〈 Berger | Dillon 〉

I think the main thing that mathematical finitists get wrong is that numbers “actually” exist—let alone ought to be a certain way.

As a finitist, I just prefer my theories stay within the realm of things hat can be explicitly exhibited. It's helpful that I can do lots of calculus in the context of this perspective tho, otherwise I wouldn't be wasting my time.

What do you mean by “explicitly exhibited”

Processes that can be completed before the universe ends. Like computing triangle ratios. Why would I settle for an approximate answer that gets better the more work I do when I can get an exact answer in a predicatably finite number of steps?(angles vs spreads in rational trig)

But why are you subjecting mathematics to constraints of what’s physical?

I'm subjecting math to the constraints of what can be completely scrutinized. I am also extremely sceptical of arguments that push their key arguments beyond what is observable as a human. Especially because I think many nice things have been neglected in light of our bias.

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.