Philosophy
The Backstage of Mathematical Thinking: How Our Brains Bring About the Abstract
A brief survey of recent insights from cognitive science
Jan Gronwald
Philosophy
Beginner’s Guide to Mathematical Constructivism
The foundational crisis in mathematics along with roughly four decades following it, was likely the most fertile period in the history of logic and studies in the foundations. After discovering the set-theoretic paradoxes, such as the paradox of the set of all sets, together with the logical ones, like Russell’
Volpin
The Beautiful Consistency of Mathematics — Alexander Yessenin-Volpin
Mathematics is often believed to bring people to madness. We hear many stories like those about Gödel, Cantor, Nash, and Grothendieck, describing geniuses haunted by insanity that is developing along with their mathematics. And there is something to it. A certain psychologist said that A paranoid person is irrationally rational.
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.
Set Theory
Refuting the Refutation of Cantor
On August 2. 2020 Cantor’s Paradise published Bruno Campello’s brief critique of Cantor’s approach in transfinite mathematics. The author…