Comment by feoren

Computations are finite, but that limit keeps going up. If we picked a number that seemed like "way more than enough" in 1960, it might be less than our phones can do now. If we picked a number from cosmology, what happens if that science changes? "Heat death" is the current consensus of our distant future, but even that is challenged. Until we know what dark energy is, we can't be sure about "heat death". So if cosmology has some breakthrough that changes our understanding, why make it so we have to go revisit all our CS proofs? Using infinity decouples the proofs from irrelevant externalities.

> the indispensability of modern math is still hotly talked about in philosophy

Meh, philosophers have to talk about something. I'll worry about what philosophers say when I see a single useful insight from the entire field. We've been waiting thousands of years, but I'm sure a useful thought is right around the corner.

And the concept of infinity is hardly modern.