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Zermelo and the Axiomatic Method

  • Woosuk Park
Chapter
Part of the Studies in Applied Philosophy, Epistemology and Rational Ethics book series (SAPERE, volume 43)

Abstract

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.

Keywords

Axiomatic method Zermelo Hilbert Deepening the foundations Implicit definition The concept of set 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Humanities and Social SciencesKAISTDaejeonKorea (Republic of)

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