第10章 「ヴィトゲンシュタインの衝撃」 n.7 - 構造の重要性
(また)「論理的形式を表現しうるためには、我々は、命題とともに(with the propositon 命題を携えて)論理(学)の外に、即ち、世界の外に出ることができなければならないだろう」(『論考』4.12)。これは(この主張は)、私がウィトゲンシュタインと最も意見が一致した時期において納得できなかった唯一の論点(問題)を引き起こしている(raises the only point)。彼の『論考』のために書いた序文の中で私は、いかなる所与の言語においても、その言語が表現しえない事物があり、そういう事物について語りうるところのより高次の言語を構成することは常に可能である、という考えを提示した。もちろんその新たな言語の中にも、それの語りえない事物がやはり存在するであろうが、それは次の(さらに高階の)言語において語ることが可能であり、そのようにして無限に(point )進む。この考えは、当時は新しいものであったが、いまでは論理学において当然のこととして一般に認められるようになっている。この考えはウィトゲンシュタインの神秘主義を片づけてしまうものであり、またゲーデルの提出したもっと新しい難問をも片付けるものだと、私は考えている。 |
Chapter 10 The Impact of Wittgenstein, n.7In emphasizing the importance of structure, I still think he was right, but as to the doctrine that a true proposition must reproduce the structure of the facts concerned, I now feel very doubtful, although at the time I accepted it. In any case, I do not think that, even if it be in some sense true, it has any great importance. For Wittgenstein, however, it was fundamental. He made it the basis of a curious kind of logical mysticism. He maintained that the form which a true proposition shares with the corresponding fact can only be shown, not said, since it is not another word in the language but an arrangement of words or corresponding things: ‘Propositions can represent the whole reality, but they cannot represent what they must have in common with reality in order to be able to represent it -- the logical form.‘To be able to represent the logical form, we should have to be able to put ourselves with the propositions outside logic, that is outside the world.' (Tractatus, 4.12 .) This raises the only point on which, at the time when I most nearly agreed with Wittgenstein, I still remained unconvinced. In my introduction to the Tractatus, I suggested that, although in any given language there are things which that language cannot express, it is yet always possible to construct a language of higher order in which these things can be said. There will, in the new language, still be things which it cannot say, but which can be said in the next language, and so on ad infinitum. This suggestion, which was then new, has now become an accepted commonplace of logic. It disposes of Wittgenstein's mysticism and, I think, also of the newer puzzles presented by Gödel. |