What Formalization Does Well

Formalization performs at least four indispensable tasks. It turns ambiguous prose into inspectable relations, separates commitments that merely look equivalent, verifies derivations under fixed rules, and follows dependency lists when a premise is replaced. These operations expose conflicts hidden by intuitive language.

The First Critique is therefore not hostile to formal work. It develops a formal language for the four modes of accounting and constructs five configurations in which P2–P6 can fail separately. The objection that the six postulates are merely six phrasings of one idea acquires a testable form.

Yet formal precision holds only inside a jurisdiction. The choice of object domain, the mapping from prose to symbol, the selection of a logic, and the decision to classify a sentence as a postulate all occur before derivation begins.

Judgment as Relation Rather Than Function

When judgment is modeled as a function, every input seems to require one output. The First Critique's ledger includes both double-hit and no-verdict: an object may meet both sides, or the present criterion may have no licensed output.

Judgment is therefore encoded more naturally as a relation. Excluded middle can be registered as a domain-wide condition requiring at least one mark. Non-contradiction can be registered as a condition preventing two marks at the same address. Neither needs to impersonate the unchosen background of every possible judgment.

Nonclassical branches need not be declared logical failures in advance. They assume different conditions. Formalization can show exactly which theorems lose standing when branches change. It cannot prove from within itself that one branch must govern every field.

What the Five Configurations Establish

The First Critique gives P2–P6 individual configurations. Each preserves the other formal conditions while making one postulate fail. If the construction works, that postulate is not derivable from the remaining ones inside the present package. P1, as the entrance translating cognition into this operational package, can be declined but cannot be separated in the same internal fashion.

The conclusion is limited and therefore dependable. It establishes independence among formal renderings. It does not prove the prose postulates true or prove that the notation preserves their full meaning. The encoding of P6, for example, retains a kind of self-class accessibility while omitting much of what “performer” means in the prose.

A fidelity registry must therefore stand beside formal proof. It records the original sentence, what the notation keeps, what it loses, which conditions it adds, and which alternative translations remain contestable. Without that ledger, machine-checkable precision can conceal philosophical decisions made during translation.

The Worker Theorem

The boundary receives its clearest expression in the worker theorem: someone who executes derivations only within fixed premises and explicit rules has not thereby completed judgment. In its compressed form, the worker can push a branch but cannot chisel the substrate.

This is no insult to execution. A proof assistant, computer, or highly trained researcher may extend a branch far beyond ordinary human capacity. That extension is real work. Successful rule-following simply does not automatically confer authority to select the rules. Why this field was drawn, why these premises were assumed, which translation is faithful, and whether failure calls for a branch change remain matters of judgment.

“Recognize the worker by the work, not by the origin” is the other half of the theorem. Whether judgment has occurred should not be predetermined by biology, machinery, professional title, or institutional identity. We ask whether the relevant work on the substrate was actually done. Origin neither grants judgment nor cancels it in advance.

Register Borrowed Instruments

Philosophy routinely borrows classical logic, probability, statistics, geometry, and computational models. Borrowing is not a defect. The defect appears when the label is removed and readers are led to believe that the result grew directly from philosophy's zero point.

The First Critique requires borrowed instruments to be registered. Name the branch, attach a propagation clause, and state which conclusions require review if the instrument changes. Formalization then becomes a tool of dependency transparency rather than an ornament of authority.

Formal language can sharpen an instrument and record where it fell. It cannot decide for philosophy why the cut belongs there. Mature formalization does not announce that everything has been mechanically settled. It reports exactly which work it completed and returns the remaining acts of judgment, without disguise, to those who use it.