“There is no way to fix the self-reference issue.”
Nonsense. There are plenty of ways, which I’ll illustrate in the future. Godel was wrong, and his theorems don’t prove what they attempt to prove.
“ I am not making any comment on the paradox at all. We could discuss that issue at length, and still not reach any conclusion.”
If you don’t think calculus resolves Zeno’s paradox, then you’re in the minority. If you think calculus doesn’t apply to Zeno’s paradox, then you’re in the minority. I can demonstrate, after a short conversation indeed, that calculus does not resolve the paradoxes — and the resolution is a necessarily finite physical reality.
“I’m a finitist, so calculus is wrong.”
I don’t think you read my article clearly. I am not saying “calculus is wrong”. I am saying, “Modern treatments of calculus doom it to be conceptually incoherent, but it can be rescued with some tweaks.” Again, you’re framing the disagreement incorrectly; you are trying to save “how mathematics works” in terms of professional academia. I am trying to save the logical sensibility of mathematics, regardless of how professionals do their calculations.