Question

I am not quite sure I interpret the following sentence correctly in Bertrand Russell's paper on existential import:

and among classes there is just one which does not exist, namely, the class having no members, which is called the null-class.

This seems to be saying that the empty set does not exist, and although I would agree with that, it seems to me that it very unlikely to be what he meant.

So my question is:

What did Russell mean when he wrote that the null-class, the class he defined as having no members, did not exist?

Answer 1

In Bertrand Russell's paper on existential import, the null-class refers to a class that has no members. Russell contends that the null-class does not exist as an actual entity. This concept is different from the empty set in mathematics.

Step-by-step explanation:

Bertrand Russell's statement about the null-class in his paper on existential import refers to the concept of a class that has no members. Russell argues that this class, which he calls the null-class, does not exist. This means that there is no actual entity that corresponds to the null-class. It is important to note that this concept is distinct from the empty set in mathematics, which does exist. The null-class is a philosophical concept used to illustrate the idea that there can be entities that have no members or instances.