Upholding Epistemic Agency: A Brouwerian Assertibility Constraint for Responsible AI

TL;DR

By making outputs answerable to challengeable warrants rather than confidence alone, the paper aims to preserve epistemic agency where automated speech enters public justification.

Abstract

Generative AI can convert uncertainty into authoritative-seeming verdicts, displacing the justificatory work on which democratic epistemic agency depends. As a corrective, I propose a Brouwer-inspired assertibility constraint for responsible AI: in high-stakes domains, systems may assert or deny claims only if they can provide a publicly inspectable and contestable certificate of entitlement; otherwise they must return "Undetermined". This constraint yields a three-status interface semantics (Asserted, Denied, Undetermined) that cleanly separates internal entitlement from public standing while connecting them via the certificate as a boundary object. It also produces a time-indexed entitlement profile that is stable under numerical refinement yet revisable as the public record changes. I operationalize the constraint through decision-layer gating of threshold and argmax outputs, using internal witnesses (e.g., sound bounds or separation margins) and an output contract with reason-coded abstentions. A design lemma shows that any total, certificate-sound binary interface already decides the deployed predicate on its declared scope, so "Undetermined" is not a tunable reject option but a mandatory status whenever no forcing witness is available. By making outputs answerable to challengeable warrants rather than confidence alone, the paper aims to preserve epistemic agency where automated speech enters public justification.

Figures (6)

• Figure 1: The Dual-Regime Structure of Entitlement. The Certificate functions as a boundary object bridging the AI-internal and AI-external dimensions. Categorical output is licensed only when an internal constructive witness (left) and public standing conditions (right) jointly satisfy the deployment contract.
• Figure 2: Nested interval refinement for a scalar score. At stages $n_1$ and $n_2$, the certified bounds $[\ell_n, u_n]$ straddle the threshold $\tau$, resulting in an Undetermined ($U$) status. At stage $n_3$, the lower bound $\ell_3$ strictly exceeds $\tau$, forcing an Asserted ($A$) status.
• Figure 3: Visual summary of the Design Lemma (Proposition 1). When a system lacks a forcing witness, a classical binary interface is forced to manufacture an unwarranted categorical output. The Brouwerian interface safely halts at Undetermined ($U$), preserving both the integrity of its internal computational guarantees and the epistemic standards of the public record.
• Figure 4: Hybrid architecture for high-stakes deployment. A classical autoregressive LLM generates fluent but epistemically unbounded outputs. The constructive wrapper acts as a structural speech-act gate, evaluating tentative claims against the deployment contract $\mathcal{C}$. It halts the system at an Undetermined ($U$) status when internal bounds fail to force the public threshold $\tau$, thereby enforcing the Brouwerian assertibility constraint without requiring fully verified foundation models.
• Figure 5: Propagation through a ReLU activation. In the straddling case ($\ell < 0 < u$), the negative portion of the input interval is compressed to zero, resulting in the output interval $[0,u]$. Because this output interval straddles the public threshold $\tau$, the resulting interface status is Undetermined ($U$).

Theorems & Definitions (7)

• Definition 1
• Proposition 1
• proof
• Proposition 2
• proof
• Definition 2: Contract--certificate bridge
• Remark 1: Interpretation