• Title/Summary/Keyword: Bernays

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Bernays and the Axiomatic Method (베르나이스와 공리적 방법)

  • Park, Woo-Suk
    • Korean Journal of Logic
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    • v.14 no.2
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    • pp.1-38
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    • 2011
  • Bernays has not drawn scholarly attention that he deserves. Only quite recently, the reevaluation of his philosophy, including the projects of editing, translating, and reissuing his writings, has just started. As a part of this renaissance of Bernays studies, this article tries to distinguish carefully between Hilbert's and Bernays' views regarding the axiomatic method. We shall highlight the fact that Hilbert was so proud of his own axiomatic method on textual evidence. Bernays' estimation of the place of Hilbert's achievements in the history of the axiomatic method will be scrutinized. Encouraged by the fact that there are big differences between the early middle Bernays and the later Bernays in this matter, we shall contrast them vividly. The most salient difference between Hilbert and Bernays will shown to be found in the problem of the uniformity of the axiomatic method. In the same vein, we will discuss the later Bernays' criticism of Carnap, for Carnap's project of philosophy of science in the late 1950's seems to be a continuation and an extension of Hilbert's faith in the uniformity of the axiomatic method.

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직관주의 논리

  • 이승온;김혁수;박진원;이병식
    • Journal for History of Mathematics
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    • v.12 no.1
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    • pp.32-44
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    • 1999
  • This paper is a sequel to [8]. Development of modern logic was initiated by Boole and Morgan. Boolean logic is one of their completed works. Cantor created the set theory along with cardinal and ordinal numbers. His theory on infinite sets brought about a remarkable development on modern mathematical theory, but generated many paradoxes (e.g. Russell Paradox) that in turn motivated mathematicians to solve them. Further, mathematicians attempted to construct sound foundations for Mathematics. As a result three important schools of thought were formed in relation to fundamentals of mathematics for the resolution of paradoxes of set theory, namely logicism developed by Russell and Whitehead, intuitionism lead by Brouwer and formalism contended by Hilbert and Bernays. In this paper, we examine the logic for intuitionism which is originated by Brouwer in 1908 and study Heyting algebra.

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