Logic and Language

Logic and Language

Copyright © James R Meyer 2012 - 2018 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: Gödel Without Tears - Or Not?

LL: Gödel’s Intuitive Error (2)

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

LL: The Platonist response to 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

LL: On web forums and Gödel’s proof

LL: A review of Buldt’s *The Scope of Gödel’s First Incompleteness Theorem*

**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)

LL: Cantors Original 1891 Diagonal Proof

Paper: On Smith-Volterra-Cantor sets and their measure (PDF)

Paper, previous v1: On Smith-Volterra-Cantor sets and their measure (PDF)

LL: König - On the foundations of set theory and the continuum problem

**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 - Are we alone in the Universe?

LL: Blog - Good Math, Bad Math?

LL: Blog - Cranks and Crackpots

**Other Stuff**

There is now a new page Halbach and Zhang’s *Yablo without Gödel* which analyzes the illogical assumptions used by Halbach and Zhang.

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.

8 Apr 2016 Are we alone in the Universe?

13 May 2015 Good Math, Bad Math?

31 Mar 2015 Cranks and Crackpots

16th Mar 2015 Bishops Dancing with Pixies?

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 - 2018

www.jamesrmeyer.com