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Conceptual Change of Definition in Mathematics: Philosophical Analysis  

Lee, Ji-Hyun (Seoul Electronics High School)
Publication Information
Journal for History of Mathematics / v.24, no.1, 2011 , pp. 63-73 More about this Journal
Abstract
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.
Keywords
definition; realism; conceptualism; nominalism;
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  • Reference
1 Prenowitz, W. & M. Jordan, Basic concepts of geometry, New York: Blaisdell, 1965.
2 Robinson, R., Definition, Oxford University Press, 1954.
3 Tall, D., Construction of objects through definition and proof, PME Working Group on AMT, Durham, NH. 1992.
4 Tugendhat, E., 논리-의미론적 예비학(하병학 역), 서울: 철학과 현실사, 1983/1999.
5 Wilder, R. L., "The role of the axiomatic method," The American Mathematical Monthly, 74(2), 115-127, 1967.   DOI   ScienceOn
6 Woozley, A, D., "Universals," In p. Edwards(Ed.), The encyclopedia of philosophy (Vol. 8, pp.194-206), New York: The Macmillan Company, 1967.
7 Hunter, D. J., Essentials of discrete mathematics, London: Jones and Bartlett Publishers, 2009.
8 Lucas, J. R., The Conceptual roots of mathematics, New York: Routledge, 2002.
9 Muller, F. A" 'The Implicit definition of the set-concept," Synthese, 138(3), 417-451, 2004.   DOI
10 Pascal, B., Pascal.의 편지 (이환 역), 서울: 지훈출판사, 2005.
11 Guthrie, W. K. C., 희랍 철학 입문: 탈레스에서 아리스토텔레스까지(박종현 역), 서울: 서광사, 1960/2004.
12 Harel, G., A, Selden, & J. Selden, "Advanced mathematical thinking: Some PME perspectives," In A. Gutierrez, p. Boero (Eds) , Handbook of research on the psychology of mathematics education: Past, present and future, Sense Publishers, 2006.
13 Heath, T. L. (1956). The thirteen books of Euclid's Elements with introduction and commentary, New York: Dover Publications.
14 조영미, 학교수학에 제시된 정의에 관한 연구, 서울대학교 박사논문, 2001.
15 Hilbert, D., Foundations of geometry (L. Unger Trans., P. Bernays Rev.), Illinois: Open court publishing company, 1899/1997.
16 Copi, I. M., 논리학 입문(민찬홍 역), 서울: 이론과 실천, 1972/1998.
17 Edwards, B. S. & M. B. Ward, "Surprises from mathematics education research: Student (mis)use of mathematical definitions," The American Mathematical Monthly, 111, 411-424, 2004.   DOI   ScienceOn
18 Gray, J., Plato's ghost: The modernist transformation of mathematics, New Jersey: Princeton University Press, 2008.
19 Alcock, L, & A, Simpson, "Definitions: Dealing with categories mathematically," For the Learning of Mathematics, 22(2), 28-34, 2002,
20 Barker, S. F., 수리철학(이종권 역), 서울: 종로서적, 1964/1983.
21 이재영, 영국 경험론 연구: 데카르트에서 리드까지, 서울: 서광사, 1999.
22 임재훈, 플라톤의 수학교육철학, 서울: 경문사, 2004.
23 조영미, 직관기하의 정의 사용 양태분석과 증명 지도에 대한 시사점, 수학교육학연구, 10(2), 215-227, 2000.
24 Abelson, R., 'Definition.' In P. Edwards(Ed.), The encyclopedia of philosophy (Vol. 2, pp. 314-324), New York: The Macmillan Company, 1967.