Two Theorems of Issue Control and the Undecidability of Adjudication: A Monotonicity-Based Analysis, with a Companion Limit on Fact-Finding

In adjudication, a judge's removal of an issue (reduction) is permitted with relative freedom, whereas the addition of an issue (expansion) after the close of argument is strictly controlled. Traditionally, this asymmetry has been understood by appeal to values such as legal certainty, the protection of reliance, equality of arms, and procedural economy—in short, as an inductive rule of experience. This article introduces the monotonicity principle of formal logic as a novel explanatory framework for the same asymmetry. The crux lies in separating the strata of inference. The pure formal logic circuit is monotonic; non-monotonicity arises not in the circuit, but at the input stage, where the judge assigns truth values. The circuit receives as its input atomic propositions obtained by decomposing normative issues into their basic units, Hohfeldian pairs—a form of decomposition that follows from the very nature of adjudication as the treatment of normative relations. Building on this separation, we map reduction onto logic-circuit-invariant, monotonic preservation of conclusions, and expansion onto the non-monotonic defeat of conclusions induced by an update at the input stage. Reduction merely severs dependency relations within the circuit, thereby preserving the validity of the remaining derivations. Expansion, by contrast, can inject new truth values into the input stage and so invalidate existing derivations; because the locus of that risk cannot be specified in advance, content-based control is difficult. Temporal cutoffs—such as the close of argument, res judicata, and preclusion—therefore become an effective means of control. Furthermore, this article demonstrates that the non-locality of expansion control is not a mere computational difficulty, but a limit in principle. For adjudication to address its own coherence (freedom from contradiction) in advance, it must examine the issues in their entirety. Yet, securing this total coherence is precisely the goal that adjudication itself seeks to achieve. Consequently, adjudication cannot establish its internal coherence prior to its own completion. We refer to this self-referential phenomenon as the undecidability of adjudication. It is similar in structure to, yet different in kind from, Gödel’s incompleteness arising from self-reference within a sufficiently strong axiomatic system; it is closer to the halting problem or computational irreducibility. The undecidability of adjudication diverges from both of these, however, in that it is closed by an external axiom: the demand for closure. Finally, we emphasize that the monotonicity principle governs the asymmetry of procedural rules, and present its counterpart—a limit on fact-finding—as a sister proposition. A judge may not create, sua sponte, a fact-finding that contradicts a proposition the parties have concordantly admitted, or that contradicts the objective public record. No one should be made a liar. The two axes emerged together from a single case, which we place at the end of the article. This framework does not replace the existing value-based justifications; it brings to light the formal substructure lying beneath them.