Explanation in mathematical conversations: an empirical investigation.
Explanation in mathematical conversations: an empirical investigation.
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数学对话中的解释：实证研究。
DOI：
10.1098/rsta.2018.0159
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Pease A
中科院分区：
文献类型：
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作者：
Pease A
对在线数学论坛的分析可以帮助揭示数学家是如何使用解释的；我们认为，这种解释的使用可能有助于提供一种简单的非正式概念化。我们从最近关于数学解释的发生和特征的哲学著作中提取了六个猜想。然后，我们用来自在线数学讨论的语料库测试了这些猜测。为此，我们采用了两种方法，一种是基于指标术语，另一种是对缺乏这种指标的评论进行随机抽样。我们的发现表明，解释在数学实践中是普遍存在的，它不仅出现在证明中，而且还出现在其他数学背景中。我们的工作也为经验主义方法在解决哲学问题上的有效性提供了进一步的证据。这篇文章是主题问题“简单证明的概念-希尔伯特的第24个问题”的一部分。
Analysis of online mathematics forums can help reveal how explanation is used by mathematicians; we contend that this use of explanation may help to provide an informal conceptualization of simplicity. We extracted six conjectures from recent philosophical work on the occurrence and characteristics of explanation in mathematics. We then tested these conjectures against a corpus derived from online mathematical discussions. To this end, we employed two techniques, one based on indicator terms, the other on a random sample of comments lacking such indicators. Our findings suggest that explanation is widespread in mathematical practice and that it occurs not only in proofs but also in other mathematical contexts. Our work also provides further evidence for the utility of empirical methods in addressing philosophical problems.This article is part of the theme issue ‘The notion of ‘simple proof’ - Hilbert's 24th problem’.