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Reasons Answerability and the Score
This page asks a static question: before a learner can improve, what makes a reason, challenge, or response publicly assessable?
The finite model separates three relations. A committive inference says what follows from an undertaking. A permissive inference says how entitlement may transmit. An incompatibility says when commitment to one content defeats entitlement to another. Applicability is itself contestable content: asserting that a rule applies does not install the rule.
This separation is influenced by Brandom's distinction between commitment and entitlement and his perspectival scorekeeping. The finite implementation and its consequences are this program's. Structured argumentation and epistemic-graph work provide nearby formal comparisons, not this project's statics; see Sources.
A candidate substrate-level representation for these relations now exists: identity-bearing reason occurrences whose staged applicability is contestable content, with rebuttal derived from a contradiction floor plus learnable incompatibility claims, and with the substrate confined to reporting enabled reasons and dependencies rather than resolving conflicts. See Normative Record and Inquiry and the reason-representation round.
Let participant j supply public acknowledgments and participant i supply the
practice used to assess them. The human-facing notation is:
-
C_i(j): commitmentsiattributes toj; -
E_i(j): entitlementsiattributes toj; -
K_i(j): incompatibilities relevant toi's assessment ofj.
The diagonal i = j is self-assessment, not a universal standard. A challenge
gains force from the challenger's entitlement to an incompatible ground.
Agreement therefore does not settle a matter automatically, and challenge does
not make the challenger an oracle.
Answerability begins here: another participant with standing can attribute consequences and raise a challenge one owes an answer to. Its record and causal companions—auditability and model-relative efficacy—are separated on Legitimacy.
The book projects qualitative scorekeeping into exact rational constraints; it is not a second source of normative truth. Logical constraints, settled records, and active endorsements determine a feasible set of credal states. The credal interval of a target is the exact minimum and maximum of its probability over that set.
Leverage is the distance by which a forced endpoint clears a decision threshold. If the feasible set is empty, the model supplies no merits direction; the inconsistency instead supports an objection against the book. Charges track declared liabilities, caps bound accumulated quantities, and fencing separates accounts. Fencing alone does not guarantee that later system effects remain bounded.
Williams's desirable-gamble approach and Walley's imprecise probability supply relevant mathematical background for intervals and coherent books. The specific accounting interpretation is this program's; see Sources.
Open / unregistered research. The relational bridge supplies finite fixtures and the consolidation supplies a frozen ledger with internally classified evidence. Neither has been promoted into the modern claims registry.
The current finite work distinguishes committive from permissive inference and models perspectival challenge. It does not provide a general compilation from the qualitative score to every quantitative object used by later theorems. A per-date linear program can decide current feasibility; it does not prove that a positive core persists along an unbounded evolving trajectory.