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
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
The three main contemporary ways to understand the foundations of mathematics.
Philosophy
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
… And Nature isn’t clear either. Nature is neither fuzzy nor not fuzzy.
Philosophy
(and he was right)
Philosophy
Platonism and Applied Mathematics
Logic
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
“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
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
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
AI since Aristotle (Part 1)