Everything about Logicism totally explained
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. Today, the bulk of modern mathematics is believed to be reducible to a logical foundation using the axioms of
Zermelo-Fraenkel set theory (or one of its extensions, such as
ZFC), which has no known inconsistencies (although it remains possible that inconsistencies in it may still be discovered).
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.)
Logicism was key in the development of
Analytic philosophy in the
twentieth century.
Neo-logicism
Neo-logicism describes a range of views claiming to be the successor of the original logicist program. More narrowly, it's 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.
Further Information
Get more info on 'Logicism'.
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