|
In a foundational controversy in twentieth-century mathematics, L. E. J. Brouwer, a supporter of intuitionism, opposed David Hilbert, the founder of formalism. == Background == The background for the controversy was set with David Hilbert's axiomatization of geometry in the late 1890s. In his biography of Kurt Gödel, John W. Dawson, Jr summarizes the result as follows: : "At issue in the sometimes bitter disputes was the relation of mathematics to logic, as well as fundamental questions of methodology, such as how quantifiers were to be construed, to what extent, if at all, nonconstructive methods were justified, and whether there were important connections to be made between syntactic and semantic notions." (Dawson 1997:48) Dawson observes that "partisans of three principal philosophical positions took part in the debate" (''ibid.'') – the logicists (Gottlob Frege and Bertrand Russell), the formalists (David Hilbert and his "school" of collaborators), and the constructivists (Henri Poincaré and Hermann Weyl); within this constructivist school was the radical self-named "intuitionist" L.E.J. Brouwer. The following sections will expand these disputes noted by Dawson. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Brouwer–Hilbert controversy」の詳細全文を読む スポンサード リンク
|