数学真理的爆炸性证明（CS SC）---用户7095611

数学证明既是确定性的典范，也是我们在文化记录中所拥有的一些最明确的合理论据。然而，它们非常明确，导致了一个悖论，因为它们的错误概率随着论据的扩展呈指数增长。在这里，我们证明，在结合演绎推理和诱拐推理的认知似是而非的信念形成机制下，数学论点可以经历我们称之为认知阶段的转变：在合理的声称错误率水平上，从不确定性到接近完全的信心的戏剧性和迅速传播的跳跃。为了证明这一点，我们分析了来自形式化推理系统Coq的48个机器辅助证明的不寻常数据集，包括从古代到21世纪数学的主要定理，以及来自Euclid、Apollonius、Spinoza和Andrew Wiles的4个手工构造的案例。我们的研究成果既与数学史和哲学的最新研究成果有关，也与认知科学的一个基本问题有关，即我们如何形成信念，并向他人证明其合理性。

原文题目：Explosive Proofs of Mathematical Truths

原文：Mathematical proofs are both paradigms of certainty and some of the most explicitly-justified arguments that we have in the cultural record. Their very explicitness, however, leads to a paradox, because their probability of error grows exponentially as the argument expands. Here we show that under a cognitively-plausible belief formation mechanism that combines deductive and abductive reasoning, mathematical arguments can undergo what we call an epistemic phase transition: a dramatic and rapidly-propagating jump from uncertainty to near-complete confidence at reasonable levels of claim-to-claim error rates. To show this, we analyze an unusual dataset of forty-eight machine-aided proofs from the formalized reasoning system Coq, including major theorems ranging from ancient to 21st Century mathematics, along with four hand-constructed cases from Euclid, Apollonius, Spinoza, and Andrew Wiles. Our results bear both on recent work in the history and philosophy of mathematics, and on a question, basic to cognitive science, of how we form beliefs, and justify them to others.

原文作者：Simon DeDeo

原文地址：https://arxiv.org/abs/2004.00055