雙語暢銷書《艾倫圖靈傳》第4章:彼岸新星(90)
When Hardy said that 317 was a prime because it was so, what did this mean?
Did it only mean that people would always agree if they did their sums right?
這否意味着人們總是接受那些他們能算對的東西？How did they know what were the 'right' rules?
他們怎麼知道什麼規則是"正確的"？
Wittgenstein's technique was to ask questions which brought words like proof, infinite, number, rule, into sentences about real life, and to show that they might make nonsense.
維特根斯坦的問題，把證明、無限、數學、規則這樣的詞語引入日常生活中，然後表明它們很可能是講不通的。As the only working mathematician in the class, Alan tended to be treated as responsible for everything that mathematicians ever said or did, and he rather nobly did his best to defend the abstract constructions of pure mathematics against Wittgenstein's attack.
作爲一個專業數學家，艾倫傾向於支持數學家們的工作，他盡力地維護純數學的抽象性，抵抗維特根斯坦的這種引入。In particular, there was an extended argument between them about the whole structure of mathematical logic.
特別是，他們倆進行了一場關於整個數理邏輯體系的爭論。Wittgenstein wanted to argue that the business of creating a watertight, automatic logical system had nothing to do with what was ordinarily meant by truth.
維特根斯坦認爲，創造一個嚴密的、確定的邏輯系統，對於追求真理而言，是沒有用的。He fastened upon the feature of any completely logical system, that a single contradiction, and a self-contradiction in particular, would allow the proof of any proposition:
他緊緊抓住這一點：完備邏輯系統的矛盾特性，會使得任何命題都能被證明。WITTGENSTEIN: … Think of the case of the Liar.
維特根斯坦：……我們來看說謊者悖論，It is very queer in a way that this should have puzzled anyone – much more extraordinary than you might think. …
所有的人都在困惑這個問題，這根本就不正常，太不正常了……Because the thing works like this: if a man says 'I am lying' we say that it follows that he is not lying, from which it follows that he is lying and so on.
一個人說"我在說謊"，我們如果假設他說的是實話，於是他就是在說謊。
