Vynikající diskuzní téma!

Z trochu jiného soudku:

Ivan Chvatík - Kde se bere matematika

http://www.cts.cuni.cz/new/data/Repcfd06722.pdf

Heidegger and Mathematics - Michael D. Pennamacoor

http://an-archos.com/pipermail/heidegger_an-archos.com/1996-May/001366.html

Martin Heidegger - Modern science, metaphysics and mathematics

http://www.scribd.com/doc/6410410/M-Heidegger-Modern-Science-Metaphysics-and-Mathematics

MAKOSHARK: Dik za prispevek, vecer mam co delat. :)

MAKOSHARK: A samozřejmě místo R by tam měl být jednotkový interval [0,1], aby Lebesgueva norma byla normovaná.

Otázka platonismu by sem měla patřit, v té souvislosti jsem nedávno narazil na takový myšlenkový experiment. Hypotéza kontinua je nerozhodnutelná ze ZFC (Zermelova-Fraenkelova teorie množin s axiomem výběru), ale Chris Freiling z nějaké zvláštní pozice platonismu zastává názor, že přesto musí být buď pravdivá, nebo nepravdivá. "Dokazuje", že je nepravdivá.

Dá se celkem lehce dokázat, že když pro každou funkci f z reálných čísel do spočetných podmnožin reálných čísel existují body x,y, že x neleží v f(y) a y neleží v f(x), tak neplatí hypotéza kontinua.

Mějme libovolnou f z R do spočetných podmnožin R. Hodíme šipkou na reálnou osu a určíme tím bod x a spočetnou podmnožinu f(x). Ta má Lebesgueovu míru nula (za předpokladu, že je měřitelná), tedy pravděpodobnost, že jiným hodem šipkou s cílem y se strefíme do f(x) je nula. Symetricky to platí i pro x v f(y). Takže neplatí hypotéza kontinua. Více viz heslo Freiling na wikipedii.

Matematika je prevazne kvantifikovany casoprostorovy jazyk. ;) ...Mashine...

The philosopher Ludwig Wittgenstein originally started out by thinking that words were related to facts in the world, then later reversed his position to conclude that the meaning of words lay in their use. Is this reflected in quantum mechanics?

I should first state my own opinion about Wittgenstein's philosophy. I never could do too much with early Wittgenstein and the philosophy of the Tractatus Logico-philosophicus, but I like very much the later ideas of Wittgenstein and his philosophy about language. In the Tractatus, which I thought too narrow, he always thought that words have a well-defined meaning, but I think that is an illusion. Words have no well-defined meaning. We can sometimes by axioms give a precise meaning to words, but still we never know how these precise words correspond to reality, whether they fit reality or not. We cannot help the fundamental situation - that words are meant as a connection between reality and ourselves - but we can never know how well these words or concepts fit reality. This can be seen in Wittgenstein's later work. I always found it strange, when discussing such matters with Bertrand Russell, that he held the opposite view; he liked the early work of Wittgenstein and could do nothing whatsoever with the late work. On these matters we always disagreed, Russell and I.

I would say that Wittgenstein, in view of his later works, would have realized that when we use such words as position or velocity, for atoms, for example, we cannot know how far these terms take us, to what extent they are applicable. By using these words, we learn their limitations.

http://www.fdavidpeat.com/interviews/heisenberg.htm