雙語暢銷書《艾倫圖靈傳》第4章:彼岸新星(91)
Well, so what? You can go on like that until you are black in the face.
Why not? It doesn't matter. … it is just a useless language-game, and why should anybody be excited?
但這只是個沒用的文字遊戲，有什麼可較勁的呢？TURING: What puzzles one is that one usually uses a contradiction as a criterion for having done something wrong.
圖靈：因爲人們通常認爲矛盾意味着錯誤，遇到矛盾就說明我們把什麼東西搞錯了，
But in this case one cannot find anything done wrong.
但在這個問題中，我們卻看不出有什麼錯誤。WITTGENSTEIN: Yes – and more: nothing has been done wrong. … where will the harm come?
維特根斯坦：是的，本來就沒有錯誤……那它有什麼不好？TURING: The real harm will not come in unless there is an application, in which a bridge may fall down or something of that sort.
圖靈：這樣看起來沒什麼不好，但如果把一個矛盾的原理用於實踐，那就會出問題。WITTGENSTEIN: … The question is: Why are people afraid of contradictions?
維特根斯坦：……問題是，爲什麼人們要害怕矛盾？It is easy to understand why they should be afraid of contradictions in orders, descriptions, etc., outside mathematics.
人們害怕數學之外的矛盾，比如順序的矛盾，描述的矛盾，這是很容易理解的。The question is: Why should they be afraid of contradictions inside mathematics?
但問題是，爲什麼人們要害怕數學內部的矛盾？Turing says, 'Because something may go wrong with the application.' But nothing need go wrong. And if something does go wrong – if the bridge breaks down – then your mistake was of the kind of using a wrong natural law. …
如果實踐當中出了問題，錯誤並不在於原理中有矛盾，而是在於你使用了不該使用的原理……TURING: You cannot be confident about applying your calculus until you know that there is no hidden contradiction in it.
圖靈：如果你不能確定微積分是沒有矛盾的，那麼你就沒有信心在實踐中使用它。
