• Journal for History of Mathematics
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• v.13 no.2
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• pp.145-150
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• 2000

This paper is intended to show that fuzzy logic can be understood in the context of the late Wittgenstein's philosophy. It introduces the view of language presupposed by fuzzy logic and parallels it with the late Wittgenstein's view of language. To make the parallel clear it contrasts the views of the early Wittgenstein and the late Wittgenstein.

• Journal for History of Mathematics
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• v.14 no.2
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• pp.77-92
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• 2001

P. Dirac's contribution to the advent of the modern quantum mechanics is undeniable. His main research guideline is the principle of mathematical beauty. What is this principle on the earth\ulcorner Are there distinctive features between pure mathematician's mind and theoretical physicist' mind about the mathematical beauty\ulcorner These problems will be analyzed with respect to Dirac's case which can reflect a historical interrelationship between science and philosophy.

• Journal for History of Mathematics
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• v.20 no.3
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• pp.105-126
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• 2007

The present paper considers how to teach mathematical concepts. In particular, we aim to a balanced, unified achievement for three elements of concept loaming such as concept understanding, computation and application through one's mathematical intuition. In order to do this, we classify concepts into three patterns, that is, intuitive concepts, logical concepts and formal concepts. Such classification is based on three kinds of philosophy of mathematics : intuitionism, logicism, fomalism. We provide a concrete, practical investigation with important nine concepts in theory of vectors from the viewpoint of three patterns of concepts. As a consequence, we suggest certain solutions for an effective concept learning in teaching theory of vectors.

• Korean Journal of Logic
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• v.21 no.1
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• pp.97-133
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• 2018

In his unpublished article, "Is Mathematics Syntax of Language?," $G{\ddot{o}}del$ criticizes what he calls the 'syntactical interpretation' of mathematics by Carnap. Park, Chun, Awodey and Carus, Ricketts, and Tennant have all reconstructed $G{\ddot{o}}del^{\prime}s$ arguments in various ways and explored Carnap's possible responses. This paper first recreates $G{\ddot{o}}del$ and Carnap's debate about the nature of mathematics. After criticizing most existing reconstructions, I claim to make the following contributions. First, the 'language relativity' several scholars have attributed to Carnap is exaggerated. Rather, the essence of $G{\ddot{o}}del^{\prime}s$ critique is the applicability of mathematics and the argument based on 'expectability'. Thus, Carnap's response to $G{\ddot{o}}del$ must be found in how he saw the application of mathematics, especially its application to science. I argue that the 'correspondence principle' of Carnap, which has been overlooked in the existing discussions, plays a key role in the application of mathematics. Finally, the real implications of $G{\ddot{o}}del^{\prime}s$ incompleteness theorems - the inexhaustibility of mathematics - turn out to be what both $G{\ddot{o}}del$ and Carnap agree about.

• The Mathematical Education
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• v.40 no.1
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• pp.125-137
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• 2001

We review the mathematics education in Korea just after the 1595 Liberation and the first, second curriculum announced in 1955 and 1963, respectively. The 3rd curriculum announced in 1973 is influenced by “New Mathematics” in America. There were theoretical research about “New Mathematics”, but no experimental research about it in the school. So, there was not much effect of “New Mathematics” in mathematics education. After that we have the 4th, 5th and 6th curriculum which is improved by the result of experience in teaching. The 7th curriculum announced in 1997 emphasized practical mathematics. In this paper, we review the mathematics education and consider some problems in the 7th curriculum. We also consider some problems in mathematics textbook authorization under the 7th curriculum. To solve these problems, we suggest some facts. Especially, we need the philosophy about mathematics education and the enough knowledge about “Mathematics for Mathematics Teachers”.

• Journal for History of Mathematics
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• v.14 no.2
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• pp.45-54
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• 2001

Jules Henri Poincare was great not only as a mathematician brit also as a philosopher of science. He received many honors for his outstanding research. He was elected to the Academie des Sciences in 1887 and was elected President of tile Academy in 1906. In 1908 he was elected to the Academie Francaise and was elected director in the year of his death. The Poincare Conjecture was selected Millennium Prize Problems fly The Clay Mathematics Institute of Cambridge, Massachusetts(CMI). The Board of Directors of CMI have designated a $1 million prize fund for the solution to his problem. In this paper, Poincare's major works, his life, his philosophy and the Poincare Conjecture are given.

