Infinite sets are well defined
And even if they're not, it's an intuitively clear concept
And even if it's not, we have the axiomatic framework of ZFC that tells us what we need to know about sets,
And even if it doesn't, it's only in niche pure set theoretic problems where ambiguity arises,
And even if it arises in other areas like algebra, in a few hundred years the logicians will come up with the correct missing axioms to settle the problems,
And even if they don't, mathematics is just a meaningless formula manipulation game,
And even if some finite mathematical concepts seem meaningful, they're just as undefined and vague as infinite sets,
And even if they're not and can be clearly defined, it's not possible to base mathematics on these simple concepts,
And even if it is, the mathematics based on them is too limited and simple to be interesting,
And even if it's not, you would have to give up on centuries worth of beautiful mathematics,
And even if you can reinterpret them in a new finite light, it's just not worth all the trouble
Amen