# SITEMAP

## 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

PDF 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

Errors in Incompleteness Proofs

Analysis of Incompleteness Proofs

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

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

## Blog Archive

Belief systems versus rationality

Fake News and Fake Mathematics

Is Mathematics Unreasonably Effective?

Platonism according to Ulf Persson

Sennimalai Kalimuthu - Crackpot or Joker?

## Menus

## Other Stuff

Easy Footnotes for Web Pages (Accessibility friendly)

Basic Footnote System Demo Page

How to setup a Dark mode switch on a web-site

Basic Dark mode Demo page for pages with Disqus comments

Hashover responsive CSS demo - without borders

Hashover responsive CSS demo - with borders

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.Site MissionPlease see the menu for numerous articles of interest. Please leave a comment or send an email if you are interested in the material on this site.

Interested in supporting this site?You can help by sharing the site with others. You can also donate at

_{}where there are full details.