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Bertrand Arthur William Russell, 3rd Earl Russell ( May 18, 1872 - February 2, 1970) was one of the most influential mathematicians, philosophers and logicians working (mostly) in the 20th century, an important political liberal, activist and a populariser of philosophy. Millions looked up to Russell as a sort of prophet of the creative and rational life; at the same time, his stance on many topics was extremely controversial. He was born in 1872, at the height of Britain's economic and political ascendancy, and died of influenza in 1970, when Britain's empire had all but vanished and her power had been drained in two victorious but debilitating world wars. At his death, however, his voice still carried moral authority, for he was one of the world's most influential critics of nuclear weapons and the American war in Vietnam.

In 1950, Russell was made Nobel Laureate in LiteratureThe Nobel Prize in literature is awarded annually to an author from any country who has produced "the most outstanding work of an idealistic tendency". The "work" in this case generally refers to an author's work as a whole, not to any individual work, th "in recognition of his varied and significant writings in which he champions humanitarian ideals and freedom of thoughtFreethought is a characteristic of individuals whose opinions are formed on the basis of an understanding and rejection of tradition, authority or established belief. This definition is especially applicable to thought based on rejection of religious dogm".

1 Russell's philosophical and logical work

1.1 Logic

In mathematical logic, Russell established Russell's paradoxRussell's paradox is a paradox discovered by Bertrand Russell in 1901 which shows that the naive set theory of Cantor and Frege is contradictory. Consider the set M to be "The set of all sets that do not contain themselves as members". Formally: A is an e, which exposed an inconsistency in naive set theoryNaive set theory 1 is distinguished from axiomatic set theory by the fact that the former regards sets as collections of objects, called the elements or members of the set, whereas the latter regards sets only as that which satisfies certain axioms. Sets and led directly to the creation of modern axiomatic set theorySet theory is the mathematical theory of sets, which represent collections of abstract objects. It has a central role in modern mathematical theory, providing the basic language in which most of mathematics is expressed. For more information on set theory. It also crippled Gottlob FregeFriedrich Ludwig Gottlob Frege ( November 8, 1848 July 26, 1925) was a German mathematician, logician, and philosopher who is regarded as a founder of both modern mathematical logic and analytic philosophy. Frege's life Frege was born in Wismar. He starte's project of reducing mathematics to logic. Nonetheless, Russell defended logicismLogicism is one of the schools of thought in the Philosophy of mathematics. Logicism is the theory that mathematics is an extension of logic and therefore all mathematics is reducible to logic. Modern philosophers believed that proof of this theory was th (the view that mathematics is in some important sense reducible to logic) and attempted this project himself, along with Alfred North WhiteheadAlfred North Whitehead ( February 15, 1861 December 30, 1947) was a British philosopher and mathematician who worked in logic, mathematics, philosophy of science and metaphysics. His best known work in mathematics is the Principia Mathematica which he wro, in the Principia Mathematica, a clean axiomatic system on which all of mathematics can be built, but which was never fully completed. Although it did not fall prey to the paradoxes in Frege's approach, it was later proven by Kurt Gödel that—for exactly that reason—neither Principia Mathematica nor any other consistent logical system could prove all mathematical truths; hence, Russell's project was necessarily incomplete.



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