Understanding in mathematics: The case of mathematical proofs

被引:0
|
作者
Hamami, Yacin [1 ,2 ,3 ]
Morris, Rebecca Lea
机构
[1] Univ Liege, Philosophy Dept, Liege, Belgium
[2] Swiss Fed Inst Technol, Dept Humanities Social & Polit Sci, Zurich, Switzerland
[3] PSL Univ, Inst Jean Nicod, Dept Cognit Studies, EHESS,ENS,CNRS, Paris, France
来源
NOUS | 2024年
关键词
STYLE;
D O I
10.1111/nous.12489
中图分类号
B [哲学、宗教];
学科分类号
01 ; 0101 ;
摘要
Although understanding is the object of a growing literature in epistemology and the philosophy of science, only few studies have concerned understanding in mathematics. This essay offers an account of a fundamental form of mathematical understanding: proof understanding. The account builds on a simple idea, namely that understanding a proof amounts to rationally reconstructing its underlying plan. This characterization is fleshed out by specifying the relevant notion of plan and the associated process of rational reconstruction, building in part on Bratman's theory of planning agency. It is argued that the proposed account can explain a significant range of distinctive phenomena commonly associated with proof understanding by mathematicians and philosophers. It is further argued, on the basis of a case study, that the account can yield precise diagnostics of understanding failures and can suggest ways to overcome them. Reflecting on the approach developed here, the essay concludes with some remarks on how to shape a general methodology common to the study of mathematical and scientific understanding and focused on human agency.
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页数:34
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