Logicism is one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic and therefore some or all mathematics is reducible to logic. Bertrand Russell and Alfred North Whitehead championed this theory fathered by Gottlob Frege. Frege gave up on the project after Russell recognized a paradox exposing an inconsistency in naive set theory. Russell and Whitehead continued on with the project in their Principia Mathematica. Jump to: navigation, search Philosophy of mathematics is that branch of philosophy which attempts to answer questions such as: why is mathematics useful in describing nature?, in which sense(s), if any, do mathematical entities such as numbers exist? and why and how are mathematical statements true?. Various approaches to... Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations related to: Mathematics Look up Mathematics on Wiktionary, the free dictionary Wikimedia Commons has media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ... Jump to: navigation, search Logic (from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of arguments, although the exact definition of logic is a matter of controversy amongst philosophers (see below). ... Jump to: navigation, search Bertrand Russell The Right Honourable Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970), was an influential British logician, philosopher, and mathematician, working mostly in the 20th century. ... Jump to: navigation, search Alfred North Whitehead, OM (February 15, 1861, Ramsgate, Kent, UK – December 30, 1947, Cambridge, MA) was a British philosopher, physicist, and mathematician who worked in logic, mathematics, philosophy of science and metaphysics. ... Friedrich Ludwig Gottlob Frege Friedrich 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. ... Russells paradox (also known as Russells antinomy) is a paradox discovered by Bertrand Russell in 1901 which shows that the naive set theory of Cantor and Frege is contradictory. ... Naive set theory1 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. ... The Principia Mathematica is a three-volume work on the foundations of mathematics, written by Alfred North Whitehead and Bertrand Russell and published in 1910-1913. ...

Kurt Gödel's incompleteness theorem is sometimes alleged to undermine the purpose of the project. The attempted resurrection of this theory is styled neo-logicism. One of the major proponents of neo-logicism is Crispin Wright. Jump to: navigation, search Kurt Gödel Kurt Gödel [kurt gøːdl], (April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher of mathematics. ... Jump to: navigation, search In mathematical logic, Gödels incompleteness theorems are two celebrated theorems proven by Kurt Gödel in 1931. ... Logicism is one of the schools of thought in the Philosophy of mathematics. ... Crispin Wright (born 1942) is a British philosopher, who has written on neo-Fregean philosophy of mathematics, Wittgensteins later philosophy, and on issues related to truth, realism, cognitivism, skepticism, knowledge and objectivity. ...