用计算复杂性解释数学真理为何成立，发现简化步骤即解释本身。
Explaining Necessary Truths
- 通过计算复杂性框架，让解释与求解过程同步生成。
- 复杂度高时无法找到简化路径，转而用修正错误作为解释理由。
- 适用于研究人类如何理解必然真理，尤其适合认知科学领域。
了解事实本身往往不够——我们还想知道为何该事实为真。尽管对偶然真理的解释已有较多研究，但对逻辑必然性真理（如数学命题）的解释机制仍不清楚。本文提出一个基于计算复杂性的框架：演绎真理的解释会随着搜索过程中发现的简化步骤一同浮现。当这些结构缺失时，人们则转向基于错误的解释，即通过纠正一个（被修正的）错误来构建虚构但具解释力的偶然原因——不犯该错误正是真理呈现此形式的理由。我们使用GPT-4o模拟人类受试者，在不同复杂度和合理性水平的SAT谜题上验证了该理论，并表明其预测可在未来的人类实验中进一步检验。
原文摘要 · Abstract (English)
Knowing the truth is rarely enough -- we also seek out reasons why the fact is true. While much is known about how we explain contingent truths, we understand less about how we explain facts, such as those in mathematics, that are true as a matter of logical necessity. We present a framework, based in computational complexity, where explanations for deductive truths co-emerge with discoveries of simplifying steps during the search process. When such structures are missing, we revert, in turn, to error-based reasons, where a (corrected) mistake can serve as fictitious, but explanatory, contingency-cause: not making the mistake serves as a reason why the truth takes the form it does. We simulate human subjects, using GPT-4o, presented with SAT puzzles of varying complexity and reasonableness, validating our theory and showing how its predictions can be tested in future human studies.
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