• Cross-Cultural Studies
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• v.33
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• pp.143-169
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• 2013

Recently, because of the danger and damages that following the steady development of scientific technologies, natural science is faced with many humane and ethical problems. So it is asserted the interdisciplinary with social and human science. However, it comes commonly that the ethical issues such as world view and one's view of life caused the development of sociology, especially development of the market economy. But in many cases, the interdisciplinary can be useful for widen the view of scholars. The interdisciplinary is actually connected with the problems of philosophy, and located in that domain. In this case, this is noticed as a model to the philosophers in 18th century, especially Denis Diderot. Diderot published De $l^{\prime}interpr{\acute{e}}tation$ de la nature during editing the Encyclopedia, from there he picked out the contents from piles of documents of Encyclopedia. Even though the contents or opinions of De $l^{\prime}interpr{\acute{e}}tation$ de la nature are inaccuracy or erroneous, it shows that how human-social science and natural science encountered. Diderot studied mathematics and then Diderot accepted to the natural science proposal, he approaches philosophy with translate English books to the French. Next he understood natural science by reading Buffon and Maupertuis, and during working for Encyclopedia, he possessed his knowledge that he can claim his opinion to other scholars. However in this De $l^{\prime}interpr{\acute{e}}tation$ de la nature, Diderot who sometimes rebutted other scholars' theory and demonstration, tried to build a philosophy on metaphysics in order to it was important for himself that he imposed the methods of science and importance of experience. Anyhow, this De $l^{\prime}interpr{\acute{e}}tation$ de la nature cause consider the recognition of Diderot in the field of natural science, and is suggested as a model about his Nature. This mean that it is an expression of his philosophy, and the content is found from natural philosophy and empirical philosophy. Like giving these attache the importance of method study for science and technique, these are targeted the promotion of popularization of natural-science and scientific-technology. Also it advocates fulfilling from reasonable philosophy to empirical philosophy. Therefore, the philosophy which was speculative and abstracted became his philosophy which was writing the meaning, as waiting the discovery of science. And at that time, the humanities made interdisciplinary with natural science.

• Journal for History of Mathematics
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• v.11 no.1
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• pp.27-35
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• 1998

As Chinese philosophy has developed by commentary for the original texts, the Nine Chapters has been greatly improved by the commentary given by Liu Hui and it was transformed from an arithmetic text to Mathematics. Comparing his commentary and Chinese philosophical development up to his date, we conclude that Liu Hui was able to make such a great leap by his thorough understanding of philosophical development.

• The Mathematical Education
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• v.51 no.2
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• pp.115-129
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• 2012

The values and methods of mathematics education which mathematics teachers tried to impart to their students have varied historically according to the situations of each institution. The cases of the mathematics education in Cambridge University and University College, London show that the peculiar meanings or values of mathematics education were transmitted on students and the methods or focus of the teaching were uniquely determined under the influences of university examinations or conditions of students. In specific, the characteristic education of Augustus De Morgan who studied in Cambridge University and then taught in University College, London reveals better the different institutional contexts. In this paper, I suggest mathematics teachers reconsider mathematics learning motivations on their institutional contexts.

• Korean Journal of Logic
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• v.22 no.3
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• pp.417-446
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• 2019

The operation theory of the Wittgenstein's Tractatus Logico-Philosophicus is the essential basis of the philosophy of mathematics of the Tractatus. Wittgenstein presents the definition of cardinal numbers on the basis of operation theory, and suggests the proof of "$2{\times}2=4$" by using the theory of operations in 6.241. Therefore, in order to explicate correctly the philosophy of mathematics, it is required to understand rigorously the theory of operations in the Tractatus. Accordingly in this paper, I will endeavor to explicate operation theory of the Tractatus as a preliminary study for explicating the philosophy of mathematics of the Tractatus. In this process, we can ascertain Frascolla's important contributions and fallacies in his reconstruction of 6.241. In particular, we can understand the background that in 6.241 Wittgenstein made mistakes and that there he dealt with the addition operation of the theory of operations, and on the basis of this, we can reconstruct correctly 6.241.