Note: Full functionality of this website requires JavaScript to be enabled in your browser.

Formal papers related to questions about infinity

This page lists formal papers that are relevant to questions of infinity, transfinity, etc.

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

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

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

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

On Considerations of Language in the Diagonal Proof

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

On Smith-Volterra-Cantor sets and their measure

New section added to paper on Gödel’s flawed paper

After comments that my PDF paper on the flaw in Gödel’s incompleteness proof is too long, I have added a new section which gives a brief summary of the flaw, while the remainder of the paper details the resultant confusion of levels of language. The paper can be seen at The Fundamental Flaw in Gödel’s Proof of his Incompleteness Theorem.

How to setup Dark mode for a web-site

I have set up this website to allow a user to switch to a dark mode, but which also allows the user to revert back to the browser/system setting. The details of how to implement this on a website are given at How to setup Dark mode on a web-site.

Easy Footnotes

How to set up a system for easy insertion or changing of footnotes in a web-page, see Easy Footnotes for Web Pages.

Recently added pages

Translation of Cantor’s “A Contribution to the Theory of Sets”

Logic and Dobbs vs Jackson WHO and Roe vs Wade

Alexander’s Sphere according to David Pierce

Indefinable Numbers

The Axiom of Choice and Well-Ordering

Shaughan Lavine’s book “Understanding the Infinite”

The Origins of Transfinite Numbers

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

Cantor’s Grundlagen and associated papers

To understand the philosophy of set theory as it is today requires a knowledge of the history of the subject. One of the most influential works in this respect was Georg Cantor’s set of six papers published between 1879 and 1884 under the overall title of Über unendliche lineare Punktmannig-faltigkeiten, which were published between 1879 and 1884. I now have English translations of Part 1, Part 2, Part 3 and the major part Part 5 (Grundlagen).

Decreasing intervals, limits, infinity and Lebesgue measure

The page Understanding sets of decreasing intervals explains why certain definitions of sets of decreasing intervals are inherently contradictory unless limiting conditions are included, and the page Understanding Limits and Infinity explains how the correct application of limiting conditions can eliminate such contradictions. The paper On Smith-Volterra-Cantor sets and their measure has additional material which gives a more formal version.