雙語暢銷書《艾倫圖靈傳》第3章:思考什麼是思考(62)

One attack on this question had already been made in the work of G. Frege, starting with his 1884 Grundlage der Arithmetik.

G.弗雷格在他1884年的《算術基礎》中，就考慮了這個問題。

This was the logistic view of mathematics, in which arithmetic was derived from the logical relationships of the entities in the world, and its consistency guaranteed by a basis in reality.

他提出一種邏輯的觀點，認為算術來自於實體的邏輯關係，它的相容性需要由現實世界中的基礎來保證。

For Frege, the number ‘1’ clearly meant something, namely the property held in common by ‘one table’, ‘one chair’, ‘one beer-mug’.

對弗雷格來說，數字"1"有明確的意義，也就是一張桌子或一個酒杯所共同擁有的意義。

The statement ‘2 + 2 = 4’ had to correspond to the fact that if any two things were put together with any other two things, there would be four things.

如果說"2+2=4"，就必須保證任何兩個東西和其它兩個東西放在一起，一定會有四個東西。

Frege’s task was to abstract the ideas of ‘any’, ‘thing’, ‘other’, and so forth, and to construct a theory that would derive arithmetic from the simplest possible ideas about existence.

弗雷格的工作就是把"任何""東西""其它"這些概念抽象化，通過最基本的客觀存在來構建算術。

Frege’s work was, however, overtaken by Bertrand Russell, whose theory was on the same lines.

然後伯特蘭•羅素超越了弗雷格的觀點，

Russell had made Frege’s ideas more concrete by introducing the idea of the ‘set’.

他通過引入"集合"的概念，把弗雷格的觀點更加具體化。

His proposal was that a set which contained just one thing could be characterised by the feature that if an object were picked out of that set, it would always be the same object.

他的主張是，如果從一個集合中取出的物體總是相等的，那麼就說，這個集合只含有一個元素。