Mathematical Explanation and the Biological Optimality Fallacy

Pure mathematics can play an indispensable role explaining empirical phenomena if recent accounts of insect evolution are correct. In particular, the prime life cycles of cicadas and the geometric structure of honeycombs are taken to undergird an inference to the best explanation about mathematical...

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Bibliographic Details
Published inPhilosophy of science Vol. 84; no. 5; pp. 916 - 930
Main Authors Wakil, Samantha, Justus, James
Format Journal Article
LanguageEnglish
Published Cambridge University of Chicago Press 01.12.2017
Cambridge University Press
Subjects
Biology
Evolution
Honeycombs
Inference
Life cycles
Mathematical analysis
Mathematics
Realism
Theoretical mathematics
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Summary:Pure mathematics can play an indispensable role explaining empirical phenomena if recent accounts of insect evolution are correct. In particular, the prime life cycles of cicadas and the geometric structure of honeycombs are taken to undergird an inference to the best explanation about mathematical entities. Neither example supports this inference or the mathematical realism it is intended to establish. Both incorrectly assume that facts about mathematical optimality drove selection for the respective traits and explain why they exist. We show how this problem can be avoided, identify limitations of explanatory indispensability arguments, and attempt to clarify the nature of mathematical explanation.
ISSN:0031-8248
1539-767X
DOI:10.1086/694154