A flip thought is "wouldn't you rather throw out infinity than logic?"

In other words, is infinity a coherent or incoherent concept? When you plug (incoherent) infinity into (otherwise coherent) logic, does infinity render logic incoherent?

Perhaps saying infinity is incoherent is to say infinity is beyond human cognitive grasp? That for all intents and purposes, when we are pointing to infinity, we are pointing to nothing?

Kinda like we point at "zero" as if it were a number, but it's not? Instead it's the absence of number? Which is why you can't divide by zero?

To be honest, fwiw, paraconsistency feels to me more like a workaround than a solution.

It seems like there's indeterminacy in there somewhere. I think we briefly touched on this in comments in connection with Wittgenstein's RFM.