Not sure we’re talking about the same thing here. I was replying to your claim that nothing in philosophy (apart from mathematics) can be formalized. The role of logic is not to solve the metaphysical problem of infinite regress.
Logic itself is a formalism.
Subject to all the constraints of formal language theory/linguistics.
It fails to address the symbol-grounding problem.
Logic, mathematics, computer science, proof theory... same thing. https://en.wikipedia.org/wiki/Proof_theory
We are eternally stuck interpreting all of our theories in the context of their meta-theoretic assumptions.