Pro and contra Hilbert : Zermelo’s set theories
Volker Peckhaus (2005)
Philosophia Scientiae
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Volker Peckhaus (2005)
Philosophia Scientiae
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Johannes Lenhard (2005)
Philosophia Scientiae
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Two conflicting interpretations of modern axiomatics will be considered. The logico-analytical interpretation goes back to Pasch, while the model-theoretical approach stems from Hilbert. This perspective takes up the distinction between logic as calculus ratiocinator versus lingua characterica that Heijenoort and Hintikka placed emphasis on. It is argued that the Heijenoort-Hintikka distinction can be carried over from logic to mathematical axiomatics. In particular, the model-theoretical...
Ryszard Wójcicki (2017)
Bulletin of the Section of Logic
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In this note I am reflecting on interrelations between three concepts of truth: (1) that employed by Hilbert arguing his formalist view on the nature of mathematics, (2) Freges idea of truth supported by mathematical intuition, and (3) known as Aristotelian correspondence idea of truth concerning any propositions not merely mathematical.
Guessous, Mohamed (1997)
Journal of Convex Analysis
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José Ferreirós (2005)
Philosophia Scientiae
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We offer a critical review of several different conceptions of the activity of foundational research, from the time of Gauss to the present. These are (1) the traditional image, guiding Gauss, Dedekind, Frege and others, that sees in the search for more adequate basic systems a logical excavation of structures, (2) the program to find sound formal systems for so-called classical mathematics that can be proved consistent, usually associated with the name of Hilbert, and (3) the historicist...
Volker Peckhaus (1996)
Philosophia Scientiae
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Lothar Göttsche (1990)
Manuscripta mathematica
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Petruševski, Ljiljana (1989)
Publications de l'Institut Mathématique. Nouvelle Série
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Petruševski, Ljiljana (1989)
Publications de l'Institut Mathématique. Nouvelle Série
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Yuri Bilu (1996)
Journal für die reine und angewandte Mathematik
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E. Odell, Th. Schlumprecht (1993)
Geometric and functional analysis
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Henk Visser (1998-1999)
Philosophia Scientiae
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Migórski, S. (1995)
Journal of Applied Mathematics and Stochastic Analysis
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