 points
0 comments2 min readLW link

Mo­dal Fix­point Co­op­er­a­tion with­out Löb’s Theorem

Andrew_Critch5 Feb 2023 0:58 UTC
133 points
32 comments3 min readLW link

An In­tro­duc­tion to Löb’s The­o­rem in MIRI Research

orthonormal22 Jan 2015 20:35 UTC
4 points
0 comments1 min readLW link

How to cheat Löb’s The­o­rem: my sec­ond try

Benya22 Aug 2012 18:21 UTC
21 points
26 comments10 min readLW link

An In­tro­duc­tion to Löb’s The­o­rem in MIRI Research

orthonormal23 Mar 2015 22:22 UTC
29 points
27 comments2 min readLW link

Bounded ver­sions of Gödel’s and Löb’s theorems

cousin_it27 Jun 2012 18:28 UTC
52 points
22 comments2 min readLW link

Löb’s Lemma: an eas­ier ap­proach to Löb’s Theorem

Andrew_Critch24 Dec 2022 2:02 UTC
29 points
16 comments3 min readLW link

Prob­a­bil­is­tic Löb theorem

Stuart_Armstrong26 Apr 2013 18:45 UTC
51 points
40 comments3 min readLW link

In­tu­itive cooperation

Adele_L25 Jul 2014 1:48 UTC
27 points
14 comments6 min readLW link

Strange Loops—Self-Refer­ence from Num­ber The­ory to AI

ojorgensen28 Sep 2022 14:10 UTC
15 points
6 comments18 min readLW link

Trust­ing Your­self (For­mally)

paulfchristiano9 Apr 2011 14:59 UTC
13 points
12 comments2 min readLW link

You Prov­ably Can’t Trust Yourself

Eliezer Yudkowsky19 Aug 2008 20:35 UTC
48 points
18 comments6 min readLW link

Es­cap­ing the Löbian Obstacle

Morgan_Rogers16 Jun 2021 0:02 UTC
14 points
10 comments7 min readLW link

Löbian emo­tional pro­cess­ing of emer­gent co­op­er­a­tion: an example

Andrew_Critch17 Jan 2023 5:59 UTC
23 points
0 comments8 min readLW link

A Löbian ar­gu­ment pat­tern for im­plicit rea­son­ing in nat­u­ral lan­guage: Löbian party invitations

Andrew_Critch1 Jan 2023 17:39 UTC
23 points
8 comments7 min readLW link

Rel­a­tivized Defi­ni­tions as a Method to Sidestep the Löbian Obstacle

homotowat27 Feb 2022 6:37 UTC
27 points
4 comments7 min readLW link

Ro­bust Co­op­er­a­tion in the Pri­soner’s Dilemma

orthonormal7 Jun 2013 8:30 UTC
120 points
147 comments7 min readLW link

Notes/​blog posts on two re­cent MIRI papers

Quinn14 Jul 2013 23:11 UTC
35 points
3 comments1 min readLW link

No Li­cense To Be Human

Eliezer Yudkowsky20 Aug 2008 23:18 UTC
57 points
54 comments8 min readLW link

An an­gle of at­tack on Open Prob­lem #1

Benya18 Aug 2012 12:08 UTC
48 points
85 comments7 min readLW link

Reflec­tion in Prob­a­bil­is­tic Logic

Eliezer Yudkowsky24 Mar 2013 16:37 UTC
112 points
168 comments3 min readLW link

Nat­u­ral­is­tic trust among AIs: The parable of the the­sis ad­vi­sor’s theorem

Benya15 Dec 2013 8:32 UTC
36 points
20 comments6 min readLW link

The Löbian Ob­sta­cle, And Why You Should Care

lukemarks7 Sep 2023 23:59 UTC
18 points
6 comments2 min readLW link

Self-Refer­en­tial Prob­a­bil­is­tic Logic Ad­mits the Payor’s Lemma

Yudhister Kumar28 Nov 2023 10:27 UTC
80 points
12 comments4 min readLW link

[Question] Why do the Se­quences say that “Löb’s The­o­rem shows that a math­e­mat­i­cal sys­tem can­not as­sert its own sound­ness with­out be­com­ing in­con­sis­tent.”?

Thoth Hermes28 Mar 2023 17:19 UTC
12 points
30 comments1 min readLW link