Logic and Language

Logic and Language

Copyright © James R Meyer 2012 - 2017 www.jamesrmeyer.com

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LL: Logic & Language Home Page

** Incompleteness**

LL: Gödel’s Incompleteness Theorem

LL: English Translation of Gödel’s Incompleteness Proof (html)

LL: English Translation of Gödel’s Incompleteness Proof (PDF)

LL: Simplified Explanation of Gödel’s proof - Intro

LL: Simplified Explanation of Gödel’s proof - Part 1

LL: Simplified Explanation of Gödel’s proof - Part 2

LL: Simplified Explanation of Gödel’s proof - Part 3

LL: Simplified Explanation of Gödel’s proof - Part 4

LL: Simplified Explanation of Gödel’s proof - Part 5

LL: Simplified Explanation of Gödel’s proof - Part 6

LL: Simplified Explanation of Gödel’s proof - Part 7

LL: Simplified Explanation of Gödel’s proof - Part 8

LL: Step by Step Guide to Gödel’s Proof: Intro

LL: Step by Step Guide to Gödel’s Proof: Part 1

LL: Step by Step Guide to Gödel’s Proof: Part 2

LL: Step by Step Guide to Gödel’s Proof: Part 3

LL: Step by Step Guide to Gödel’s Proof: Part 4

LL: Step by Step Guide to Gödel’s Proof: Part 5

LL: Step by Step Guide to Gödel’s Proof: Part 6

LL: The Flaw in Gödel’s Proof of his Incompleteness Theorem

Paper: 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 (PDF)

LL: Errors in Incompleteness Proofs

LL: Analysis of Incompleteness Proofs

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: 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 (PDF)

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

LL: Gödel’s Substitution Function

LL: The Halting Problem and Incompleteness Proofs

LL: Church’s *“An Unsolvable Problem”*

LL: Yet Another Flawed Incompleteness Proof

LL: Gödel, Minds, and Machines

LL: World’s shortest explanation of Gödel’s Proof?

LL: Review by Russell O’Connor of the paper demonstrating the flaw in Gödel’s proof

LL: How to show how a disproof of Gödel’s proof is wrong - if it really is

**The Infinite**

LL: The Courant & Robbins Contradiction

LL: Sums of infinitely many fractions 1

LL: Sums of infinitely many fractions 2

LL: A list with no Diagonal number

LL: English Translation of Cantor’s 1874 Proof of Non-Denumerability (html)

LL: English Translation of Cantor’s 1874 Proof of Non-Denumerability (PDF)

**Paradoxes**

**Other Topics**

**Books**

LL: Book: The Shackles of Conviction

LL: The Shackles of Conviction: Excerpts

LL: MathFiction Review of book ‘The Shackles of Conviction’ by Dr Kasman

**Miscellaneous**

**Blog Archive**

LL: Blog - Artificial Intelligence

LL: Blog - Bishops Dancing with Pixies?

LL: Blog - Cranks and Crackpots

**Other Stuff**

It has come to my notice that, when asked about the demonstration of the flaw in his proof (see A Fundamental Flaw in an Incompleteness Proof by Peter Smith PDF), Smith refuses to engage in any logical discussion, and instead attempts to deflect attention away from any such discussion. If any other reader has tried to engage with Smith regarding my demonstration of the flaw, I would be interested to know what the outcome was.

There is a new addition to the page Yet another flawed incompleteness proof, where Berto’s proof of incompleteness in his book *There’s something about Gödel* comes under scrutiny.

I found that making, adding or deleting footnotes in the traditional manner proved to be a major pain. So I developed a different system for footnotes which makes inserting or changing footnotes a doddle. You can check it out at Easy Footnotes for Web Pages (Accessibility friendly).

I have now added a new section to my paper on Russell O’Connor’s claim of a computer verified incompleteness proof. This shows that the flaw in the proof arises from a reliance on definitions that include unacceptable assumptions - assumptions that are not actually checked by the computer code. See also the new page Representability.

There is now a new page on Chaitin’s Constant (Chaitin’s Omega), which demonstrates that Chaitin has failed to prove that it is actually algorithmically irreducible.

13 May 2015 Good Math, Bad Math?

16th Mar 2015 Bishops Dancing with Pixies?

23rd Feb 2015 Artificial Intelligence

31 Mar 2015 Cranks and Crackpots

For convenience, there are now two pages on this site with links to various material relating to Gödel and the Incompleteness Theorem

– a page with general links:

– and a page relating specifically to the Gödel mind-machine debate:

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Copyright © James R Meyer 2012 - 2017

www.jamesrmeyer.com