現代数学の系譜工学物理雑談古典ガロア理論も読む75

[過去ﾛｸﾞ] 現代数学の系譜工学物理雑談古典ガロア理論も読む75 (1002ﾚｽ)
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558: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE  [sage] 2019/08/21(水) 07:03:08.47 ID:6H2tIaYx

>>557
つづき

それで直観について補足すると下記
（PDFでP642）
Yet two puzzles remain. First: why do we not have Pr(p < q) = 1/2, given the symmetry of the
set-up? Despite the mathematical argument above, the intuition that p < q and q < p are equiprobable
remains strong. What should we say about this intuition? Freiling appears to think we should give such
intuitions priority. He writes (in a slightly different context) that his argument [1] depends upon
a principle
...not meant to be a mathematical statement of the Lebesgue measurability of a certain type of
set. Rather, it is an expression of an obvious, almost physical intuition concerning the
inherently nonmathematical notions of prediction, accuracy, and time independence.
Yet an appeal to symmetry, where we cannot produce a coherent mathematical model, is unreliable,
as we know from the many paradoxes associated with the Principle of Insufficient Reason.
ってところ
これが、きっと、Pruss氏が、この論文を引用した理由で
（>>157より）
Denis
I think it is ok, because the only probability measure we need is uniform probability on {0,1,…,N-1}
が、Pruss氏は「それDenisの直観でしかない」ということよ（＾＾；

つづく

http://rio2016.5ch.net/test/read.cgi/math/1565872684/558

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