• Title/Summary/Keyword: Zeno's paradoxes

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A Study on the Educational Implications of Zeno's Paradoxes through Philosophical Investigation (제논의 역설에 대한 철학적 검토를 통한 교육적 시사점 고찰)

  • Baek, Seung Ju;Choi, Younggi
    • Journal for History of Mathematics
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    • v.33 no.6
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    • pp.327-343
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    • 2020
  • This study investigate philosophical discussions related to the Zeno's paradoxes in order to derive the mathematics educational implications. The paradox of Zeno's motion is sometimes explained by the calculus theories. However, various philosophical discussions show that the resolution of Zeno's paradox by calculus is not a real solution, and the concept of a continuum which is composed of points and the real number continuum may not coincide with the physical space and time. This is supported by the fact that the hyperreal number system of nonstandard analysis could be another model of a straight line or time and that an alternative explanation of Zeno's paradox was possible by the hyperreal number system. The existence of two different theories of the continuum suggests that teachers and students may not have the same view of the continuum. It is also suggested that the real world model used in school mathematics may not necessarily match the student's intuition or mathematical practice, and that the real world application of mathematics theory should be emphasized in education as a kind of 'correspondence.'

The role of Zeno on the infinite of Aristotle (아리스토텔레스의 무한론에 대한 제논의 역할)

  • Kang, Dae-Won;Kim, Kwon-Wook
    • Journal for History of Mathematics
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    • v.22 no.1
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    • pp.1-24
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    • 2009
  • In this paper we have inferred the influence of Zeno on the construction of the potential infinite of Aristotle based on arguments of Zeno's paradoxes. When we examine the potential infinite of Aristotle as the basis of the ancient Greek mathematics, we can see that they did not permit the concept of the actual infinite necessary for calculus. The reason Why they recognized the potential infinite, denying the actual infinite as seen in Aristotle's physics could be found in their attempt to escape the illogicality shown in Zeno's arguments. Accordingly, this paper could provided one of reasons why the ancient Greeks had used uneasy exhaustion's method instead of developing the quadrature involving the limit concept.

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Zeno Series, Collective Causation, and Accumulation of Forces

  • Yi, Byeong-Uk
    • Korean Journal of Logic
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    • v.11 no.2
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    • pp.127-170
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    • 2008
  • This paper aims to present solutions to three intriguing puzzles on causation that Benardete presents by considering the results of infinite series of telescoping events. The main conceptual tool used in the solutions is the notion of collective causation, what many events cause collectively. It is straightforward to apply the notion to resolve two of the three puzzles. It does not seem as straightforward to apply it to the other puzzle. After some preliminary clarifications of the situation that Benardete describes to present the puzzle, however, we can apply the notion to resolve it as well.

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