Article ID: CBB874681327

What were the genuine Banach spaces in 1922? Reflection on axiomatisation and progression of the mathematical thought (2020)

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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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Authors & Contributors
Burnett, D. Graham
Pincus, Steven
Levy, Jonathan I.
Xu, Zelin
Gimbel, Steven
Hacking, Ian
Journals
Historia Mathematica
Ziran Kexueshi Yanjiu (Studies in the History of Natural Sciences)
Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
Synthese
Almagest
Foundations of Science
Publishers
Oxford University Press
Southern Illinois University at Carbondale
Université de Montréal (Canada)
Princeton University
Carocci Editore
Meltemi
Concepts
Philosophy of mathematics
Epistemology
Mathematics
Mathematical analysis
Philosophy of science
Infinitesimals
People
Reichenbach, Hans
Husserl, Edmund
Cauchy, Augustin Louis
Banach, Stefan
Takebe, Katahiro
Gödel, Kurt
Time Periods
20th century, early
19th century
18th century
Edo Era (Japan, 1603-1868)
20th century
20th century, late
Places
China
France
Japan
Sweden
Alexandria (Egypt)
Great Britain
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