Gödel – Cantor's Archive

Philosophy

Wittgenstein Didn’t Absolutely Agree with Gödel’s Theorems and Russell’s Paradox

(and he was right)

Gödel

Gödel’s Constitutional Quarrel

“The examiner was intelligent enough to quickly quieten Gödel and say ‘Oh god, let’s not go into this’ and broke off the examination at this point, greatly to our relief” — Oskar Morgenstern Kurt Gödel (1906–1978) was the greatest logician who ever lived. At the age of 24, he

History

The Limit of Logic and The Rise of The Computer

AI since Aristotle (Part 2)

Gödel

Gödel’s First Incompleteness Theorem in Simple Symbols and Simple Terms

The following piece explains a particular symbolic expression (or version) of Kurt Gödel’s first incompleteness theorem. It also includes a particular expression (or example) of a Gödel sentence (i.e., “This statement is false”)

Logic

Only So Much We Can Prove

A Glimpse of Incompleteness

Logic

Mind vs. Machine: A Philosophical Corollary of Gödel’s Incompleteness Theorem

Canadian mathematician Simon Kochen recalled in his tribute to Kurt Gödel how during his PhD exam, he was asked to name five of Gödel’s theorems. The essence of the question was that each of the theorems either gave birth to a new branch of, or revolutionized, modern mathematical logic.

Analysis

Cantor’s Diagonal Argument

“Diagonalization seems to show that there is an inexhaustibility phenomenon for definability similar to that for provability” — Franzén…

Gödel

Kurt Gödel’s Brilliant Madness

Hungarian polymath John von Neumann (1903–1957) once wrote that Kurt Gödel was “absolutely irreplaceable” and “in a class by himself”.

Philosophy

Platonist Roger Penrose “Sees” Mathematical Truths

What does Roger Penrose mean when he claims to “see” mathematical truths?

Mathematics

A Computability Proof of Gödel’s First Incompleteness Theorem

A computability proof of Gödel’s incompleteness theorem equally as strong as Gödel’s version, but much easier to deduce