Zermelo and the axiomatic method

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This chapter intends to examine the widespread assumption, which has been uncritically accepted, that Zermelo simply adopted Hilbert’s axiomatic method in his axiomatization of set theory. What is essential in that shared axiomatic method? And, exactly when was it established? By philosophical reflection on these questions, we are to uncover how Zermelo’s thought and Hilbert’s thought on the axiomatic method were developed interacting each other. As a consequence, we will note the possibility that Zermelo, in his early as well as late thought, had views about the axiomatic method entirely different from that of Hilbert. Such a result must have far-reaching implications to the history of set theory and the axiomatic method, thereby to the philosophy of mathematics in general.
Publisher
Springer International Publishing AG
Issue Date
2018
Language
English
Article Type
Book Chapter
Citation

Studies in Applied Philosophy, Epistemology and Rational Ethics, v.43, pp.59 - 86

ISSN
2192-6255
DOI
10.1007/978-3-319-95147-8_5
URI
http://hdl.handle.net/10203/262826
Appears in Collection
HSS-Journal Papers(저널논문)
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