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
The position of what’s sometimes called semantic realism is that every statement is bivalent as well as being evidence-transcendent.
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.
Set Theory
Yet a bit more Introduction to Foundational Mathematics
Logic
Here’s a fun 2-minute guide to the infamous Axiom of Choice, one of the stranger mathematical curiosities.
Logic
Introduction to Mathematics for non-Mathematicians
Logic
Many philosophers and logicians have analysed the forms of arguments and shown us that the same forms occur across many different cases…
Philosophy
What does Roger Penrose mean when he claims to “see” mathematical truths?
Arithmetic
The strange debate and controversy in K-12 math education
Automata Theory
A Theory On How Simple Structures Generate Complex Systems
Wiener
American mathematician Norbert Wiener (1894–1964) was by all accounts, a very peculiar man. After graduating from high school at 11 years old, he entered Tufts College and within three years was awarded an A.B. in mathematics.