论文标题
积极的证据：它们是什么，为什么重要以及如何写它们
Motivated proofs: What they are, why they matter and how to write them
论文作者
论文摘要
数学家判断具有或缺乏各种不同品质的证据，包括例如解释力，深度，纯洁，美丽和合身。数学实践的哲学家已经开始研究这种品质的性质。但是，数学家经常将注意力集中在另一种理想的证明质量上：被动机。直觉上，积极进取的证据没有“令人困惑”的步骤，但他们几乎没有得到进一步的分析。在本文中，我开始对积极的证据进行哲学调查。我建议只有当数学家才能确定（i）每个步骤要执行的任务时，才有动机； （ii）每个步骤都可以合理地来。我认为积极的证据可以促进理解，传达新的数学资源并刺激新发现。因此，他们具有明显的认识益处，并直接有助于数学知识的有效传播和进步。鉴于他们的好处，我还讨论了我们如何产生积极的证据的更实际问题。最后，我考虑了动机的证据与证据之间的关系，这些证明与证明是解释性，美丽和合适的。
Mathematicians judge proofs to possess, or lack, a variety of different qualities, including, for example, explanatory power, depth, purity, beauty and fit. Philosophers of mathematical practice have begun to investigate the nature of such qualities. However, mathematicians frequently draw attention to another desirable proof quality: being motivated. Intuitively, motivated proofs contain no "puzzling" steps, but they have received little further analysis. In this paper, I begin a philosophical investigation into motivated proofs. I suggest that a proof is motivated if and only if mathematicians can identify (i) the tasks each step is intended to perform; and (ii) where each step could have reasonably come from. I argue that motivated proofs promote understanding, convey new mathematical resources and stimulate new discoveries. They thus have significant epistemic benefits and directly contribute to the efficient dissemination and advancement of mathematical knowledge. Given their benefits, I also discuss the more practical matter of how we can produce motivated proofs. Finally I consider the relationship between motivated proofs and proofs which are explanatory, beautiful and fitting.
