• Korean Journal of Logic
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• v.6 no.2
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• pp.1-22
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• 2003

타당한 논증과 논리적 귀결에 대한 프라위츠와 더밋의 증명 이론적 정의는 그 적절성을 위해 이른바 "근본 가정"과 "도입규칙들은 자체적으로 정당한 규칙들이다"는 두 논제들을 전제하고 있다. 이 글에서는 어떤 규칙들 특히 도입규칙들이 자체적으로 정당하다는 두 번째 논제가 어떻게 이해될 수 있는지 살펴보고, 이 논제를 보다 분명히 드러내 보이려는 한 신도를 비판적으로 검토할 것이다. 그런 과정 중에 이 두 논제의 관계도 보다 분명히 드러내 보일 것이다.

• Journal for History of Mathematics
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• v.24 no.4
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• pp.45-59
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• 2011

Constructionists believe that mathematical knowledge is obtained by a series of purely mental constructions, with all mathematical objects existing only in the mind of the mathematician. But constructivism runs the risk of rejecting the classical laws of logic, especially the principle of bivalence and L. E. M.(Law of the Excluded Middle). This philosophy of mathematics also does not take into account the external world, and when it is taken to extremes it can mean that there is no possibility of communication from one mind to another. Two constructionists, Brouwer and Dummett, are common in rejecting the L. E. M. as a basic law of logic. As indicated by Dummett, those who first realized that rejecting realism entailed rejecting classical logic were the intuitionists of the school of Brouwer. However for Dummett, the debate between realists and antirealists is in fact a debate about semantics - about how language gets its meaning. This difference of initial viewpoints between the two constructionists makes Brouwer the intuitionist and Dummettthe the semantic anti-realist. This paper is confined to show that Dummett's proposal in favor of intuitionism differs from that of Brouwer. Brouwer's intuitionism maintained that the meaning of a mathematical sentence is essentially private and incommunicable. In contrast, Dummett's semantic anti-realism argument stresses the public and communicable character of the meaning of mathematical sentences.