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Permanence as a principle of practice
Historia Mathematica ( IF 0.5 ) Pub Date : 2020-10-22 , DOI: 10.1016/j.hm.2020.08.001
Iulian D. Toader

The paper discusses Peano's argument for preserving familiar notations. The argument reinforces the principle of permanence, articulated in the early 19th century by Peacock, then adjusted by Hankel and adopted by many others. Typically regarded as a principle of theoretical rationality, permanence was understood by Peano, following Mach, and against Schubert, as a principle of practical rationality. The paper considers how permanence, thus understood, was used in justifying Burali-Forti and Marcolongo's notation for vectorial calculus, and in rejecting Frege's logical notation, and closes by considering Hahn's revival of Peano's argument against Pringsheim's reading of permanence as a logically necessary principle.



中文翻译:

永久性作为实践原则

本文讨论了Peano关于保留熟悉符号的论点。该论点加强了永久性原则,该原则由孔雀在19世纪初提出,后来由汉克尔(Hankel)调整并被许多其他人所采纳。永久性通常被视为理论上的合理性原则,而皮亚诺(Peano)跟随马赫(Mach)并反对舒伯特(Schubert)则将其理解为实践上的合理性原则。本文考虑了如此理解的永久性如何被用来证明Burali-Forti和Marcolongo的矢量演算的正当性​​,并拒绝弗雷格的逻辑性,并通过考虑哈恩(Hahn)对Peano反对普林斯海姆(Pringsheim)的阅读永久性的论点的复活作为逻辑上必要的原则而结束。

更新日期:2020-10-22
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