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[Phys-L] Re: 2+2=4



That's why it was in lit..

The Nobel site bio discusses his interest in Frege and Peano.


http://nobelprize.org/literature/laureates/1950/russell-bio.html


More:


"His works in the sciences concerned with human knowledge and
mathematical logic are epoch-making and have been compared to Newton's
fundamental results in mechanics. Yet it is not these achievements in
special branches of science that the Nobel Prize is primarily meant to
recognize. What is important, from our point of view, is that Russell
has so extensively addressed his books to a public of laymen, and, in
doing so, has been so eminently successful in keeping alive the interest
in general philosophy."


http://nobelprize.org/literature/laureates/1950/press.html


bc, who exaggerated below, and endured the descriptive course
"Philosophy of Mathematics" at USC [1959].


p.s. apropos: he wrote a relativity book! The ABC of Relativity, 1925.
Probably w/ contraction and dilation?

"Russell's first mathematical work, An Essay on the Foundations of
Geometry, was published in 1897. This work was heavily influenced by
Immanuel Kant. Russell soon realized that the conception it laid out
would have made Albert Einstein's schema of space-time impossible, which
he understood to be superior to his own system. Thenceforth, he rejected
the entire Kantian program as it related to mathematics and geometry,
and he maintained that his own earliest work on the subject was nearly
without value."

And, relating to 2 + 2 :


Interested in the definition of number, Russell studied the work of
George Boole, Georg Cantor, and Augustus de Morgan, and he became
convinced that the foundations of mathematics were tied to logic. In
1900 he attended a philosophical congress in Paris where he became
familiar with the work of the Italian mathematician, Giuseppe Peano. He
mastered Peano's new symbolism and his set of axioms for arithmetic.
Peano was able to define logically all of the terms of these axioms with
the exception of 0, number, successor, and the singular term, the.
Russell took it upon himself to find logical definitions for each of
these. He eventually discovered that Gottlob Frege had independently
arrived at equivalent definitions for 0, successor, and number, and the
definition of number is now usually referred to as the Frege-Russell
definition. It was largely Russell who brought Frege to the attention of
the English-speaking world.

http://www.answers.com/topic/bertrand-russell







John Denker wrote:

Bernard Cleyet wrote:

I thought Russell got a Nobel for answering this?


No, he didn't.

For starters, there is no Nobel prize for mathematics.

=======================

If you want to have an "explanation" for 2 + 2 = 4, you need
to start by defining 2, defining 4, defining +, et cetera.

A conventional way to do this is in terms of the _Peano axioms_.

From there, the proof that SS0 + SS0 = SSSS0 takes about ten
lines. You can google for the Peano axioms, but far and away
the most accessible presentation of this topic (including the
aforementioned proof) can be found in
Douglas Hofstadter, _G�del, Escher, Bach_

The book is a masterpiece. It the sort of book that if I didn't
already know it had a Pulitzer prize, I would assume it did. OTOH
it doesn't appeal to every taste.

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