ALL systems of epistemological inquiry start with axioms (or assumptions or presuppositions, if you prefer), even yours, whether you recognize it or not.
Properly, the question is not whether these axioms are provable - by definition, they cannot, they are self-evident, at least to the person holding them as axiomatic - but whether it is justifiable to treat them as such. Our observations are consistent with a reality that conforms to the principle of uniformity, and so from the scientific viewpoint, that axiom is justified. If our observations were not consistent with the principle of uniformity, then clearly, treating it as axiomatic would be unjustifiable and we'd have a problem. They aren't, so we don't.
You're free to disagree, of course, and I expect you will.
I'll also note that even if we couldn't justify our own axioms (even if not to your satisfaction), it in no way relieves you of the intellectual obligation to justify your own. Put another way, even if we're completely and utterly wrong, that says nothing about the truth value of your proposition.
Properly, the question is not whether these axioms are provable - by definition, they cannot, they are self-evident, at least to the person holding them as axiomatic - but whether it is justifiable to treat them as such. Our observations are consistent with a reality that conforms to the principle of uniformity, and so from the scientific viewpoint, that axiom is justified. If our observations were not consistent with the principle of uniformity, then clearly, treating it as axiomatic would be unjustifiable and we'd have a problem. They aren't, so we don't.
You're free to disagree, of course, and I expect you will.
I'll also note that even if we couldn't justify our own axioms (even if not to your satisfaction), it in no way relieves you of the intellectual obligation to justify your own. Put another way, even if we're completely and utterly wrong, that says nothing about the truth value of your proposition.
