RUI: STS: Standard Research Grant: Mathematical Explanation in Science

本项目将分析进化生物学中数学解释的案例研究，以告知关于科学中数学解释本质的哲学辩论。它将在连续三个夏季进行，并将充分利用哲学、数学和生物学的本科生研究人员；具体而言，它将通过让高级本科生参与该项目，将研究和教育结合起来。这样做将有助于扩大参与科学的范围，使数学和哲学的学生接触到这些学科经常缺乏的合作研究风格；它将为机构的跨学科性提供一个模式，促进自然科学和人文科学之间的智力和后勤联系。该项目的成果将通过会议发言和在学术期刊上发表文章的方式广泛传播。该项目的一个首要目标是证明，与科学实践的方法论和产出密切接触，可以产生既有趣又与工作科学家直接相关的哲学见解。本项目的结果有可能对正在进行的关于数学和实证科学之间关系的哲学研究做出贡献。特别关注数学在科学中的解释作用是哲学文献中当前非常活跃的辩论领域。PI一直是这些辩论的主要贡献者。目标是产生与生物学和应用数学相关的研究成果。这两个核心例子，周期性的蝉和蜜蜂蜂巢，都是生物学家和数学家之间持续争论的主题，涉及到什么因果机制，不同参数优化所起的作用，以及什么数学工具，如果有的话，本质上涉及到。因此，该项目的目的不仅是利用几个学科的数据，而且要提供真正跨学科兴趣的研究成果。

General Audience SummaryThis project will analyze case studies of mathematical explanation in evolutionary biology to inform the philosophical debate about the nature of mathematical explanation in science. It will take place over three consecutive summers, and will make essential use of undergraduate researchers in philosophy, mathematics, and biology; specifically, it will integrate research and education by involving advanced undergraduate students in the project. Doing so will serve to broaden the scope of participation in science by exposing students in mathematics and in philosophy to a collaborative style of research that is often lacking in these disciplines; it will provide a model for institutional interdisciplinarity, fostering intellectual and logistical connections between the natural sciences and the humanities. The results of this project will be widely disseminated through conference presentations and publication of articles in scholarly journals. One overriding goal of the project is to demonstrate that close engagement with the methodology and outputs of scientific practice can yield philosophical insights that are both interesting in their own right and of direct relevance to working scientists.Technical SummaryThe results of the proposed project have the potential to contribute to ongoing philosophical research into the relation between mathematics and the empirical sciences. The particular focus on the explanatory role of mathematics in science is an area of very active current debate in the philosophical literature. The PI has been a leading contributor to these debates. The goal is to produce research outputs that are of relevance to biology and to applied mathematics. Both of the two core examples, periodical cicadas and bee honeycombs, are the subject of ongoing debate among biologists and mathematicians concerning what causal mechanisms are involved, the role played by optimization of different parameters, and what mathematical apparatus, if any, is essentially involved. Thus the project aims not merely to draw on data from several disciplines but to provide research outputs that are of genuine cross-disciplinary interest.