It may well be that the search for "truth" has brought us here. However, we found out that "truth" is always a relative. It has to be rooted in assumptions/axioms.
So I would say, it runs on, good choices of axioms and the ability to perform logical deductions.
Set Theory is an attempt to come up with axioms that are so simple that no-one who is not completely out of it's mind would doubt their "truth". This is stuff like:
- There exists a set
- Two sets are equal if all their elements are equal
- We can form subsets from sets, by picking out elements
The only exception is the axiom of choice, which is less intuitively evident, but a technical necessity to build and reason about infinite sets like the real numbers.
So I would say, it runs on, good choices of axioms and the ability to perform logical deductions.
Set Theory is an attempt to come up with axioms that are so simple that no-one who is not completely out of it's mind would doubt their "truth". This is stuff like:
- There exists a set
- Two sets are equal if all their elements are equal
- We can form subsets from sets, by picking out elements
The only exception is the axiom of choice, which is less intuitively evident, but a technical necessity to build and reason about infinite sets like the real numbers.