• Korean Journal of Logic
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• v.9 no.2
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• pp.117-175
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• 2006

이 논문은 매디가 왜 수학적 실재론을 포기하고 그녀 특유의 수학적 자연주의를 표방하게 되었는지를 탐구하려 한다. 이 문제에 관하여 널리 받아들여지고 있는 한 가설에 따르면, 매디의 입장 변화는 콰인-퍼트남 필수불가결성 논증을 비판하고 포기함으로써 야기되었다. 필자는 이 가설이 지닌 설득력을 인정하지만, 그것만으로는 실재론의 포기의 충분한 이유가 될 수 없다고 생각하며, 그 대신 과학과 수학의 유비 문제가 매디의 입장 변화를 이해하는 데 더 나은 조망을 제공한다는 점을 보여주고자 한다. 이를 위해서는 콰인과 괴델에 크게 빚졌던 실재론자 시절 매디의 사유가 얼마만큼 수학과 과학의 유비에 지배되었는지를 살펴보아야 하는 동시에, 왜 매디가 이 유비를 포기함으로써 실재론을 포기하게 되는지를 이해하여야 한다. 아울러 이 유비의 포기에 대한 다소의 비판적 검토를 통해 매디의 수학적 존재론의 지적 여정을 왜 필자가 존재론적 퇴보라 믿는지에 대한 몇 가지 이유가 시사될 것이다.

• Korean Journal of Logic
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• v.11 no.1
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• pp.1-31
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• 2008

최근 가장 영향력 있는 수학적 실재론과 관련된 논변은 버지스와 로젠의 딜레마이다. 일종의 반-유명론적 논증인 버지스-로젠 딜레마는 유명론자들이 취할 수 있는 제한된 선택지를 제시한 후 그 어느 선택지도 적절하지 못함을 주장하는 것이다. 논자 역시 버지스-로젠 딜레마가 성립한다면 유명론이 가망 없는 전략임에 동의한다. 그러나 논자는 그들의 논의가 유명론 대 실재론이라는 대립구도 대신, 유명론 대 수학 및 과학이라는 잘못된 대립구도를 전제하고 있음을 본 논문을 통해 밝히고자 한다. 간략히 말해, 논자는 버지스-로젠 딜레마는 수학자 및 과학자들의 주장이 글자 그대로 실재론을 함의함을 전제하는데, 이것은 실제 수학 및 과학 활동과 일치하지 않을뿐더러, 이를 입증하기 위해서는 철학적 가정이 개입해야 함을 밝히고, 그 과정에서 유명론의 가능성을 모색하고자 한다. 이러한 논자의 전략은 유명론 진영 안의 특정한 입장을 지지하는 것은 아니다. 버지스-로젠 딜레마는 특정한 유명론의 문제라기보다는 유명론 자체의 가능성과 관련된 것이기 때문이다.

• Journal for History of Mathematics
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• v.24 no.1
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• pp.63-73
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• 2011

This paper analyses conceptual change from Euclid's dictionary definition to Hilbert's mathematical definition about primitive terms in Geometry. Realism, conceptualism, nominalism about mathematical objects are related to this conceptual change.

• Journal for History of Mathematics
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• v.10 no.1
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• pp.33-38
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• 1997

본고는 수학적으로 취급된 Cantor의 무한을 소개하기보다는 그가 가졌던 무한에 대한 태도는 매우 종교적이었고 철학적으로는 실재론적인 입장에 있다는 것을 보이려고 한다. 이를 위해 먼저 Cantor의 초한수론과 무한의 역사를 약술하고 그의 무한관이 기독교 신앙과 중세 철학에 근거해 있음을 제시한다. 또한 Cantor의 초한수론은 당시의 세계관과 시대정신에 도전하고 있음을 밝히려 한다.

• Korean Journal of Logic
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• v.17 no.2
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• pp.349-358
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• 2014

Human being has attempted to solve the problem of imperfect knowledge for a long time. In 1982 Pawlak proposed the rough set theory to manipulate the problem in the area of artificial intelligence. The rough set theory has two interesting properties: one is that a rough set is considered as distinct sets according to distinct knowledge bases, and the other is that distinct rough sets are considered as one same set in a certain knowledge base. This leads to a significant philosophical interpretation: a concept (or an event) may be understood as different ones from different perspectives, while different concepts (or events) may be understood as a same one in a certain perspective. This paper claims that such properties of rough set theory produce a mathematical model to support critical realism and theory ladenness of observation in the philosophy of science.

• Journal for History of Mathematics
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• v.20 no.3
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• pp.17-26
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• 2007

Following $G\ddot{o}del's$ own arguments, this paper explores his views on mathematics, its object, and mathematical intuition. The major claim is that we simply cannot classify the $G\ddot{o}del's$ view as robust Platonism or realism, since it is conceivable that both Platonistic ontology and intuitionistic epistemology occupy a central place in his philosophy and mathematics.

