Devil's advocate for why ontology is meaningless and vacuous.

[robvalue]

Yes, everything depends on experience. It's all we have. The evidence for my claim (which isn't meant to be absolute) is that it has consistently proved to be the case. Any deviation results in total failure.

Is there an escape from solipsism that can be had by means other than intuition?  Can experience tell us anything about the world as it exists outside of our consciousness?  It seems that anything we might know or speculate about such realities is derivative of our intellectual properties and can go as far as those, rather than our senses, are able to take us.

Not to mention, a body of scientific knowledge such as mathematics is wholly dependent on axioms that can be known apart from experience, that is, they don't much seem to require any verification outside of their own definitions, and the functions or qualities that these involve, to be understood as true or false.

I would say no, there is no escape from solipsism. All we can do is make pragmatic assumptions. But we needn't even make all of them, really. For example, I don't have to assume anything is "real". It's real to me, and that's as good as it's ever going to get.

Yes, mathematics is an abstract system which is defined by strict rules. Such systems only need to be internally consistent. They may or may not relate to reality in any useful way. Mathematics is not scientific knowledge, though. It's a tool. It's used to describe scientific knowledge.