〈 Berger | Dillon 〉

but again it seems like there’s a fundamental assumption that mathematics or pure reason has to necessarily pertain to that which is physically instantiated

It is an assumption, you're right. But I want my mathematics to be epistomologically stronger then the formalist position suggests, and I'm willing to do the work to substantiate that.

Your position is more subtle than most finitists.. do you not think then that mathematics and observation could ever be disentangled?

Honestly my position as a finitist is a derivative of my position as a materialist. I'm skeptical that anything can be disentangled from observation, experience, and action. I will say that robust trig over finite fields is super interesting and doesn't require any analysis.

Interesting point.. and one that is indeed difficult to parlay with via Twitter

I’m curious what your answer is as a finitist to Zeno’s Paradox?

At a certain level we can't subdivide the universe further. Im comfortable with the universe happening in discrete steps. I'm not a physicist by any stretch of the imagination but that seems a natural conclusion to me.

But shouldn’t finitism, if it’s truly the case, what that smallest subdivision is? But this is s testable hypotheses, and to me seems to miss the point that mathematics truly is a human construct, and not subject to experiment