[NoahZuniga]

While axioms are in some sense arbitrary, it is helpful if they are consistent (informally: you can't prove something that "is false"; formally: you can't prove p and not p). Also other people like it if your axioms feel obvious.

[scoofy]

My point is that axioms "feeling obvious" is exactly a signal that they will be useful. The point of deductive reasoning based on axioms is that it is a shortcut to fill in problems of induction, which is what happens when we use pure empiricism.

If you really want to go down the road of solipsism, read Karl Popper.