[gowld]

Maybe not "vague", but "underspecified".

ZFC models the set of real numbers, but only provides a model for a measure-zero amount of specific individual real numbers. It just says "yeah they exist".

People like Wildberger believe that anything that exists in math should have some way of determining its exact value, otherwise, what is "it"?

[syzarian]

That I understand. I objected to the idea that the theory was vague rather than that the theory contains objects that are vague. Even so, if one thinks the theory contains vague objects then we run into considerations such as the following:

https://mathoverflow.net/questions/44102/is-the-analysis-as-...

I suppose being a finitist allows one the get around what Hankins wrote.