No Certificate, No Categorical Speech Act: A Brouwerian Assertibility Constraint for Public Reason

AI systems should refuse to make definitive claims without transparent justification: Rather than converting uncertainty into confident-sounding answers, the paper proposes that high-stakes AI systems must provide publicly inspectable "certificates" showing why they're entitled to assert or deny something—otherwise they must return "Undetermined." This prevents AI from displacing the reasoning work that citizens need to do to make informed decisions.

Three-status outputs protect democratic accountability: The framework replaces binary yes/no answers with three options (Asserted, Denied, Undetermined), where "Undetermined" is mandatory when sufficient justification cannot be provided. This design prevents AI from falsely appearing authoritative and preserves space for human deliberation and contestation.

Certificates must be contestable, not just internal: The paper distinguishes between a system's internal confidence and its public standing to make claims. A certificate serves as a "boundary object" that makes the system's reasoning visible and open to challenge by citizens, experts, and other stakeholders—essential for maintaining democratic epistemic agency.

Refusing false completeness is a norm of responsible AI speech: Drawing on mathematical intuitionism, the paper argues that responsible AI should resist the temptation to provide complete answers to every question. Acknowledging the limits of what can be justified is not a bug but a feature of systems designed for high-stakes public reasoning.