Das Kalenderblatt 090809

08/08/2009 - 15:37 von WM | Report spam
[...] "point" has no meaning unless it is defined, and this involves
the specification of some sort of procedure. "All the points of a
line" as a purely intuitional concept apart from the rules by which
points are determined, can have no operational meaning, and
accordingly is to be held for mathematics as an entirely meaningless
concept. [...] "All the points of a line" means no more than "All the
rules for determining points on a line". [...] In other words, we have
no more reason to describe the points on a line as non-denumerable
than the non-terminating decimals. The repudiation of the diagonal
Verfahren for the decimals at the same time removes all reason for
thinking the points on a line non-denumerable.
In fact, a consistent application of the operational criterion of
meaning appears to demand the complete discard of the notion of
infinities of different orders. We never have "actual" infinites [...]
but only rules for operation which are not self-terminating. How can
there be different sorts of non-self-terminatingness? At any stage in
the process the rule either permits us to go on and take the next step
or it does not [...] and that is all there is to it. [...] Mengenlehre
is similarly supposed to have established the existence of
transcendentals by showing that all algebraic numbers are denumerable.
This proof I would reject, holding that the mere act of assigning
operational meaning to the transcendentals of itself ensures that they
are denumerable. As a matter of fact, only a few transcendentals have
been established. Mengenlehre is powerless to show whether any given
number, such as e or pi, is transcendental or not, and the detailed
analysis necessary in any given case for establishing transcendence is
not avoided by Mengenlehre. From the operational view a transcendental
is determined by a program of procedure of some sort; Mengenlehre has
nothing to add to the situation. And this, as far as my elementary
reading goes, exhausts the contributions which Mengenlehre has made in
other fields.

P.W. Bridgman: "A physicist's second reaction to Mengenlehre", Scripta
Mathematica, Vol. II, 1934.

Gruß, WM

Lesen sie die antworten

#1 Herbert Newman
12/08/2009 - 02:30 | Warnen spam
Am Sat, 8 Aug 2009 06:37:29 -0700 (PDT) schrieb WM:

[bla bla bla]

(P.W. Bridgman: "A physicist's second reaction to Mengenlehre", Scripta
Mathematica, Vol. II, 1934.)

Ich denke, dass das, was für Herrn Bridgmans Artikel gilt, wohl auch für
Ihre diversen "Produktionen" gilt, Herr Professor Dr. Mückenheim:

"I have no intention to be satirical, but science and particularly
mathematics depend on /generality/ and you write from the point of view of
personal experience the best you can. This paper should then be printed in
a psychiatric magazine but not in a mathematical one."


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