I'm reading David Papineau's Philosophical Devices, and there's a section on numbers and set theory. But there's not deeper hint on why it's important to philosophy.

I guess that in mathematics we can think of formulas for building the elements of some set, such as the set of even numbers, the set of odd numbers, the set of all the prime numbers (which I guess that until this date, have no formula) so perhaps it's important to make formulas for some objects in philosophy?

I guess I can see the importance of the knowledge of the axiom of comprehension (and the Russell set), which states that for any condition C, there exists a set A such that (for any x)(x is an element of A iff x satisfies C). It is there to remind us that such axiom can't hold without some exceptions. Although I fail to see where one would create an object (in philosophy) and then notice a similarity of this object and Russell's set.

Note: If you know better tags, please edit. I've tried to use the tag set theory, but It does not exist.