| Thinking hardly|
or hardly thinking?
|Major trains of thought|
|The good, the bad|
and the brain fart
|Come to think of it|
“”The fundamental cause of the trouble is that in the modern world the stupid are cocksure while the intelligent are full of doubt.
|—Bertrand Russell, Mortals and Others|
Bertrand "Bertie" Russell (1872—1970) was a British mathematician,
liberal, pacifist, socialist, philosopher and logician. He also wrote books and essays for popular audiences; a good many of these were full of his signature snark about religion. Russell's Teapot is a good example of this. Along with Gottlob Frege and Ludwig Wittgenstein, he is considered one of the founders of modern analytic philosophy and one of the greatest logicians of the 20th century.
He coauthored Principia Mathematica with A. N. Whitehead (not to be confused with Isaac Newton's Philosophiæ Naturalis Principia Mathematica), which attempted to use symbolic logic to derive mathematics from basic axioms (1+1=2 is proved in Volume II). It is highly regarded by many mathematicians, but is pretty unreadable unless you have a brain the size of a planet, or no life (and that's still no guarantee). The book was an attempt to make Hilbert's Program a reality by its use of a finite and small set of axioms with which one could (in principle) derive all of modern mathematics. PM is essentially an attempt to make all of mathematics constructive.
Austrian logician Kurt Gödel eventually proved that PM is incomplete, which means that it does not have the ability to produce theorems that prove everything within its particular domain (all of mathematics in this case). The reason for this was essentially that Russell and Whitehead overlooked meta-mathematics, and did not believe (or it did not ever occur to them) that their system could be used to reason about meta-mathematical concepts. Gödel observed that you could in fact use PM with meta-mathematics, and he promptly invented Gödel-numbering, which allows one to prove things about PM itself in PM. Contrary to popular belief, he did not prove that it was "wrong", "inconsistent", "useless", or any other adjective that implies incorrect.
Russell's crowning achievement was having the character of Professor Yaffle from the much loved UK children's television series Bagpuss modelled on him.
- History of Western Philosophy (1946)
- Why I Am Not a Christian (1929)
- See the Wikipedia article on Bertie's Principia Mathematica.
- The Theologian's Nightmare, science fiction by Bertrand Russell
- Slides talking about the constructivism in PM
- Bertrand Russell Stanford Encyclopedia on Bertrand Russell
- Bertrand Russell
- In Praise of Idleness, Bertrand Russell's famous essay on economics and socialism.
- Bertrand Russell Discusses Mankind's Future (1960)
- "I have imagined myself in turn a Liberal, a Socialist, or a Pacifist, but I have never been any of these things, in any profound sense."—Autobiography, Vol. II, p. 38.
- Principia Mathematica, Prefatory Statement of Symbolic Conventions Stanford Encyclopedia of Philosophy, Last review 23 June 2021.
- Logic since 1900, Britannica, Paul Vincent Spade.