• Journal for History of Mathematics
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• v.14 no.1
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• pp.83-100
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• 2001

The paper analyzes the philosophy of mathematics and outlook on the mathematics education as the philosophy of mathematics in the history of mathematics. We have found that various views of the human society have led us to the various philosophy of mathematics. This change of philosophy have important implications to the didactics of mathematics. This study tries to find out the direction of outlook on the mathematics education in the future.

• 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.30 no.4
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• pp.247-258
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• 2017

The goal of this essay is to examine metaphors for mathematics and to discuss philosophical problems related to them. Two metaphors for mathematics are well known. One is a tree and the other is a building. The former was proposed by Pasch, and the latter by Hilbert. The difference between these metaphors comes from different philosophies. Pasch's philosophy is a combination of empiricism and deductivism, and Hilbert's is formalism whose final task is to prove the consistency of mathematics. In this essay, I try to combine two metaphors from the standpoint that 'mathematics is a part of the ecosystem of science', because each of them is not good enough to reflect the holistic mathematics. In order to understand mathematics holistically, I suggest the criteria of the desirable philosophy of mathematics. The criteria consists of three categories: philosophy, history, and practice. According to the criteria, I argue that it is necessary to pay attention to Pasch's philosophy of mathematics as having more explanatory power than Hilbert's, though formalism is the dominant paradigm of modern mathematics. The reason why Pasch's philosophy is more explanatory is that it contains empirical nature. Modern philosophy of mathematics also tends to emphasize the empirical nature, and the synthesis of forms with contents agrees with the ecological analogy for mathematics.

• 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.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.

• 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 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 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.29 no.1
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• pp.31-44
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• 2016

This essay aims to suggest roughly the "philosophy of limits." The limits mainly refer to those of human experiences and rational thoughts. The philosophy of limits consist of three theses and two consequences(L, M). (1) The limits are necessarily supervenient in the course of searching knowledge. (2) The limits cannot be dissipated ultimately. (3) To recognize the limits is not only an intellectual recognition but also a beginning of whole personality's reaction. (L) It is a rational decision to accept the limits and leave the margins (yeoback/yeoheuck) rather than to try to remove them. (M) To leave the margins (yeoback/yeoheuck) is characteristic of being human, and enables one to harmoniously communicate with others. To justify the philosophy of limits, this essay examine the limits discussed in mathematics and philosophy: set theory, Godel's Incompleteness Theorem, Galois Theorem in mathematics; and Hume, Kant, Kierkegaard, and Wittgenstein in philosophy. I try to interpret consciousness of limits in various cultures. I claim that consciousness of the limits contribute to lucidity of human identity, communication between persons, stimulation of creative thinking.

• 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.