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Incompleteness
Gödel’s Incompleteness Theorem
Online English Translation of Gödel’s Incompleteness Proof
Gödel’s 1934 Undecidability lectures
Formal papers related to incompleteness
Simplified Explanation of Gödel’s proof - Intro
Simplified Explanation of Gödel’s proof - Part 1
Simplified Explanation of Gödel’s proof - Part 2
Simplified Explanation of Gödel’s proof - Part 3
Simplified Explanation of Gödel’s proof - Part 4
Simplified Explanation of Gödel’s proof - Part 5
Simplified Explanation of Gödel’s proof - Part 6
Simplified Explanation of Gödel’s proof - Part 7
Simplified Explanation of Gödel’s proof - Part 8
Step by Step Guide to Gödel’s Proof: Intro
Step by Step Guide to Gödel’s Proof: Part 1
Step by Step Guide to Gödel’s Proof: Part 2
Step by Step Guide to Gödel’s Proof: Part 3
Step by Step Guide to Gödel’s Proof: Part 4
Step by Step Guide to Gödel’s Proof: Part 5
Step by Step Guide to Gödel’s Proof: Part 6
The Flaw in Gödel’s Proof of his Incompleteness Theorem
Formal Paper: The Fundamental Flaw in Gödel’s Proof of his Incompleteness Theorem
PDF Paper, previous v5: The Fundamental Flaw in Gödel’s Proof of his Incompleteness Theorem
PDF Paper, previous v4: The Fundamental Flaw in Gödel’s Proof of his Incompleteness Theorem
PDF Paper, previous v3: The Fundamental Flaw in Gödel’s Proof of his Incompleteness Theorem
PDF Paper, previous v2: The Fundamental Flaw in Gödel’s Proof of his Incompleteness Theorem
PDF Paper, previous v1: The Fundamental Flaw in Gödel’s Proof of his Incompleteness Theorem
PDF Paper, previous v0: The Fundamental Flaw in Gödel’s Proof of his Incompleteness Theorem
Analysis of Incompleteness Proofs
Errors in Incompleteness Proofs
Errors in incompleteness proofs by Kleene and Rogers
PDF Paper: A Fundamental Flaw in an Incompleteness Proof by Peter Smith
PDF Paper: previous v1: A Fundamental Flaw in an Incompleteness Proof by Peter Smith
PDF Paper: previous v2: A Fundamental Flaw in an Incompleteness Proof by Peter Smith
PDF Paper: A Fundamental Flaw in Incompleteness Proofs by S. C. Kleene
PDF Paper: A Fundamental Flaw in Incompleteness Proofs by Gregory Chaitin
PDF Paper: A Fundamental Flaw in an Incompleteness Proof by George Boolos
PDF Paper: A Fundamental Flaw in an Incompleteness Proof by Stanisław Świerczkowski
PDF Paper, previous v1: A Fundamental Flaw in an Incompleteness Proof by Stanisław Świerczkowski
PDF Paper: An Error in a Computer Verified Proof of Incompleteness by John Harrison
PDF Paper: An Error in a Computer Verified Proof of Incompleteness by Russell O’Connor
PDF Paper previous v1: An Error in a Computer Verified Proof of Incompleteness by Russell O’Connor
PDF Paper: An Error in a Computer Verified Proof of Incompleteness by Natarajan Shankar
Peter Smith’s Gödel Without (Too Many) Tears - Or Not?
Responses to the demonstration of the flaw in Gödel’s proof
The Platonist response to the flaw in Gödel’s proof
A brief history of meta-mathematics
The Halting Problem and Incompleteness Proofs
Church’s “An Unsolvable Problem”
A review of Buldt’s “The Scope of Gödel’s First Incompleteness Theorem”
An appraisal of Jean-Yves Girard’s lecture on Incompleteness
World’s shortest explanation of Gödel’s Proof ?
