バートランド・ラッセル『私の哲学の発展』第7章 「数学原理ーその哲学的側面」 n.4-2


 この状況(論理的パラドクスの発見による動揺)に対して、哲学者達や数学者達は、多種多様な方法で反応を示した。数学的論理学(mathematical logic 記号論理学)が嫌いで、それは何も生み出さない(不毛だ)と非難していたポアンカレ(Jules-Henri Poincare、1854-1912:フランスの数学者、科学哲学者)は、狂喜して叫んだ。「それはもはや何も生まないものではない。それは矛盾を生む(のだ)」と。それはそれで結構であったが、しかし、そう言ったところで問題の解決にはまったくならなかった。ゲオルグ・カントール(Georg Ferdinand Ludwig Philipp Cantor, 1845-1918:ドイツの数学者で素朴集合論の確立者)の仕事をみとめなかった他の数学者のなかには(『不思議の国のアリス』に出てくる)三月兎の解決法を採用したものもいた。(即ち、こう言った。)「その話題にはもう飽きた。話を変えよう(じゃないか)」。この解決法もまた私には不十分だと思われた(注:皮肉)。けれども、しばらして、数学的論理学を理解し、かつ、論理学の言葉で(in terms of logic 論理学の観点から)問題を解決することが是非とも必要であると認識した人々によって、まじめな解決の試みがなされることになった。これらの試みの最初のものは、たF・P・ラムゼイ(Frank Plumpton Ramsey, 1903-1930:ケンブリッジ大学出身の数学者)の試みであったが、彼は不幸にも早死にして仕事を未完成のままに残した。しかし『プリンキピア・マテマティカ(数学原理)』の出版に先だつ数年間、私はそうした人々の後の(=『プリンキピア・マテマティカ』出版後の)解決の試みを知る便宜をもたず、事実上、文字通り、困惑の中にただひとり捨ておかれたのである。(注:そういった解決法はもちろん『プリンキピア・マテマティカ』出版後に出てきたもの。みすず書房版の野田氏の訳し方だと早とちりの人は誤解しそう。)

Chapter 7: Principia Mathematica: Philosophical Aspects, n.4 At first I thought there must be some trivial error in my reasoning. I inspected each step under a logical microscope, but I could not discover anything wrong. I wrote to Frege about it, who replied that arithmetic was tottering and that he saw that his Law V was false. Frege was so disturbed by this contradiction that he gave up the attempt to deduce arithmetic from logic, to which, until then, his life had been mainly devoted. Like the Pythagoreans when confronted with incommensurables, he took refuge in geometry and apparently considered that his life’s work up to that moment had been misguided. For my part, I felt that the trouble lay in logic rather than in mathematics and that it was logic which would have to be reformed. I was confirmed in this view by discovering a recipe by means of which a strictly infinite number of contradictions could be manufactured. Philosophers and mathematicians reacted in various different ways to this situation. Poincare, who disliked mathematical logic and had accused it of being sterile, exclaimed with glee, ‘it is no longer sterile, it begets contradiction’. This was all very well, but it did nothing towards the solution of the problem. Some other mathematicians, who disapproved of Georg Cantor, adopted the March Hare’s solution: ‘I’m tired of this. Let’s change the subject.’ This, also, appeared to me inadequate. After a time, however, there came to be serious attempts at solution by men who understood mathematical logic and realized the imperative necessity of a solution in terms of logic. The first of these was F. P. Ramsey, whose early death unfortunately left his work incomplete. But during the years before the publication of Principia Mathematica, I did not have the advantage of these later attempts at solution, and was left virtually alone with my bewilderment.
 Source: My Philosophical Development, chap. 7:1959.  
 More info.:https://russell-j.com/beginner/BR_MPD_07-040.HTM

コメントを残す

メールアドレスが公開されることはありません。