[過去ﾛｸﾞ] 現代数学の系譜11 ガロア理論を読む32 [無断転載禁止]©2ch.net (700ﾚｽ)

現代数学の系譜11 ガロア理論を読む32 [無断転載禁止]©2ch.net http://rio2016.5ch.net/test/read.cgi/math/1495369406/

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108: 現代数学の系譜11 ガロア理論を読む [sage] 2017/05/22(月) 15:18:33.36 ID:0yI+BCI1 >>103 追加引用 https://en.wikipedia.org/wiki/Finitism Finitism (抜粋) History Today most classical mathematicians are considered Platonist and readily use infinite mathematical objects and a set-theoretical universe.[citation needed] Views regarding infinite mathematical objects Aristotle especially promoted the potential infinity as a middle option between strict finitism and actual infinity (the latter being an actualization of something never-ending in nature, in contrast with the Cantorist actual infinity consisting of the transfinite cardinal and ordinal numbers, which have nothing to do with the things in nature): But on the other hand to suppose that the infinite does not exist in any way leads obviously to many impossible consequences: there will be a beginning and end of time, a magnitude will not be divisible into magnitudes, number will not be infinite. If, then, in view of the above considerations, neither alternative seems possible, an arbiter must be called in. ??Aristotle, Physics, Book 3, Chapter 6 http://rio2016.5ch.net/test/read.cgi/math/1495369406/108

109: 現代数学の系譜11 ガロア理論を読む [sage] 2017/05/22(月) 15:23:13.43 ID:0yI+BCI1 >>107 学術さん、乙です。どうも。スレ主です。 >無限集合が存在しなくなっちゃったらとリスクヘッジするのもおすすめ。 ちょうど引用した>>108のAristotle, Physics, Book 3, Chapter 6 But on the other hand to suppose that the infinite does not exist in any way leads obviously to many impossible consequences: there will be a beginning and end of time, a magnitude will not be divisible into magnitudes, number will not be infinite. If, then, in view of the above considerations, neither alternative seems possible, an arbiter must be called in. それから Aristotle especially promoted the potential infinity as a middle option between strict finitism and actual infinity (the latter being an actualization of something never-ending in nature, in contrast with the Cantorist actual infinity consisting of the transfinite cardinal and ordinal numbers, which have nothing to do with the things in nature): が、ぴったりかな 所詮、古代ギリシャのAristotle, の哲学の中か・・（＾＾ http://rio2016.5ch.net/test/read.cgi/math/1495369406/109

111: 現代数学の系譜11 ガロア理論を読む [sage] 2017/05/22(月) 16:02:01.85 ID:0yI+BCI1 もちろん、私は、古代ギリシャのAristotleみたく、無限を認める立場です >>108のAristotle ”But on the other hand to suppose that the infinite does not exist in any way leads obviously to many impossible consequences: there will be a beginning and end of time, a magnitude will not be divisible into magnitudes, number will not be infinite. If, then, in view of the above considerations, neither alternative seems possible, an arbiter must be called in.” などを読むと、「ああ、古代ギリシャ哲学はこんなに深い議論をしていたんだ・・」と思います もっとも、21世紀の現代数学は、これを遙かに凌駕していますけどね・・（＾＾ まあ、過去スレで渕野先生を引用したけど、”猫に小判”（レベル違い？）だったかな。(文系)High level people たち、全然理解できてなかったことが よく分かりましたけどね・・（＾＾ http://rio2016.5ch.net/test/read.cgi/math/1495369406/111

113: 現代数学の系譜11 ガロア理論を読む [sage] 2017/05/22(月) 16:16:55.71 ID:0yI+BCI1 >>111 補足 (理系) Low level person（スレ主）は、英語に弱いので、google訳を利用すると ”But on the other hand to suppose that the infinite does not exist in any way leads obviously to many impossible consequences: there will be a beginning and end of time, a magnitude will not be divisible into magnitudes, number will not be infinite. If, then, in view of the above considerations, neither alternative seems possible, an arbiter must be called in.” 　↓訳 "しかし一方で、無限が決して存在しないと仮定すると、明らかに多くの不可能な結果につながる： 時間には、始まりと終わりがあり、 （連続な）強さ（マグニチュード）は、分割できなくなり（最小単位が必ず存在することになり） 数は、無限ではなくなる。 上記の考察より、 どちらの選択肢も可能ではないとすれば（”on the other hand”と対になる側（引用されていない）とどちらも可能でないなら）、 調停者.（arbiter）を導入しなければならない。" 調停者.（arbiter）が、>>108 "Aristotle especially promoted the potential infinity as a middle option between strict finitism and actual infinity (the latter being an actualization of something never-ending in nature, in contrast with the Cantorist actual infinity consisting of the transfinite cardinal and ordinal numbers, which have nothing to do with the things in nature)"だと http://rio2016.5ch.net/test/read.cgi/math/1495369406/113

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