>>12609821>aren't pairs of rational points just objects that you have defined axiomatically?Yes, but the only things that I've taken to be axioms are the natural numbers. If you subscribe to set theory, you assume the (platonic) existence of infinite sets, which is nonsensical and much larger leap of faith than assuming the natural numbers exist.
>"realness"When did I say anything about the realness of things? All I care about is proper mathematical definitions. And just like Euclid didn't define what a point is, you haven't defined what a set is.
My claim is that infinite set theory is nonsensical. Finite sets are perfectly fine, but just negating a perfectly reasonable concept does not imply you get a new well-defined concept.
>I stand in place and use a stick to draw a circle around me, then walk in a straight direction, I believe my path will intersect the circle that was drawn at some point.Exactly, you believe this. In reality, this is an approximate statement, since you will never draw a perfect circle, you can never do something perfectly straight, and reality likely has some discrete resolution.
Mapping this approximate belief to mathematics is not immediately justified. Maybe, since the "length" diagonal of a square can't be computed (since it requires you to complete an infinite process to complete truly), it means that the notion of length is inherently approximate? Not only physically, but also theoretically.
>>12609827>I have never said I try to "collect" an infinite amount of anythinggroup, gather, etc. there are 100 different other words I could have used here. And I don't mean you need to be able to physically realize this gathering, I am saying that even theoretically, it is nonsensical to talk about this. Once again, just because you add a negation in front a reasonable concept (finite), it does not immediately make the negation of the concept reasonable.
cont.
