This is going to sound very dim, but here goes: why is that obvious? Please be patient; I thought I understood the principle of induction, but I must be missing something key about it if it inherently cannot be justified by evidence that it works.

By the way, did you mean 'by reference to experience'? Because if not, not only do I not understand why that's obvious, but I also don't understand why it's relevant to what I wrote.

I may cite my experiences as evidence to back up my axioms, but whether or not you accept them as evidence will probably depend on whether or not you've had similar experiences, or are at least prepared to accept my different ones as valid. So, to me, experience and evidence are two different concepts which interact in a non-straightforward way.

That said, I would cite my experience that the principle of induction provides results that are consistent as evidence that it's correct. But, to my way of thinking, that means that it's justified by both experience and by evidence. I'm therefore assuming you mean something altogether different.