Review by Russell O’Connor of the paper demonstrating the flaw in Gödel’s proof
How to show how a disproof of Gödel’s proof is wrong - if it really is
On web forums and Gödel’s proof
Yet Another Flawed Incompleteness Proof
Francesco Berto - Yet Another Flawed Incompleteness Proof
Bernd Buldt - Yet Another Flawed Incompleteness Proof
Dan Gusfield - Yet Another Flawed Incompleteness Proof
Byunghan Kim - Yet Another Flawed Incompleteness Proof
Dennis Müller - Yet Another Flawed Incompleteness Proof
Sebastian Oberhoff - Yet Another Flawed Incompleteness Proof
Arindama Singh - Yet Another Flawed Incompleteness Proof
Antti Valmari - Yet Another Flawed Incompleteness Proof
David Pierce on Gödel’s incompleteness proof
Articles by J. R. Lucas relating to Gödel’s Incompleteness Proof
Minds, Machines and Gödel (1961)
Satan Stultified: A Rejoinder To Paul Benacerraf (1968)
Review of Mechanism, Mentalism and Metamathematics (Judson Webb) (1982)
A paper read to the Turing Conference at Brighton on April 6th, 1990
The Implications of Gödel’s Theorem (1998)
The Implications of Gödel’s Theorem - handout (1998)
Commentary on Turing’s ‘Computing Machinery and Intelligence’ (2007)
A response to a paper by Professor Feferman (2011)
A list of criticisms and discussions of the Gödelian argument
The Infinite
Actual, Completed and Potential Infinity
Formal papers related to questions about infinity
The Courant & Robbins Contradiction
Sums of infinitely many fractions 1
Sums of infinitely many fractions 2
The Axiom of Choice and Well-Ordering
Understanding Limits and Infinity
Understanding sets of decreasing intervals
The Diagonal Proof - Version 1
Surjections and Cardinal Numbers
The Origins of Transfinite Numbers
Proof of more Real numbers than Natural numbers?
Cantor’s religious beliefs and his transfinite numbers
A list with no Diagonal number
On David Hilbert’s “On the Infinite” (Über das Unendliche)
Why do people believe weird things?
Shaughan Lavine’s “Understanding the Infinite”
Online English Translation of Cantor’s 1874 Proof of Non-Denumerability
PDF English Translation of Cantor’s 1874 Proof of Non-Denumerability
Online English translation of Giuseppe Vitali’s paper: “On the problem of measuring sets of points”
PDF Paper: On Considerations of Language in the Diagonal Proof
PDF Paper: On Considerations of Language in the Diagonal Proof - v1
PDF Paper: On the Reality of the Continuum and Russell’s Moment of Candour
PDF Paper: On Smith-Volterra-Cantor sets and their measure
PDF Paper, previous v5: On Smith-Volterra-Cantor sets and their measure
PDF Paper, previous v4: On Smith-Volterra-Cantor sets and their measure
PDF Paper, previous v3: On Smith-Volterra-Cantor sets and their measure
PDF Paper, previous v2: On Smith-Volterra-Cantor sets and their measure
PDF Paper, previous v1: On Smith-Volterra-Cantor sets and their measure
Set Theory
Set Theory 1: Different types of set theories
Set Theory 2: Russell’s paradox
Set Theory 3: Natural Set Theory
Paradoxes
Other Topics
Alexander’s Sphere and Impossible Objects
The Law of the Excluded Middle
How to tell if someone is a crackpot
Logic and Dobbs vs Jackson WHO and Roe vs Wade
Mark Balaguer and Platonism: Part 1
Mark Balaguer and Platonism: Part 2
The Consistency of Arithmetic by Storrs McCall
Thinking and Being by Irad Kimhi
Books
Book: The Shackles of Conviction
The Shackles of Conviction: Excerpts
MathFiction Review of book ‘The Shackles of Conviction’ by Dr Kasman
Miscellaneous
The development of this website
Answers to some Quora questions
Dishonest tricks used in Arguments
Articles by Keith Devlin
Blog Archive
Belief systems versus rationality
Fake News and Fake Mathematics
Is Mathematics Unreasonably Effective?
Platonism according to Ulf Persson
Kalimuthu Sennimalai - Crackpot or Joker?
The Dead End Path of the Consciousness Myth
The Duplicity of Mark Chu-Carroll
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Rationale: Every logical argument must be defined in some language, and every language has limitations. Attempting to construct a logical argument while ignoring how the limitations of language might affect that argument is a bizarre approach. The correct acknowledgment of the interactions of logic and language explains almost all of the paradoxes, and resolves almost all of the contradictions, conundrums, and contentious issues in modern philosophy and mathematics.
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