Das alte Lied

24/07/2015 - 16:16 von WM | Report spam
Offenbar fiel es Cantor schwer, in harter mathematischer Sprache zu formulieren, was ihm vorschwebte. Seine "Definition" konnte einem kritischen Denker wie Kronecker durchaus bedenklich erscheinen. [Herbert Meschkowski: "Georg Cantor: Leben, Werk und Wirkung", 2. Aufl. BI, Mannheim (1981) p. 229]

The bulk of Frege's critique of Hilbert consists of criticizing Hilbert's lack of terminological clarity, {{That kind of accusation occurs often. Something is accused to be not formal enough or unclear or completely meaningless. This objection is always advisable if the text is not comprehensible by the reader or inacceptable to him, however without a counter argument being available presently or in general. Hint: I do not want to judge in the Frege-Hilbert controversy. I only aim at the dwarfs who believe to stand on the shoulders of these giants.}} particularly as this applies to the differences between sentences and various collections of thoughts. He takes Hilbert to task for misleadingly using the same sentences to express different thoughts, and points out repeatedly that Hilbert's use of axioms as definitions needs considerably more-careful treatment than Hilbert affords it. The more-substantial criticism flows naturally from this terminological critique: Frege takes it that once one disentangles Hilbert's terminology, it becomes clear that he is simply not talking about the axioms of geometry at all, since the sets of thoughts he actually deals with are the misleadingly-expressed thoughts about e.g. real numbers. And, adds Frege, one cannot infer the consistency of the geometric axioms proper from that of the thoughts Hilbert treats. [Patricia Blanchette (2009)] http://plato.stanford.edu/entries/frege-hilbert/

Gruß, WM
 

Lesen sie die antworten

#1 Pirx42
24/07/2015 - 17:24 | Warnen spam
Am 24.07.2015 um 16:16 schrieb WM:
Offenbar fiel es WM schwer, in harter mathematischer Sprache zu formulieren, was ihm vorschwebte.



Seine "Definition" konnte einem kritischen Denker durchaus bedenklich erscheinen. [Ich]

Ähnliche fragen