[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49 (658ﾚｽ)
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446(3): 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE [sage] 2018/01/13(土) 11:37:38.46 ID:rUYSYDib(7/17) AAS
>>438 補足
pdf：A peculiar connection between the Axiom of Choice and predicting the future THE MATHEMATICAL ASSOCIATION OF AMERICA Monthly February 2008
については、当時哲学者がいろいろ議論したらしい（下記のpdfご参照）
だが、数学者の投稿は見つからなかった！！（＾＾
そして、過去スレ47にも書いたが、The Mathematics of Coordinated Inference: A Study of Generalized Hat Problems (Developments in Mathematics) 2013 edition by Hardin, Christopher S., Taylor, Alan D. (2013) （>>439）
では、上記の未来予測可能とか、任意の関数の値が予測可能とする論は、全部捨てられている
その話も、ちょろっと、まとめPDFに入れて貰えると面白いと思うよ
で、時枝も同じだよ
https://link.springer.com/chapter/10.1007/978-3-319-58507-9_10
Philosophical Aspects of an Alleged Connection Between the Axiom of Choice and Predicting the Future, Pawel Pawlowski First Online: 06 September 2017
Abstract
In 2008 Christopher Hardin and Alan Taylor published an article titled
“Peculiar connection between the axiom of choice and predicting the future” in which they claim that if some system can be described as a function from a set of some instants of time to some set of states,
then there is a way to predict the next value of the function based on its previous input. Using their so-called μμ -strategy one can randomly choose an instant t and the probability that the strategy is correct at t
(i.e. that the output for a strategy for input t is exactly the same as the value of the function) equals 1.
Mathematical aspects of this article are sound, but the background story about the correlation between theorems and philosophical aspects of predicting the future faces certain problems. The goal of my paper is to bring them up.
つづく
447(2): 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE [sage] 2018/01/13(土) 11:38:56.64 ID:rUYSYDib(8/17) AAS
>>446 つづき
[PDF]A Proof of Induction?
https://quod.lib.umich.edu/cgi/p/pod/dod-idx/proof-of-induction.pdf?c=phimp;idno=3521354.0007.002
philosophers’imprint
A George 著 Department of Philosophy Amherst College- ?2007 - ?被引用数: 10 - ?関連記事
“Hardin-Taylor rule”, I shall call it ? that will, for any arbitrarily chosen function f, correctly predict most values of f on the basis of its past be- havior; that is, for most t the rule will correctly predict f (t) on the basis of f 's values at all s < t.
I shall first sketch the proof's central idea and then turn to assess the result's philosophical significance. We begin by well-ordering R, the set of all functions from R to. R. (Here the Axiom of Choice must be employed, a fact to which we shall return.) That is ...
[PDF]Justifying Induction Mathematically: Strategies and Functions
http://media.philosophy.ox.ac.uk/assets/pdf_file/0003/36651/LogiqueetAnalyseFinal08.pdf
A PASEAU 著 Logique & Analyse 203 (2008), 263?269 - ?被引用数: 2 - ?関連記事
2008/08/27 - page 265 i i i i i i i i. JUSTIFYING INDUCTION MATHEMATICALLY: STRATEGIES AND FUNCTIONS. 265. These objections are answerable to a degree.
The use of the Axiom of. Choice is indeed essential; but these days the ... Hardin-Taylor proof as providing a reliable present-predicting strategy. Once it is appreciated, the Hardin-Taylor proof can no longer plausibly be called a predictive strategy. Because it is so nonconstructive, it fails to yield a strat- egy.
以上
450(1): 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE [sage] 2018/01/13(土) 11:45:53.91 ID:rUYSYDib(10/17) AAS
>>442
はいはい
Sergiu Hart氏のPDFで、”1Source unknown. I heard it from Benjy Weiss, who heard it
from ..., who heard it from ... . For a related problem, see
http://xorshammer.com/2008/08/23/set-theory-and-weather-prediction/ ”
を辿って行くと
一つの根拠が、Chris Hardin and Alan Taylor’s paperに行き着く
だが、これが間違いだったと、彼らが自分達が後の論文で訂正しているよ（参考>>446-447）
それは、過去すれ47に書いた
453: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE [sage] 2018/01/13(土) 12:01:09.92 ID:rUYSYDib(12/17) AAS
>>450 補足
>一つの根拠が、Chris Hardin and Alan Taylor’s paperに行き着く
>だが、これが間違いだったと、彼らが自分達が後の論文で訂正しているよ（参考>>446-447）
>それは、過去すれ47に書いた
これだな
現代数学の系譜 工学物理雑談 古典ガロア理論も読む47
2chｽﾚ:math
(抜粋)
スレ46 2chｽﾚ:math
「Taylor氏らは、[HT08b] の結論を否定している。（[HT09] および（成書）The Mathematics of Coordinated Inference: A Study of Generalized Hat Problems ）」
つまりは、”Corollary 3.4 does tell us that the μ-strategy will be correct at t with probability 1.”（>>148）は、「数学的に無価値」でしたということですよ（＾＾
(引用終り)
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