[xelxebar]

Ultra-finitist logic is a perfectly rigorous field of study in its own right. I think OP is making a point that this logic and us related branches are quite understudied.

It's encouraging to note that with things like Homotopty Type Theory, we're finally starting to come to grips with Fundamentals that aren't tied to the ZFC implementation.

[eastWestMath]

But ultrafinitism isn't actually interesting as a mathematical theory. As the previous poster said, its appeal lies in its "realness". Intuitionistic and linear logic are substantially more interesting.

[coolsdude2282]

But this was why I posed it as a question, everyone says this is somehow 'more interesting' but is that because it is actually qualitatively more interesting or are more interesting things coming out of it simply due to the fact that it is more popular quantitatively with researchers? If it is qualitatively more interesting, what about it makes it so?

I likened it to functional programming because finitism makes things interesting via its purity and restriction in an analogous way.

[eastWestMath]

But it's not similarly interesting, linear and intuitionistic logic are. Finitism is just kind of stupid.