雙語暢銷書《艾倫圖靈傳》第4章:彼岸新星(68)
Alan might have been thinking of the 'oracle' in Back to Methuselah, through whose mouth Bernard Shaw answered the unsolvable problems of the politicians with 'Go home, poor fool'!
Less clear from his remarks in the paper was to what extent he regarded such 'intuition', the ability to recognise a true but unprovable statement, as corresponding to anything in the human mind. He wrote that
在艾倫的論文中，有一點沒有說清楚，那就是這種直覺可以達到什麼程度，是隻能判定一個不可證明的命題，還是能夠解決人類的所有問題。他是這樣寫的：Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two faculties, which we may call intuition and ingenuity.
數學可以看成是這兩種過程的組合，我們可以稱之爲直覺和推導
(We are leaving out of account that most important faculty which distinguishes topics of interest from others; in fact, we are regarding the function of the mathematician as simply to determine the truth or falsity of propositions.)
（在此我們假設數學家的作用只是判定一個命題的真僞）。The activity of the intuition consists in making spontaneous judgments which are not the result of conscious trains of reasoning…
直覺活動包括做出一些無意識的、自然形成的判斷……and he claimed that his ideas on 'ordinal logics' represented one way of formalising this distinction.
艾倫還說，序數邏輯就是對這種組合的形式化。But it was not established that 'intuition' had anything to do with the incompleteness of finitely defined formal systems.
但是，即使引入了直覺，這仍然對有限定義的形式系統的不完備性起不到什麼作用。After all, no one knew of this incompleteness until 1931, while intuition was a good deal older.
人們在1931年才知道不完備性，但直覺卻早就已經有了。
