We develop a formal theory of cognitive debt: the stock of unverified reasoning obligations that accumulates when individuals use AI as a substitute rather than a complement for first-principles cognition. The model features two state variables per agent, cognitive capital and cognitive debt, and a multiplicative production technology in which cognitive capital functions as collateral that determines the return to AI adoption. We establish six propositions. Rational agents incur positive cognitive debt because the costs are deferred, partially external, and masked by short-run productivity gains. Tranquil periods lower subjective risk assessments, raise AI substitution intensity, and compound leverage, generating a cognitive Minsky moment in which subjective risk falls while true systemic fragility rises. Expected crisis losses are convex in aggregate leverage. Post-crisis, output-target pressure can produce a false-correction loop in which agents patch AI failures with more AI. The decentralised equilibrium over-adopts substitutive AI relative to the social optimum because of systemic risk, cognitive public goods, and arms-race externalities. In a two-type heterogeneous-agent economy, high-cognitive-capital agents adopt AI more intensively and may eventually erode their unaided cognitive capital below that of initially lower-skilled agents.

翻译：我们构建了认知债务的形式化理论：当个体将人工智能视为第一性原理认知的替代品而非补充品时，积累的未经验证的推理义务存量。该模型为每个智能体设置两个状态变量——认知资本与认知债务，并采用乘性生产技术，其中认知资本作为决定人工智能采用回报率的抵押品。我们提出六项命题。理性智能体会产生正向认知债务，因为其成本被延迟、部分外部化，且被短期生产力提升所掩盖。平稳期降低主观风险评估值，提高人工智能替代强度，并复合杠杆效应，引发"认知明斯基时刻"——主观风险下降而真实系统性脆弱性上升。危机预期损失呈凸性随总杠杆率变化。危机后，产出目标压力可能形成"虚假修正循环"，即智能体用更多人工智能修补人工智能失效。由于系统性风险、认知公共品与军备竞赛外部性，分散均衡状态对替代型人工智能的过度采纳程度高于社会最优水平。在异质性双类型智能体经济中，高认知资本智能体更密集地采用人工智能，最终可能使其未受辅助的认知资本侵蚀至低于初始低技能智能体的水平。