[8note]

Your soul example is not axiomatic.

The actual axiom is that real things are observable/that empiricism is true. That's not even a required secular thing; secular folks can believe in souls as well, or be rationalists, where what's real does not depend on what you can observe.

But for some subset of us, the soul is not measurable, nor can youcreate a test to determine whether something has a soul or not, so souls do not exist, by comparison to something like the electrical charge.