# Gödelian Logic

TagLast edit: 21 Dec 2021 8:54 UTC by

Gödelian Logic refers to logic, math, and arguments in the style of Kurt Gödel. Specifically—his two incompleteness theorems, and one completeness theorem. Due to their tricky and subtle nature, his incompleteness theorems are possibly the most misunderstood theorems of all time.

“All the limitative theorems of metamathematics and the theory of computation suggest that once the ability to represent your own structure has reached a certain critical point, that is the kiss of death: it guarantees that you can never represent yourself totally. Gödel’s Incompleteness Theorem, Church’s Undecidability Theorem, Turing’s Halting Theorem, Tarski’s Truth Theorem — all have the flavour of some ancient fairy tale which warns you that “To seek self-knowledge is to embark on a journey which … will always be incomplete, cannot be charted on any map, will never halt, cannot be described.”—Douglas Hofstadter, Gödel, Escher, Bach

### Gödel’s Completeness Theorem

This theorem is less well known than the other two, which came after it, but also less misunderstood.

### Probabilistic Solutions

One way you might think to get around Gödel’s Incompleteness, is to leave behind logical certainty, and instead assign probabilities to logical statements.

# Godel’s Com­plete­ness and In­com­plete­ness Theorems

25 Dec 2012 1:16 UTC
80 points

# Reflec­tion in Prob­a­bil­is­tic Logic

24 Mar 2013 16:37 UTC
112 points

# [Book re­view] Gödel, Escher, Bach: an in-depth explainer

29 Sep 2021 19:03 UTC
98 points

# Se­cond-Order Logic: The Controversy

4 Jan 2013 19:51 UTC
64 points

# Un­der­stand­ing Gödel’s In­com­plete­ness Theorem

6 Apr 2022 19:31 UTC
12 points

# A Proof of Löb’s The­o­rem us­ing Com­putabil­ity Theory

16 Aug 2023 18:57 UTC
71 points
(unstableontology.com)

# Strange Loops—Self-Refer­ence from Num­ber The­ory to AI

28 Sep 2022 14:10 UTC
15 points

# Gödel’s Le­gacy: A game with­out end

28 Jun 2020 18:50 UTC
42 points

# Gödel In­com­plete­ness: For Dummies

12 Jul 2020 9:13 UTC
9 points

# [Question] Godel in sec­ond-or­der logic?

26 Jul 2020 7:16 UTC
6 points

# Gödel and Bayes: quick question

14 Apr 2011 6:12 UTC
2 points

# Ex­plained: Gödel’s the­o­rem and the Banach-Tarski Paradox

6 Jan 2012 17:23 UTC
16 points

# Bounded ver­sions of Gödel’s and Löb’s theorems

27 Jun 2012 18:28 UTC
52 points

# A dis­carded re­view of ‘Godel, Escher Bach: an Eter­nal Golden Braid’

16 Dec 2011 5:51 UTC
12 points

# For­mal­is­ing cousin_it’s bounded ver­sions of Gödel’s theorem

29 Jun 2012 23:24 UTC
17 points

# MIRI course list book re­views, part 1: Gödel, Escher, Bach

1 Sep 2013 17:40 UTC
27 points

# We won’t be able to recog­nise the hu­man Gödel sentence

5 Oct 2012 14:46 UTC
11 points

# You Prov­ably Can’t Trust Yourself

19 Aug 2008 20:35 UTC
48 points

# Com­plete­ness, in­com­plete­ness, and what it all means: first ver­sus sec­ond or­der logic

16 Jan 2012 17:38 UTC
79 points

# Clar­ifi­ca­tion of AI Reflec­tion Problem

10 Dec 2011 22:30 UTC
33 points

# [Question] What’s go­ing on with “prov­abil­ity”?

13 Oct 2019 3:59 UTC
23 points

# Threat­en­ing to do the im­pos­si­ble: A solu­tion to spu­ri­ous coun­ter­fac­tu­als for func­tional de­ci­sion the­ory via proof theory

11 Feb 2023 7:57 UTC
5 points

# Eve­lyn Evelyn

7 Nov 2023 16:55 UTC
1 point

# Pro­gram­ming AGI is impossible

30 May 2023 23:05 UTC
1 point

# [Question] Can we get around Godel’s In­com­plete­ness the­o­rems and Tur­ing un­de­cid­able prob­lems via in­finite com­put­ers?

17 Apr 2023 15:14 UTC
−11 points