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series i–iii · foundations
part i

contradiction: the geometry of structural conflict

when what a system says and what it does cannot be jointly satisfied

abstract

this paper introduces the contradiction trap — a dialectical and game-theoretic mechanism for detecting structural bias, motivated asymmetry, and narrative drift in institutional and algorithmic decision systems. grounded in epistemic game theory, the trap recasts contradiction as a falsifiable evidential event: whenever a system’s stated rationale and observable behaviour cannot be jointly sustained, the resulting inconsistency becomes a measurable signal of underlying deviation. formalised as a one-move, strictly competitive epistemic game in which every admissible response incurs coherence loss, the trap generates informational payoffs that convert contradiction into diagnostic evidence. the framework provides a portable audit instrument for domains that claim impartiality but exhibit asymmetric behaviour — governance, organisational reasoning, and algorithmic architectures alike. by treating inconsistency not as a logical failure but as a data-bearing phenomenon, the contradiction trap establishes the epistemic foundations of the mathematics of integrity: a unified evidential paradigm in which legitimacy is demonstrated not through assertion, but through resistance to structured, adversarial challenge.

keywords

mathematics of integrityepistemic game theorydialectical inferencecontradiction analysisstructural asymmetrycoherence lossmotivated deviationepistemic diagnosticsadversarial reasoningalgorithmic accountabilityinstitutional reasoningreasoning integrityphilosophy of logicevidential audit design