logicism
The approach to the philosophy of mathematics pioneered by Frege and Russell . According to logicism the truths of mathematics are logical truths, deducible by logical laws from basic logical axioms . The programme of showing this started with Frege's brilliant demonstration that elementary truths of counting (e.g. ‘there are four apples here’) can be formalized using only the quantifiers and identity. No irreducible mention of number is demanded. The greatest achievement of logicism was Principia Mathematica (1912) by Russell and Whitehead . The problem for the programme was that the complexity necessary to avoid paradoxes led to a mapping of mathematics onto set theory, with its own structures and axioms, rather than to anything recognizable as ‘purely’ logical.

Philosophy dictionary. . 2011.

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  • logicism — /loj euh siz euhm/, n. Logic, Math. the doctrine, developed chiefly by Gottlob Frege and Bertrand Russell, that mathematics can be reduced to logic. [1935 40; LOGIC + ISM] * * * In the philosophy of mathematics, the thesis that all mathematical… …   Universalium

  • logicism — noun The doctrine that mathematics is a branch of logic in that some or all mathematics is reducible to logic. See Also: logicist …   Wiktionary

  • Logicism — one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic and therefore all mathematics is reducible to logic. Bertrand Russell and Alfred North Whitehead championed this… …   Mini philosophy glossary

  • logicism — log·i·cism …   English syllables

  • logicism — noun (philosophy) the philosophical theory that all of mathematics can be derived from formal logic • Topics: ↑philosophy • Hypernyms: ↑philosophical doctrine, ↑philosophical theory …   Useful english dictionary

  • logicist — logicism …   Philosophy dictionary

  • Логицизм — (logicism), науч. филос. направление, исследующее основания математики и стремящееся свести понятия и принципы математики к понятиям и принципам логики формальной. В числе первых философов, предложивших этот подход, были Фреге и Рассел. Хотя Л.,… …   Народы и культуры

  • mathematics, philosophy of — Branch of philosophy concerned with the epistemology and ontology of mathematics. Early in the 20th century, three main schools of thought called logicism, formalism, and intuitionism arose to account for and resolve the crisis in the foundations …   Universalium

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