• Journal for History of Mathematics
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• v.22 no.4
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• pp.97-114
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• 2009

Whitehead is a greatest mathematical philosopher who expanded mathematical concepts and method in philosophy. In view of Whitehead that he emphasizeson metaphysical perspective, mathematical truth and empirical connection of reality, it explicates that it tends to empiricism and rationalism of mathematical philosophy. In this paper, we try to research his unique perspective of mathematical philosophy. His perspective on organic philosophy is combination of empiricism trend and rationalism trend of mathematical philosophy.

• Journal for History of Mathematics
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• v.23 no.2
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• pp.59-74
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• 2010

Though considering of philosophy of mathematics can be optional to theoretical mathematicians, that of philosophy of mathematics-education is supposed to be indispensible to mathematics-educators. So it is natural for mathematics-educators to ask what kind of philosophy might be more desirable for mathematics-education. In this context, this essay reviews two kinds of major philosophy of mathematics, Platonism and formalism. However it shows that humanism could be more plausible alternative philosophy of mathematicseducation. In the course of entailing such a result it introduces an episode of lecture for Laplace-transformation as a speculative evidence from experience.

• Journal for History of Mathematics
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• v.24 no.4
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• pp.21-31
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• 2011

In this paper I claim that Lobachevsky's philosophy of mathematics is a kind of reservoir of contemporary philosophy of mathematics. I discuss how his philosophy contributed to the rise of non-Euclidean geometry.

• Journal for History of Mathematics
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• v.9 no.2
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• pp.22-29
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• 1996

20세기 수리철학은 전기와 후기로 나누어 볼 수 있다. 수학의 기초에 대한 논의가 활발하던 시기인 20세기 초로부터 G$\ddot{o}$del의 불완전성 정리가 발표된 30여년간을 전기로 하고, 후기를 실재론과 반실재론읜 대립과 새로운 수리철학이 대두된 최근 30여년간의 기간이라 한다면, 본고는 이미 잘 알려진 전기의 수학기초론 보다는 후기의 달라진 수리철학을 수학의 '새로운 패러다임' 으로 규정하고 그 내용과 성격을 살펴본다.

• Journal for History of Mathematics
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• v.17 no.2
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• pp.9-14
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• 2004

The present paper investigate the trace to the course of its development of Mathematical philosophy. Of the main questions which naturally suggest themselves, it will be considered by the changing process of Mathematical philosophy. The explicit sources for a history of Mathematical philosophy.,or more especially, for the relation of mathematics to philosophy, are relatively few. There is, moreover, much disagreement and dispute on the extent, influence and relation of mathematics to the philosophy of individual thinkers. A passing emphasis must be laid on the mutual influence of mathematics and philosophy on each other in the course of their development.

• Journal for History of Mathematics
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• v.18 no.4
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• pp.17-28
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• 2005

This paper aims to introduce a function and a role of history and philosophy of mathematics. Through historical examples it shows that history and philosophy of mathematics have the function to evaluate mathematics and the role to form it.

• Journal of Educational Research in Mathematics
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• v.25 no.1
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• pp.59-74
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• 2015

It is an increasing research area to explore mathematics learning from discursive perspectives. However, there have been little studies conducted on why and how discursive perspectives in mathematics learning were adopted and developed. Especially, not much discussion has been done on the later Wittgenstein's philosophical stance in terms of the relationship between language and thought as a background of discursive approach to learning mathematics. This study aims to explore the later Wittgenstein on language to get better understanding about discursive approaches to mathematics learning. For the attainment of this aim, first the later philosophy is compared with the former philosophy in depth. Then the later philosophy is discussed focusing on how his point of view on the world and the language have been changed. After providing an account of his later philosophy, it is clarified that what is discursive approaches to learning mathematics and how this philosophy brace the approaches. This research concludes with implications and limitations, as well as suggestions for future researches.

• Journal for History of Mathematics
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• v.18 no.1
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• pp.67-74
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• 2005

The purpose of this paper is to analysis with contents on thoughts and problems of philosophy of mathematics concerning around harmonical types of metaphysics and philosophy of mathematics. Moreover, we were gratefully acknowledged that the questions at issue of metaphysics and philosophy of mathematics are possible only in a philosophical position of mathematics in relation to nature of mathematical ion. These attitudes, important as they are in the study of an individual thinker, also have a pronounced effect on the future relation of mathematics to philosophy. And we can guess that many mathematician's research will have significant meaning in the future.

• Korean Journal of Logic
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• v.23 no.2
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• pp.117-159
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• 2020

In the early Wittgenstein's Tractatus, both philosophy of logic and that of mathematics belong to the most crucial subjects of it. What is the philosophical view of the early Wittgenstein in the Tractatus? Did he, for example, accept Frege and Russell's logicism or reject it? How did he stipulate the relation between logic and mathematics? How should we, for example, interpretate "Mathematics is a method of logic."(6.234) and "The Logic of the world which the proposition of logic show in the tautologies, mathematics shows in equations."(6.22)? Furthermore, How did he grasp the relation between mathematical equations and tautologies? In this paper, I will endeavor to answer these questions.

• Communications of Mathematical Education
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• v.15
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• pp.1-7
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• 2003

수학사 및 수리철학에 관한 연구는 교사양성 대학에서 더욱 강조되어야 할 부분임에도 불구하고 그에 관한 연구가 미진하다. 자연대의 수학과는 수학 그 자체가 중요하겠지만, 교사양성 대학에서는 수학 내용자체 뿐만 아니라, 수학의 역사적인 측면과 수학에 관한 인식론적인 측면이 함께 요구되어 진다. 절대적인 것으로 인식되어 온 수학에 대한 잘못된 선입견은 수학교육에도 심각한 악영향을 끼칠 수 있다. 그러나 괴델의 불완전성 정리 등으로 인해 수학에서의 논리체계는 더 이상 절대적이지 않다는 것을 알 수 있다. 본 연구에서는 숱한 오류들의 극복을 통해 발전해 온 수학사적인 측면과 그로 인하여 수학에 관한 인식론적 변화를 수학에서의 큰 사건들을 중심으로 살펴보고자 한다. 구체적으로 유클리드 기하에서 비유클리드 기하의 발견, 칸토어의 무한한 역설의 발생, 역설을 극복하기 위한 수학기토론의 탄생, 괴델의 불완전성 정리로 이어지는 과정들을 살펴보고, 그로 인해 도출되어지는 수학교육적 시사점을 논의해 보며, 이르르 바탕으로 교사양성 대학에서의 수학사 및 수리철학 강좌의 운영 방안을 제시한다.