By Norman D. Willis
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Additional resources for Challenging False Logic Puzzles
Indeed, one of Gödel’s contemporaries, the noted philosopher of science Carl Hempel, recalled that “it was quite customary for students to study at various universities,” staying at each one perhaps “a term or a year or several years” . Hempel himself, for example, began at the University of Göttingen and moved successively to Heidelberg, Berlin, and Vienna before finally returning to Berlin for his doctorate. That Gödel chose to remain at the University of Vienna throughout his years as a university student was somewhat exceptional; and after receiving his doctorate he stayed on to become a Dozent, leaving finally only as a result of political and economic circumstances.
As his correspondence with Dedekind makes clear, that discovery took place in December 1873, at a time when his interests were turning “away from trigonometric series to an analysis of [the notion of] continuity” . Both Cantor and Dedekind were aware that the real numbers were, in some vague sense, far more numerous than the rationals. But the precise notion of denumerability needed to make that intuition precise was lacking, and though Cantor established the uncountability of the reals in his paper 1874, he gave precedence there to the theorem that the algebraic numbers could be enumerated by the integers – a result due apparently to Dedekind (to whom, however, Cantor failed to give credit ).
Education” that “wearied, hindered, and suppressed” students’ interests, energies, and aspirations . ” 7 The geometry notebooks contain little in the way of Euclidean deductions. They are devoted rather to elaborate perspective drawings, including polyhedra and projections of cylinders and cones. 18 Logical Dilemmas Certainly the faculty/student ratio appears to have been quite favorable, and many of the faculty were highly qualified: Of the twenty-one full-time faculty employed by the Realgymnasium during all or part of Gödel’s years there, eleven held the doctorate.