In the philosophy of mathematics, the thesis that all mathematical propositions are expressible as or derivable from the propositions of pure logic. Gottlob Frege attempted to establish the thesis in his Die Grundlagen der Arithmetik (1884) and other works; Bertrand Russell argued for logicism in The Principles of Mathematics (1903) and attempted a formal proof with Alfred North Whitehead in Principia Mathematica (1910–13).
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Kurt Gödel's incompleteness theorem is sometimes alleged to undermine the purpose of the project. (However, one can argue that the basic spirit of Logicism remains valid, though in a somewhat less powerful sense than was originally thought.)
Neo-logicism describes a range of views claiming to be the successor of the original logicist program. More narrowly, it is defined as attempts to resurrect Frege's programme through the use of Hume's Principle. Two of the major proponents of neo-logicism are Crispin Wright and Bob Hale.