Logic – Cantor's Archive

Logic

Formal Logic vs. Material Logic?

In a purely logical argument, even if the premises aren’t in any way (semantically) connected to the conclusion, the argument may still be both valid and sound. Professor Edwin D. Mares displays what he sees as a problem with purely formal logic when he offers us the following example

Logic

Lewis Carroll’s Infinite Premises

The British writer, mathematician and logician Charles Lutwidge Dodgson (which was Lewis Carroll’s real name) worked in the fields of geometry, matrix algebra, mathematical logic and linear algebra. Dodgson was also an influential logician. (He introduced the Method of Trees; which was the earliest use of a truth tree.

Philosophy

Logicism, Formalism, and Intuitionism

The three main contemporary ways to understand the foundations of mathematics.

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’

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

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

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

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.

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

Logic

Logic, Intuition and Paradox

AI since Aristotle (Part 1)