Philosophy
Wittgenstein Didn't Absolutely Agree with Gödel’s Theorems and Russell’s Paradox
(and he was right)
Gödel
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