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Well, so what? You can go on like that until you are black in the face.
好吧，那又能怎么样呢？你如果要把自己绕进去，那就会把脸给憋紫……
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。
