Logic and Language
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Copyright   James R Meyer    2012 - 2020 https://www.jamesrmeyer.com

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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

 

The Flaw in Gödel’s Proof of his Incompleteness Theorem

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

Paper, previous v4: The Fundamental Flaw in Gödel’s Proof of his Incompleteness Theorem

Paper, previous v3: The Fundamental Flaw in Gödel’s Proof of his Incompleteness Theorem

Paper, previous v2: The Fundamental Flaw in Gödel’s Proof of his Incompleteness Theorem

Paper, previous v1: The Fundamental Flaw in Gödel’s Proof of his Incompleteness Theorem

Paper, previous v0: The Fundamental Flaw in Gödel’s Proof of his Incompleteness Theorem

 

Errors in Incompleteness Proofs

Analysis of Incompleteness Proofs

 

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

Paper: A Fundamental Flaw in an Incompleteness Proof by Peter Smith

Paper: previous v1: A Fundamental Flaw in an Incompleteness Proof by Peter Smith

Paper: previous v2: A Fundamental Flaw in an Incompleteness Proof by Peter Smith

Paper: A Fundamental Flaw in Incompleteness Proofs by S. C. Kleene

Paper: A Fundamental Flaw in Incompleteness Proofs by Gregory Chaitin

Paper: A Fundamental Flaw in an Incompleteness Proof by George Boolos

Paper: A Fundamental Flaw in an Incompleteness Proof by Stanisław Świerczkowski

Paper, previous v1: A Fundamental Flaw in an Incompleteness Proof by Stanisław Świerczkowski

Paper: An Error in a Computer Verified Proof of Incompleteness by John Harrison

Paper: An Error in a Computer Verified Proof of Incompleteness by Russell O’Connor

Paper previous v1: An Error in a Computer Verified Proof of Incompleteness by Russell O’Connor

Paper: An Error in a Computer Verified Proof of Incompleteness by Natarajan Shankar

 

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

 

The Infinite

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

Understanding Limits and Infinity

Understanding sets of decreasing intervals

Real numbers and Language

The Diagonal Proof

The Diagonal Proof - Version 1

Paper: On Considerations of Language in the Diagonal Proof

Paper: On Considerations of Language in the Diagonal Proof - v1

Paper: On the Reality of the Continuum and Russell’s Moment of Candour

A list with no Diagonal number

Cantor’s 1874 Proof

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

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

Cantor’s 1884 Proof of Non-Denumerability: Original German (Über eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen)

Cantors Original 1891 Diagonal Proof

The Power Set Proof

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)

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

Cardinal 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

Paper: On Smith-Volterra-Cantor sets and their measure

Paper, previous v5: On Smith-Volterra-Cantor sets and their measure

Paper, previous v4: On Smith-Volterra-Cantor sets and their measure

Paper, previous v3: On Smith-Volterra-Cantor sets and their measure

Paper, previous v2: On Smith-Volterra-Cantor sets and their measure

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

König - On the foundations of set theory and the continuum problem (Online English Translation)

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

Why do people believe weird things?

Shaughan Lavine’s “Understanding the Infinite

 

Paradoxes

Paradoxes

Liar Paradox

Balls in the Urn Paradox (Ross-Littlewood)

Berry Paradox

Bertrand Paradox

Church’s Paradox by Gödel

Curry’s Paradox

Drinker Paradox

Goodman’s Paradox

Grelling-Nelson Paradox

Halbach and Zhang’s Yablo without Gödel

Platonist Rod Paradox

Quine’s Paradox

Richard’s Paradox

Smullyan’s Paradoxes

Surprise Examination Paradox

Wang’s Paradox

Yablo’s Paradox

A referee’s comments: laughable or depressing?

 

Other Topics

Alexander’s Horned Sphere

Chaitin’s Constant Error

Computer-checked Proofs

Formal Language

How to tell if someone is a crackpot

Language, Logic and Intuition

Logic and Language

Mark Balaguer and Platonism

Mathematical proofs

Natural language and reality

Numbers, chairs and unicorns

Platonism

Platonism’s Logical Blunder

Pseudo-mathematics

The Consistency of Arithmetic by Storrs McCall

The Indispensability Argument

The Myths of Platonism

Thinking and Being by Irad Kimhi

Turing’s Uncomputable Number

Typical discussion about my work

The Continuum Hypothesis

 

Books

Book: The Shackles of Conviction

The Shackles of Conviction: Excerpts

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

Book: The Infinity Delusion

 

Miscellaneous

About

Contact

Glossary

Site Design

Sitemap

Answers to some Quora questions

Moved Comments

 

Blog Archive

A Failure to understand

A John Searle Inanity

Are we alone in the Universe?

Artificial Intelligence

Bishops Dancing with Pixies?

Cranks and Crackpots

Descartes’ Platonism

Fake News and Fake Mathematics

Good Math, Bad Math?

Is Mathematics Unreasonably Effective?

Man versus Machine

Moderate Platonism

Ned Block’s Blockhead

Platonism according to Ulf Persson

Random selection of numbers

The Chinese Room

The duplicity of Mark Chu-Carroll

The Mary’s Room fallacy

The Mind-Body problem

 

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

Basic Dark mode Demo page for pages with Disqus comments

 

Hashover responsive CSS demo - without borders

Hashover responsive CSS demo - with borders

 

Citroen C4 1.6 HDi service

Citroen C4 1.6 HDi Brakes

 

Copyright   James R Meyer   2012 - 2020
https://www.jamesrmeyer.com