Philosophy

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

(and he was right)

Philosophy

(and he was right)

Gödel

“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

AI since Aristotle (Part 2)

Gödel

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

A Glimpse of Incompleteness

Logic

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

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

Gödel

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

Philosophy

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

Mathematics

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