论文标题
嘈杂的演绎推理：人类如何构建数学以及数学如何构建宇宙
Noisy Deductive Reasoning: How Humans Construct Math, and How Math Constructs Universes
论文作者
论文摘要
我们介绍了数学推理的计算模型，该模型是根据该数学是一个从根本上随机过程的。也就是说，在我们的模型上，在某些公理系统中是否认为给定公式是定理的，不是确定的问题，而是受概率分布的控制。然后，我们证明该框架对数学实践的几个方面提供了令人信服的说明。其中包括：1）数学家生成研究计划的方式，2）贝叶斯数学启发式学模型的适用性，3）绑架性推理在数学中的作用，4）4）命题的多种证据可以增强我们对该命题的信念的多种证明，以及5）具有多种形式系统的性质的性质，是可以进行多种形式系统的宇宙。因此，通过将数学模型视为不完全可预测的模型，我们就对数学的认识论和实践产生了一种新的富有成果的观点。
We present a computational model of mathematical reasoning according to which mathematics is a fundamentally stochastic process. That is, on our model, whether or not a given formula is deemed a theorem in some axiomatic system is not a matter of certainty, but is instead governed by a probability distribution. We then show that this framework gives a compelling account of several aspects of mathematical practice. These include: 1) the way in which mathematicians generate research programs, 2) the applicability of Bayesian models of mathematical heuristics, 3) the role of abductive reasoning in mathematics, 4) the way in which multiple proofs of a proposition can strengthen our degree of belief in that proposition, and 5) the nature of the hypothesis that there are multiple formal systems that are isomorphic to physically possible universes. Thus, by embracing a model of mathematics as not perfectly predictable, we generate a new and fruitful perspective on the epistemology and practice of mathematics.