• Journal of Educational Research in Mathematics
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• v.18 no.1
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• pp.1-24
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• 2008

The purpose of this study is to uncover weaknesses in the constructivism in mathematics education and to search for ways to complement these deficiencies. We contemplate the relationship between the capability of construction and the performance of it, with the view of the 'Twofold-Structure of Mind.' From this, it is claimed that the construction of mathematical knowledge should be to experience and reveal the upper layer of Mind, the Reality. Based on the examination on the conflict and relation between the structuralism and the constructivism, with reference to the 'theory of principle' and the 'theory of material force' in Neo-Confucianist theory, it is asserted that the construction of mathematical knowledge must be the construction of the structure of mathematical knowledge. To comprehend the processes involved in the construction of the structure of mathematical knowledge, the epistemology of Michael Polanyi is studied. And also, the theory of mathematization, the historico-genetic principle, and the theory on the levels of mathematical thinking are reinterpreted. Finally, on the basis of the theory of twofold-structure, the roles and attitudes of teachers and students are discussed.

• Journal of Educational Research in Mathematics
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• v.18 no.1
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• pp.137-156
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• 2008

This article discusses the purpose of mathematics education based on the epistemology of Michael Polanyi. According to Polanyi, studying is seeking after the truth and pursuing the reality. He opposes to separate humanity and knowledge on account that no knowledge possibly exists without its owners. He assumes tacit knowledge hidden under explicit knowledge. Tacit knowing is explained with the relation between focal awareness and subsidiary awareness. In the epistemology of Polanyi, teaching and learning of mathematics should aim for change of students' minds in whole pursuing the intellectual beauty, which can be brought about by the operation of their minds in whole. In other words, mathematics education should intend the cultivation of mind. This can be accomplished when students learn mathematical knowledge as his personal knowledge and obtain tacit mathematical knowledge.

• Journal of Educational Research in Mathematics
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• v.26 no.2
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• pp.173-188
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• 2016

Research on didactic transposition in mathematics education has about 25-year and about 35-year long history in and out of Korea, respectively. This study attempts to investigate in trends of those research and to suggest tasks needed to be tackled. Major findings are followed. First, studies done in Korea tended to focus on the application of the didactic transposition theory for proving its effectiveness in understanding mathematics textbooks and mathematics lessons in-depth. It is suggested to conduct meta-analysis of the accumulated results or analysis of further applications of the didactic transposition theory to improve theoretical aspects of didactic transposition. Second, new categories for extreme teaching phenomenon were found and new typology in knowledge to be considered in the didactic transposition was developed in a few studies done in other subject matter education. Application of these to mathematics education may enhance research in didactic transposition of mathematical knowledge. Third, praxeology or a complex of praxeology for Korean school mathematics should be explored as did in other countries. Fourth, there have been rich attempts to link perspectives in didactic transposition to other perspectives or fields such as anthropology, human and education in technology era, praxeology theory in economics, epistemology in other countries but not in Korea. It is suggested to extend the scope of discussion on didactic transposition and to relate various concepts given in other disciplines. Fifth, clarification or negotiation of meaning for the main terms used in the discussion on didactic transposition such as personalization, contextualization, depersonalization, decontextualization, Topaze Effect, Meta-Cognitive Shift is suggested by comparing researchers' various descriptions or uses of the terms.

• Cartoon and Animation Studies
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• s.51
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• pp.391-411
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• 2018

The purpose of this thesis is to examine ontology of digital photo image based on a Simulacre concept of Gilles Deleuze & Jean Baudrillard. Traditionally, analog image follows the logic of reproduction with a similarity with original target. Therefore, visual reality of analog image is illuminated, interpreted, and described in a subjective viewpoint, but does not deviate from the interpreted reality. However, digital image does not exist physically but exists as information that is made of mathematical data, a digital algorithm. This digital image is that newness of every reproduction, that is, essence of subject 'once existing there' does not exist anymore, and does not instruct or reproduce an outside target. Therefore, digital image does not have the similarity and does not keep the index instruction ability anymore. It means that this digital image is converted into a virtual area, and this is not reproduction of already existing but display of not existing yet. This not-being of digital image changes understanding of reality, existence, and imagination. Now, dividing it into reality and imagination itself is meaningless, and this does not make digital image with technical improvement but is a new image that is basically completely different from existing image. Eventually, digital image of the day passes step to visualize an existent target, nonexistent things have been visualized, and reality operates virtually. It means that digital image does not reproduce our reality but reproduces other reality realistically. In other words, it is a virtual reproduction producing an image that is not related to a target, that is to say Simulacre. In the virtually simulated world, reality has an infinite possibility, and it is not a picture of the past and present and has a possibility as the infinite virtual that is not fixed, is infinitely mutable, and is not actualized yet.