Why can't we prove an axiom but only assume that it is true?

Question

I'm not talking about definition. If we do hold the law of causality to be univerasal, then it should follow that an axiom is the result of some cause. Yet we cannot prove that the cause exists. We can't even discover the cause, and we can only assume that it is "self-evident"

Answer 1

An axiom is only self evident as a certain point in the context of a defined logic. As you describe the law of causality, you assume that always cause is followed by effect. But even in physics this is not true. And there again you are with definition: the axiom is not an absolute value, but a value of orientation in the context of a defined logic. When you change the logic, the axioms change, too.
Its a good question which goes to the basics of thinking and research.
(you might be interested what goes on today in theoretical physics and mathematics)

Answer 2

The law of causality only dictates every CAUSE has an EFFECT.

then it should follow that an axiom is the result of some cause

No, an axiom is the result of a verifable, repeatable effect.

Yet we cannot prove that the cause exists

The effect did that for us. Otherwise we would have no cause for the effect and it would violate the law of causality.

We can't even discover the cause, and we can only assume that it is "self-evident"

Well, that is the point. The law as stated, doesn't have to pove that a cause has a cause or an effect causes a cause. Just simply that a cause, has an effect.

Answer 3

Tough question and indeed I do not have a straight answer.

However, I believe that we can prove nothing unless we can begin somewhere with an axiom that is proved only by the experience of repetitive consistency. Philosophers who try to question even axioms end up in questions rather than any answers.

Answer 4

Axioms are continuously genuine (by using definition they're so). each and every theorem is derived in keeping with those axioms. for this reason each and every theorem is an occasion.!! in case you modify axioms you will get distinctive theorems. as an occasion analyze theorems in Euclidean Geometry and Riemann's Geometry.