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Logicism

This was a movement in philosophy and mathematics in the late nineteenth and early twentieth centuries to subsume mathematics under logic. Its chief proponents were Gottlob Frege and Bertrand Russell. The mission of the logicists was to strengthen the already high epistemological status of mathematics and analysis by reducing mathematics to logic. Frege in his work developed a meta-mathematical hierarchy of concepts and extensions of concepts over objects, and pioneered the augmentation of classical sentential logic with logic functions. Russell detected flaws in some of Frege’s work on the logical definition of arithmetic, including that described by the now infamous Russell’s Paradox (in which the set of all sets excluding themselves belongs to itself if it does not belong to itself, but does not belong to itself if it does belong to itself), but did not diminish the extraordinary and prolific contribution of Frege to mathematics.

Logicism was ultimately regarded as a failed project by the mathematical and philosophical community at large, due to the apparent impossibility of describing all of the principles required for a working arithmetic and algebra without referring to intuitive, existential, abstract or non-logical constructs and assumptions.

Editor(s): Long, B.

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