 ... mathematics, creates not only the numbers one and two, but also all finite ordinal numbers, inasmuch as one of the elements of the two-oneness may be thought of as a new two-oneness, which process may be repeated indefinitely; this gives rise still...  Bulletin of the American Mathematical Society - Page 74by American Mathematical Society - 1914Full view - About this book
 | E.W. Beth - 1965 - 226 pages
...two-oneness may be thought of as a new two-oneness, which process may be repeated indefinitely — Finally this basal intuition of mathematics, in which...never be thought of as a mere collection of units." This conception is still further elaborated in a much more recent statement of Brouwer's views16 from... | |
 | Roberto Torretti - 1990 - 396 pages
...thinking, the intuition of the bare two-oneness. [ . . . ] This basal intuition of mathematics [ . . . ] gives rise immediately to the intuition of the linear...never be thought of as a mere collection of units" (Brouwer 1913, pp. 85-86). 28 A second lemma follows: If two points move with constant speed on different... | |
 | Markus Schmitz - 1997 - 464 pages
...zeitliches - Aufnahmemilieu für alle mathematischen Wesenheiten zum von Brouwer so genannten Kontinuum: "Finally this basal intuition of mathematics, in which the connected and the separate, the 229 Frege, Grundlagen §12, S.41. 230 Brouwer, Intuitionism S.80. Die unmittelbare Motivation für... | |
 | Markus Schmitz - 1997 - 464 pages
...zeitliches - Aufnahmemilieu für alle mathematischen Wesenheiten zum von Brouwer so genannten Kontinuum: "Finally this basal intuition of mathematics, in which the connected and the separate, the 230 Brouwer, Intuitionism S.80. Die unmittelbare Motivation für Brouwers von ihm gegenüber Kant so... | |
 | John Lane Bell - 2005 - 354 pages
...process may be repeated indefinitely; this gives rise still further to the smallest infinite ordinal CO. Finally this basal intuition of mathematics, in which the connected and the separate, the Finally this basal intuition of mathematics, in which the connected and the separate, the continuous... | |
 | Paul Ashton - 2006 - 423 pages
...as a dis-continuity, a jump beyond numeration for which no mathematical schema can fully account — 'the "between," which is not exhaustible by the interposition...never be thought of as a mere collection of units'. Brouwer, 'Intuitionism and Formalism', in Paul Bernacerraf and Hillary Putnam (eds.), Philosophy of... | |
 | James Robert Brown - 1999 - 181 pages
...may be repeated indefinitely; this gives rise still further to the smallest infinite ordinal number . Finally this basal intuition of mathematics, in which...never be thought of as a mere collection of units. (ibid.: 80) This is pretty obscure stuff. It was written early in his career. Alas, four decades later... | |
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