双语畅销书《艾伦图灵传》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?
但这只是个没用的文字游戏，有什么可较劲的呢？TURING: What puzzles one is that one usually uses a contradiction as a criterion for having done something wrong.
图灵：因为人们通常认为矛盾意味着错误，遇到矛盾就说明我们把什么东西搞错了，
But in this case one cannot find anything done wrong.
但在这个问题中，我们却看不出有什么错误。WITTGENSTEIN: Yes – and more: nothing has been done wrong. … where will the harm come?
维特根斯坦：是的，本来就没有错误……那它有什么不好？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.
图灵：这样看起来没什么不好，但如果把一个矛盾的原理用于实践，那就会出问题。WITTGENSTEIN: … The question is: Why are people afraid of contradictions?
维特根斯坦：……问题是，为什么人们要害怕矛盾？It is easy to understand why they should be afraid of contradictions in orders, descriptions, etc., outside mathematics.
人们害怕数学之外的矛盾，比如顺序的矛盾，描述的矛盾，这是很容易理解的。The question is: Why should they be afraid of contradictions inside mathematics?
但问题是，为什么人们要害怕数学内部的矛盾？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. …
如果实践当中出了问题，错误并不在于原理中有矛盾，而是在于你使用了不该使用的原理……TURING: You cannot be confident about applying your calculus until you know that there is no hidden contradiction in it.
图灵：如果你不能确定微积分是没有矛盾的，那么你就没有信心在实践中使用它。
