The Nullification Operator: Minimal Removal, Coherence and the Theory of Non-Knowledge

This paper introduces the nullification operator as a general method for restoring coherence in a finite base of constraints that contains explicit contradictions. The operator removes the smallest and least important set of elements required to eliminate inconsistency, where importance is defined by a priority structure called Constraint Tiebreaking Logic (CTL). Rather than modifying inference rules, the operator acts on the premise base before inference takes place. As a result, classical reasoning is recovered on the coherent remainder of the original base. The paper defines the operator formally, proves its soundness, completeness and minimality, and shows that it can be iterated until reaching a fixpoint. In the finite case, the fixpoint corresponds to a maximal coherent subset of the original base selected according to CTL. The approach integrates ideas from belief revision, constraint satisfaction and minimal diagnosis, while maintaining classical logic as the inference engine. The philosophical interpretation of the operator is grounded in the Theory of Non-Knowledge, which treats contradiction as a sign of representational saturation rather than failure, and coherence as a finite operational structure. Under this view, knowledge is not an absolute totality, but a minimal unit stabilized by intervention. The method provides a constructive model for acting under contradiction, offering a formal science of stability without assuming the existence of holistic knowledge.