What were the genuine Banach spaces in 1922? Reflection on axiomatisation and progression of the mathematical thought

IF 0.7 2区哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE

Archive for History of Exact Sciences Pub Date : 2019-10-26 DOI:10.1007/s00407-019-00239-7

Frédéric Jaëck

引用次数: 1

Abstract

This paper provides an analysis of the use of axioms in Banach’s Ph.D. and their role in the progression of Banach’s mathematical thought. In order to give a precise account of the role of Banach’s axioms, we distinguish two levels of activity. The first one is devoted to the overall process of creating a new theory able to answer some prescribed problems in functional analysis. The second one concentrates on the epistemological role of axioms. In particular, the notion of norm completeness, as it appears in Banach’s text, can be interpreted as an epistemic linchpin between several a priori inhomogeneous domains of mathematical thought.

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1922年真正的巴拿赫空间是什么？关于数学思想公理化和发展的思考

本文分析了公理在巴纳赫博士学位中的使用及其在巴纳奇数学思想发展中的作用。为了准确地说明巴拿赫公理的作用，我们区分了两个活动级别。第一个是关于创造一个能够回答函数分析中一些规定问题的新理论的总体过程。第二部分集中论述了公理的认识论作用。特别是，Banach文本中出现的范数完备概念，可以被解释为数学思想的几个先验非均匀领域之间的认识关键。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Archive for History of Exact Sciences 管理科学-科学史与科学哲学

CiteScore

1.30

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Archive for History of Exact Sciences casts light upon the conceptual groundwork of the sciences by analyzing the historical course of rigorous quantitative thought and the precise theory of nature in the fields of mathematics, physics, technical chemistry, computer science, astronomy, and the biological sciences, embracing as well their connections to experiment. This journal nourishes historical research meeting the standards of the mathematical sciences. Its aim is to give rapid and full publication to writings of exceptional depth, scope, and permanence.