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Copyright   James R Meyer    2012 - 2024 https://www.jamesrmeyer.com

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Logic & Language Home Page

 

Incompleteness

Gödel’s Incompleteness Theorem

Gödel’s contradiction

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

 

Step by Step Guide to Gödel’s Proof: Intro

 

 

Analysis of Incompleteness Proofs

Errors in Incompleteness Proofs

 

Errors in incompleteness proofs by Kleene and Rogers

 

PDF Paper: The Impossibility of Representation of a Gödel Numbering Function by a Formula of the Formal System

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

 

Hilbert’s tenth problem

 

Gödel’s Proposition V

Peter Smith’s Gödel Without (Too Many) Tears - Or Not?

Gödel’s Intuitive Error No. 2

Gödel quotations

Responses to the demonstration of the flaw in Gödel’s proof

The Platonist response to the flaw in Gödel’s proof

Nagel & Newman

Gödel, Escher, Bach

The Diagonal Lemma

Gödel’s Substitution Function

Representability

The Halting Problem and Incompleteness Proofs

Church’s “An Unsolvable Problem”

Intuitionism

True but unprovable

Gödel, Minds, and Machines

Gödel links

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 

 

The Infinite

Infinity

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

Lebesgue Measure Theory

The Axiom of Choice and Well-Ordering

Understanding Limits and Infinity

Understanding sets of decreasing intervals

Real numbers and Language

Online English Translation of Cantor’s Original 1891 Diagonal Proof: “Über eine elemtare Frage de Mannigfaltigkeitslehre”

The Diagonal Proof

The Diagonal Proof - Version 1

Cardinal Numbers

Surjections and Cardinal Numbers

Indefinable Numbers

The Origins of Transfinite Numbers

Proof of more Real numbers than Natural numbers?

Cantor’s religious beliefs and his transfinite numbers

Cantor’s invented numbers

A list with no Diagonal number

The Power Set Proof

On David Hilbert’s “On the Infinite” (Über das Unendliche)

Why do people believe weird things?

Shaughan Lavine’s “Understanding the Infinite”

 

Cantor’s 1874 Proof

Online English Translation of Cantor’s 1874 Proof of Non-Denumerability

PDF English Translation of Cantor’s 1874 Proof of Non-Denumerability

PDF Cantor’s 1874 Proof of Non-Denumerability: Original German (Über eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen)

 

Online English Translation of Cantor’s 1878 paper “A Contribution to the Theory of Sets” (Ein Beitrag zur Mannigfaltigkeitslehre)

 

König - “On the foundations of set theory and the continuum problem: Part 1” (Online English Translation)

PDF König - “On the foundations of set theory 1…” Original German (Über die Grundlagen der Mengenlehre und das Kontinuumproblem: 1)

König - “On the foundations of set theory and the continuum problem: Part 2” (Online English Translation)

PDF König - “On the foundations of set theory 2…” Original German (Über die Grundlagen der Mengenlehre und das Kontinuumproblem: 2)

 

PDF Cantor’s 1884 paper “On infinite linear point manifolds” - Original German (Über unendliche, lineare Punktmannichfaltigkeiten)

Online English translation of Part 1 of Cantor’s “Über unendliche lineare Punktmannig-faltigkeiten” (On infinite linear point-sets)

Online English translation of Part 2 of Cantor’s “Über unendliche lineare Punktmannig-faltigkeiten” (On infinite linear point-sets)

Online English translation of Part 3 of Cantor’s “Über unendliche lineare Punktmannig-faltigkeiten” (On infinite linear point-sets)

Online English translation of Cantor’s “Grundlagen einer allgemeinen Mannigfaltigkeitslehre” (Foundations of a general theory of sets)

 

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

 

The Continuum Hypothesis

 

Set Theory

 

Paradoxes

 

Other Topics

 

Books

 

Miscellaneous

 

Blog Archive

 

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Other Stuff

 

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Copyright   James R Meyer   2012 - 2024
https://www.jamesrmeyer.com