Mathematics, Philosophy of
Philosophy of mathematics, branch of philosophy that is concerned with two major questions: one concerning the meanings of ordinary mathematical sentences and the other concerning the issue of whether abstract objects exist. The first is a straightforward question of interpretation: What is the...
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Bertrand RussellBertrand Russell, British philosopher, logician, and social reformer, founding figure in the analytic movement in AngloAmerican philosophy, and recipient of the Nobel Prize for Literature in 1950. Russell’s contributions to logic, epistemology, and the philosophy of mathematics established him as…

Henri PoincaréHenri Poincaré, French mathematician, one of the greatest mathematicians and mathematical physicists at the end of 19th century. He made a series of profound innovations in geometry, the theory of differential equations, electromagnetism, topology, and the philosophy of mathematics. Poincaré grew…

Alfred North WhiteheadAlfred North Whitehead, English mathematician and philosopher who collaborated with Bertrand Russell on Principia Mathematica (1910–13) and, from the mid1920s, taught at Harvard University and developed a comprehensive metaphysical theory. Whitehead’s grandfather Thomas Whitehead was a selfmade…

Gottlob FregeGottlob Frege, German mathematician and logician, who founded modern mathematical logic. Working on the borderline between philosophy and mathematics—viz., in the philosophy of mathematics and mathematical logic (in which no intellectual precedents existed)—Frege discovered, on his own, the…

Hilary PutnamHilary Putnam, leading American philosopher who made major contributions to metaphysics, epistemology, the philosophy of mind, the philosophy of language, the philosophy of science, the philosophy of mathematics, and the philosophy of logic. He is best known for his semantic externalism, according…

Leopold KroneckerLeopold Kronecker, German mathematician whose primary contributions were in the theory of equations and higher algebra. Kronecker acquired a passion for number theory from Ernst Kummer, his instructor in mathematics at the Liegnitz Gymnasium, and earned his doctor’s degree at the University of…

Philosophy of mathematicsPhilosophy of mathematics, branch of philosophy that is concerned with two major questions: one concerning the meanings of ordinary mathematical sentences and the other concerning the issue of whether abstract objects exist. The first is a straightforward question of interpretation: What is the…

Sir Michael A.E. DummettSir Michael A.E. Dummett, English philosopher who did influential work in the philosophy of language, metaphysics, logic, the philosophy of mathematics, and the history of analytic philosophy. He was also one of the foremost expositors of the work of the German mathematical logician Gottlob Frege…

PhilolausPhilolaus, philosopher of the Pythagorean school, named after the Greek thinker Pythagoras (fl. c. 530 bc). Philolaus was born either at Tarentum or, according to the 3rdcenturyad Greek historian Diogenes La?rtius, at Croton, in southern Italy. When, after the death of Pythagoras, dissension was…

Sir Edmund Taylor WhittakerSir Edmund Taylor Whittaker, English mathematician who made pioneering contributions to the area of special functions, which is of particular interest in mathematical physics. Whittaker became a fellow of Trinity College, Cambridge, in 1896. After being elected a fellow of the Royal Society of…

Stanis?aw Le?niewskiStanis?aw Le?niewski, Polish logician and mathematician who was a cofounder and leading representative of the Warsaw school of logic. Le?niewski was the son of one of the civil engineers chiefly responsible for the construction and supervision of the transSiberian railroad. After preliminary…

Louis CouturatLouis Couturat, French philosopher and logician who sought a universal language and symboliclogic system to study the history of philosophy and the philosophy of mathematics. Educated at the école Normale Supérieure in philosophy and mathematics, Couturat became a professor at the University of…