• Korean Journal of Logic
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• v.18 no.1
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• pp.39-64
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• 2015

The most difficult problem for mathematical Platonism is the epistemological problem raised by Paul Benacerraf and Hartley Field. Recently, Mark Balaguer argued that his version of mathematical Platonism, Full Blooded Plantonism (FBP), can solve the epistemological problem. In this paper, I show that there are serious problems with Balaguer's argument. First, I analyse Balaguer's argument and reveal a formal defect in his argument. Then I raise an objection based on an analogical argument. Finally, I disarm some potential moves from Balaguer.

• 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 for History of Mathematics
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• v.15 no.1
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• pp.93-98
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• 2002

In this paper, we critically survey the mathematical Platonism in respect to its abstract, ahistorical, asocial and acultural character. The uncertainty of man's concepts is investigated with special attention to evolutionary theory, philosophical and epistemological developments regarding the cognitive unconsciousness and the embodied mind. We research into the implication of the Darwin machine theory for human consciousness and Wittegenstein's philosophy of mathematics.

• Research in Mathematical Education
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• v.7 no.1
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• pp.1-10
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• 2003

This research reviewed literatures on proof in mathematics education. Several views of proof can be classified (and identified) such as psychological approach (Platonism, empiricism), structural approach (logicism, formalism, intuitionism) and social approach (ontology, axiomatic systems). All these views of proof are valuable in mathematics education society. The concept of proof can be found in the form of analytic knowledge not of constructive knowledge. Human beings developed their knowledge in the sequence of constructive knowledge to analytic knowledge. Therefore, in mathematics education, the curriculum of mathematics should involve the process of cognitive knowledge development.

• Research in Mathematical Education
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• v.5 no.2
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• pp.127-132
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• 2001

Mathematics holds a key position among many subjects of school education. Besides having an instrumental value, mathematics for the general public has been underestimated. Thus, in this paper we examine how western educational theorists have emphasized the value of mathematics as humanities form of education. First of all, we discuss Platonism as a philosophical basis of the ancient Greek mathematics education. Next, we examine the thoughts of Froebel, who provided the theoretical basis for the public education since 19th century, and discuss the value of mathematics teaching in their humanistic educational thoughts. Also, we examine the humanistic value of mathematics education in Dewey\\`s educational philosophy, which criticized the traditional western ethics and epistemology, and established instrumentalism. In this paper, we recognize the humanistic values of mathematics education through the historical examination of the philosophies of mathematics education.

• School Mathematics
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• v.6 no.4
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• pp.313-324
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• 2004

One of the major roots of the value and power of mathematical knowledge is the belief on ‘the Pythagorian-Platonic divine mathematicity of the universe’ and the ‘pre-established harmony between mathematics and physics’. This kind of the nature of mathematical knowledge demands strongly the school mathematics to become a subject for humanity education going beyond the practical usefulness. Here, investigating the roots of the thought of mathematical education, we tried to clarify that the traditional educational ideal which has maintained the theoretical knowledge-centered mathematical education is the education of humanity, and investigate the way today's mathematical pedagogy should first turn to if it should realize this ideal.

• Journal of Educational Research in Mathematics
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• v.18 no.2
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• pp.223-237
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• 2008

In this paper, We focus on grasping De Morgan's perspectives on mathematics education systematically. His perspectives can be summarized as followings. First, historico-genesis of mathematics must be considered in the teaching and learning of mathematics. Second, mathematical conception of students must be formulated progressively. Third, it is important to use errors which come out continually in the process of passing from inductive stage to deductive stage. Fourth, personal knowledge of students is important in the teaching and learning of mathematics. These De Morgan's four perspectives are the way of approach for experiencing moral certainty first of all to get to mathematical certainty. Moral certainty which he presented is a combination of rationality and humanity to fill up gaps between Platonism and general public education.