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《算术基础》中，就考虑了这个问题。

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.

他提出一种逻辑的观点，认为算术来自于实体的逻辑关系，它的相容性需要由现实世界中的基础来保证。

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

对弗雷格来说，数字"1"有明确的意义，也就是一张桌子或一个酒杯所共同拥有的意义。

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.

如果说"2+2=4"，就必须保证任何两个东西和其它两个东西放在一起，一定会有四个东西。

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""东西""其它"这些概念抽象化，通过最基本的客观存在来构建算术。

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

然后伯特兰•罗素超越了弗雷格的观点，

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

他通过引入"集合"的概念，把弗雷格的观点更加具体化。

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.

他的主张是，如果从一个集合中取出的物体总是相等的，那么就说，这个集合只含有一个元素。