Quantum Physics
Nature Isn’t Fuzzy: Quantum Uncertainty, Inconsistency and Paradox
… And Nature isn’t clear either. Nature is neither fuzzy nor not fuzzy.
Philosophy
Philosophy
Wittgenstein Didn't Absolutely Agree with Gödel’s Theorems and Russell’s Paradox
(and he was right)
Philosophy
Raymond L. Wilder’s Anthropology of Mathematics
Platonism and Applied Mathematics
Logic
The Basics of Logical Identity
Firstly we can say that logical identity is reflexive. In other words, everything (or every thing) is identical to itself. In symbols: ∀x (x = x) To translate: For every x (or for every thing), x must equal x (or everything must be identical to itself). That is, everything has the
Philosophy
Professor E. Brian Davies’s Mathematical Empiricism
This commentary is on the relevant parts of Davies’s book, Science in the Looking Glass. The following is not a book review.
Philosophy
The Demons of the Mathematicians
There is a rich history of mathematicians, philosophers, and other thinkers invoking demons (real or imaginary) in their reasonings. The tradition goes back at least to the iconic ancient Greek philosopher Socrates.
Philosophy
A Modern Day Mathematical Platonist — Alain Badiou
Alain Badiou (1937-) is a French philosopher. At one point he was the chair of Philosophy at the École normale supérieure (ENS) and founder
Differential Equations
The “Well-Posedness” of Differential Equations: the Sense of Hadamard
An overwhelmingly large portion of our modeling of the universe is accomplished by posing and solving differential equations..
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”)
Penrose
Is Roger Penrose a Platonist or a Pythagorean?
Roger Penrose is not only a mathematical physicist: he’s also a pure mathematician.
Logic
The Proposition P is Determinately True… Regardless!
The position of what’s sometimes called semantic realism is that every statement is bivalent as well as being evidence-transcendent.
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.