Das Kalenderblatt 101105

04/11/2010 - 10:47 von WM | Report spam
[...] suppose for the sake of argument that physical regions are
literally modeled by subsets of R^3. Then the argument goes like this:
working in a set theory with the Axiom of Choice, we perform the
Banach–Tarski construction, which is physically ridiculous; we
conclude that Choice has been empirically disconfirmed. But isn’t it
at least as reasonable to conclude that the full power set of R^3 was
a poor choice as a model for physical regions? Indeed, given the many
internal mathematical considerations in favor of the axiom, wouldn’t
it be considerably more reasonable to conclude that physical regions
are more effectively modeled by measurable subsets of R^3? If, for
example, our set theory includes sufficient large cardinals, we might
count
Banach–Tarski as a good reason to model physical space in L(R), where
all sets of reals are measurable. [...] In particular, we should be
alert to the ways that applied mathematics can generate phantom
physical questions, and we should no longer expect science to provide
the sort of methodological guidance for mathematics that it once did.
{{Den Primat der Physik und der Ratio kann man in matheologische
Fragen ebensowenig wie in theologischen Fragen erwarten. Denn in
beiden Fàllen wird der Ventilglaube ventiliert, dass eine
Einbahnstraße zur Realitàt führt: Die Mathematik beeinflusst die
Realitàt, die Realitàt beeinflusst aber nicht die Mathematik. Dasselbe
Weltbild herrscht in theologischen Kreisen: Gott kann auf die Welt
wirken, die Welt wirkt aber nicht auf Gott. - Allerdings kann man da
mit Hilfe von Gebeten wenigstens den Versuch unternehmen}}

[Penelope Maddy: "How applied mathematics became pure", Reviev
Symbolic Logic 1 (2008) 16 - 41]

Gruß, WM
 

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#1 fiesh
04/11/2010 - 15:59 | Warnen spam
On 2010-11-04, WM wrote:
[...] suppose for the sake of argument that physical regions are
literally modeled by subsets of R^3. Then the argument goes like this:
working in a set theory with the Axiom of Choice, we perform the
Banach–Tarski construction, which is physically ridiculous; we
conclude that Choice has been empirically disconfirmed. But isn’t it
at least as reasonable to conclude that the full power set of R^3 was
a poor choice as a model for physical regions? Indeed, given the many
internal mathematical considerations in favor of the axiom, wouldn’t
it be considerably more reasonable to conclude that physical regions
are more effectively modeled by measurable subsets of R^3? If, for
example, our set theory includes sufficient large cardinals, we might
count
Banach–Tarski as a good reason to model physical space in L(R), where
all sets of reals are measurable. [...] In particular, we should be
alert to the ways that applied mathematics can generate phantom
physical questions, and we should no longer expect science to provide
the sort of methodological guidance for mathematics that it once did.
{{Den Primat der Physik und der Ratio kann man in matheologische
Fragen ebensowenig wie in theologischen Fragen erwarten. Denn in
beiden Fàllen wird der Ventilglaube ventiliert, dass eine
Einbahnstraße zur Realitàt führt: Die Mathematik beeinflusst die
Realitàt, die Realitàt beeinflusst aber nicht die Mathematik. Dasselbe
Weltbild herrscht in theologischen Kreisen: Gott kann auf die Welt
wirken, die Welt wirkt aber nicht auf Gott. - Allerdings kann man da
mit Hilfe von Gebeten wenigstens den Versuch unternehmen}}

[Penelope Maddy: "How applied mathematics became pure", Reviev
Symbolic Logic 1 (2008) 16 - 41]



Zeige doch, dass du verstanden hast, was du zitierst, und erklaere dem
Kalenderblattleser, was L(R) ist.

fiesh

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