> The last three illustrate a more practical perspective. Suppose a universal decree, that math is no longer allowed to be done in ZFC, you could only use ZF, was imposed on mathematicians. This doesn't really change anything - all that mathematicians will do is, if they were perfectly fine with choice before, simply replace instances of "vector space" with "vector space with a basis", or "commutative ring" with "commutative ring with a maximal ideal", because the types of mathematical objects they care about are the ones with these desirable properties
Lol, I would love that. That's the book I want to read. I am weird, maybe, but I find the full-generality of mathematics to be exhausting when I just want to understand how numbers and geometry work. I will never care about the details of infinite sets.
I am reminded by a quote from Jaynes' probability text: that in their opinion, infinite objects are only meaningful when explicitly provided via a limiting process from finite objects. It is not, as far as I can tell, a widespread stance, but it's the one I subscribe to.
(Thanks for the lengthy reply, though. Just, it reminds me of the stuff I already find exhausting.)
Lol, I would love that. That's the book I want to read. I am weird, maybe, but I find the full-generality of mathematics to be exhausting when I just want to understand how numbers and geometry work. I will never care about the details of infinite sets.
I am reminded by a quote from Jaynes' probability text: that in their opinion, infinite objects are only meaningful when explicitly provided via a limiting process from finite objects. It is not, as far as I can tell, a widespread stance, but it's the one I subscribe to.
(Thanks for the lengthy reply, though. Just, it reminds me of the stuff I already find exhausting.)