Das Kalenderblatt 101221

20/12/2010 - 09:35 von WM | Report spam
Krieg der Frösche und der Màuse (18)

Towards the end of his Address on the Unity of Knowledge, delivered at
the 1954 Columbia University bicentennial celebrations, Weyl
enumerates what he considers to be the essential constituents of
knowledge. At the top of his list comes

…intuition, mind's ordinary act of seeing what is given to it. (Weyl
1954, 629)

In particular Weyl held to the view that intuition, or insight—rather
than proof—furnishes the ultimate foundation of mathematical
knowledge. {{Was sonst? Formal beweisen làsst sich schließlich jede
Dummheit - und sei sie noch so groß: Unzugàngliche Kardinalzahlen oder
unnennbare Namen. Notfalls macht man sie zum Axiom. Seit der
transfiniten Mengenlehre hat "Beweis" einen anrüchigen Klang in der
Mathematik. Seitdem muss man nàmlich zwischen "streng bewiesen" und
"möglich" oder gar "genau richtig" streng und genau unterscheiden.}}
Thus in his Das Kontinuum of 1918 he says:

In the Preface to Dedekind (1888) we read that “In science, whatever
is provable must not be believed without proof.” This remark is
certainly characteristic of the way most mathematicians think.
Nevertheless, it is a preposterous principle. As if such an indirect
concatenation of grounds, call it a proof though we may, can awaken
any “belief” apart from assuring ourselves through immediate insight
that each individual step is correct. In all cases, this process of
confirmation—and not the proof—remains the ultimate source from which
knowledge derives its authority; it is the “experience of truth” (Weyl
1987, 119) {{like Zermelos "proof" of the well-ordering assertion is
the experience of untruth}}.

[John L. Bell: "Hermann Weyl", Stanford Encyclopedia of Philosophy
(2009)]
http://plato.stanford.edu/entries/weyl/index.html

Gruß, WM
 

Lesen sie die antworten

#1 honghanru
20/12/2010 - 11:05 | Warnen spam
On 20 Dez., 09:35, WM wrote:
Krieg der Frösche und der Màuse (18)

Towards the end of his Address on the Unity of Knowledge, delivered at
the 1954 Columbia University bicentennial celebrations, Weyl
enumerates what he considers to be the essential constituents of
knowledge. At the top of his list comes

…intuition, mind's ordinary act of seeing what is given to it. (Weyl
1954, 629)

In particular Weyl held to the view that intuition, or insight—rather
than proof—furnishes the ultimate foundation of mathematical
knowledge. {{Was sonst? Formal beweisen làsst sich schließlich jede
Dummheit - und sei sie noch so groß: Unzugàngliche Kardinalzahlen oder
unnennbare Namen. Notfalls macht man sie zum Axiom. Seit der
transfiniten Mengenlehre hat "Beweis" einen anrüchigen Klang in der
Mathematik. Seitdem muss man nàmlich zwischen "streng bewiesen" und
"möglich" oder gar "genau richtig" streng und genau unterscheiden.}}
Thus in his Das Kontinuum of 1918 he says:

In the Preface to Dedekind (1888) we read that “In science, whatever
is provable must not be believed without proof.” This remark is
certainly characteristic of the way most mathematicians think.
Nevertheless, it is a preposterous principle. As if such an indirect
concatenation of grounds, call it a proof though we may, can awaken
any “belief” apart from assuring ourselves through immediate insight
that each individual step is correct. In all cases, this process of
confirmation—and not the proof—remains the ultimate source from which
knowledge derives its authority; it is the “experience of truth” (Weyl
1987, 119) {{like Zermelos "proof" of the well-ordering assertion is
the experience of untruth}}.

[John L. Bell: "Hermann Weyl", Stanford Encyclopedia of Philosophy
(2009)]http://plato.stanford.edu/entries/weyl/index.html

Gruß, WM



Hallo WM,

ich habe Hermann Weyl´s Symetrie gelesen, ein sehr interresantes Buch.
Er ist ein echter Mathematiker.

Übrigens, frohe Weihnachten und gute Rutsch ins neue Jahr!

Grüße , Fei

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