Das Kalenderblatt 091011

10/10/2009 - 21:53 von WM | Report spam
The clear understanding of formalism in mathematics has led to a
rather fixed dogmatic position which reads: Mathematics is what can be
done within axiomatic set theory using classical predicate logic. I
call this doctrine the Grand Set Theoretic Foundation. [...]
Even in the 1940's, with the growth of abstract algebra, axiomatic
set theory was not regarded as a central doctrine. It was not until
about 1950 that the Grand Set Theoretic Foundation was finally
complete and officially accepted under the slogan which might have
read: "Mathematics is exactly that subject which can be developed by
logical rules of proof from the Zermelo-Fraenkel axioms for set
theory." This foundation scheme had its popular version in the "new
math" for schools. It also had its philosophical doctrine, a version
of Platonism, that the world of sets is that constructed in the
standard cumulative hierarchy of all ranked sets. [...] The Zermelo-
Fraenkel axioms are then (a selection of) the facts true for all sets
in this hierarchy. This is sometimes claimed to describe the ultimate
Platonic reality which underlies all mathematics: Perhaps the Zermelo-
Fraenkel axioms do not describe everything, but with a little more
insight we will understand all the axioms necessary and then at least
in principle all mathematical problems can be settled from the axioms.
It is my contention that this Grand Set Theoretic Foundation is a
mistakenly one-sided view of mathematics and also that its precursor
doctrine (Dedekind cuts) was also one-sided.

OF MATHEMATICS", The American Mathematical Monthly, Vol. 88, No. 7
(1981) 462-472.]

Der Mann, der die Welt hàtte veràndern können:
(s. Ende des Berichtes.)

Gruß, WM

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#1 WM
10/10/2009 - 22:12 | Warnen spam
On 10 Okt., 21:53, WM wrote:

Der Mann, der die Welt hàtte veràndern können:http://www.ams.org/notices/199510/maclane.pdf
(s. Ende des Berichtes.)

Falsch erinnert. Richtig ist: S. 1136 oben.

Gruß, WM

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