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      무한 개념의 진화 : Bolzano를 중심으로 = Bolzano and the Evolution of the Concept of Infinity

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      https://www.riss.kr/link?id=A101558642

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      다국어 초록 (Multilingual Abstract)

      The concept of infinity, as with other scientific concepts, has a history of evolution. In the present work we intend to discuss the subject matter with regard to Bolzano since he is considered to be the first to accept the idea of actual infinity not just from a metaphysical perspective but from a mathematical one. Like modem platonists, Bolzano defended the infinite set itself regardless of the construction process; this is based on the principal of comprehension and unicity of denotation regarding all concepts. In addition, instead of considering as paradoxical the fact that a one-to-one correspondence existed between an infinite set and its parts, he regarded it in a positive way as a special characteristic. While the Greek era recognized the existence of only one infinity, Balzano acknowledged the existence of various types of infinity and formulated a logical definition for it. The question of infinity is a touchstone of constructive method which holds an increasingly important role in mathematics. The present study stops with just a brief reference to the subject matter and we will leave further in-depth investigation for later.
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      The concept of infinity, as with other scientific concepts, has a history of evolution. In the present work we intend to discuss the subject matter with regard to Bolzano since he is considered to be the first to accept the idea of actual infinity not...

      The concept of infinity, as with other scientific concepts, has a history of evolution. In the present work we intend to discuss the subject matter with regard to Bolzano since he is considered to be the first to accept the idea of actual infinity not just from a metaphysical perspective but from a mathematical one. Like modem platonists, Bolzano defended the infinite set itself regardless of the construction process; this is based on the principal of comprehension and unicity of denotation regarding all concepts. In addition, instead of considering as paradoxical the fact that a one-to-one correspondence existed between an infinite set and its parts, he regarded it in a positive way as a special characteristic. While the Greek era recognized the existence of only one infinity, Balzano acknowledged the existence of various types of infinity and formulated a logical definition for it. The question of infinity is a touchstone of constructive method which holds an increasingly important role in mathematics. The present study stops with just a brief reference to the subject matter and we will leave further in-depth investigation for later.

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      참고문헌 (Reference)

      1 Dedekind, R, "Was sind und was sollen die Zahlen?, Braunschweig, Vieweg. Trad. Les nombres. Que sont-ils et à quoi servent-ils? Publié avec Continuité et nombres irrationnels"

      2 Levy, T, "Thābit ibn Qurra et l'infini numérique" 2000

      3 Kaufmann Felix, "The infinite in mathematics" 1978

      4 Hilbert, D, "Sur l'infini, dans J. Largeault (dir.), Logique mathématique. Textes, A. Colin"

      5 Descartes, R, "Principes de la philosophie, in Œuvres et lettres de Descartes, Bibliothèque de la Pléiade, Gallimard"

      6 Cavailles, J, "Philosophie des mathématiques" Herman 1962

      7 Sierpinski Waclaw, "Leçons sur les nombres transfinis"

      8 Leibniz G.W.F, "Lettre à Jean Bernoulli. in Mathematische Schriften" 535 (535): 1698

      9 Bolzano, B, "Les paradoxes de l'infini"

      10 Badiou Alein, "Le Nombre et les nombres" Seuil 1990

      1 Dedekind, R, "Was sind und was sollen die Zahlen?, Braunschweig, Vieweg. Trad. Les nombres. Que sont-ils et à quoi servent-ils? Publié avec Continuité et nombres irrationnels"

      2 Levy, T, "Thābit ibn Qurra et l'infini numérique" 2000

      3 Kaufmann Felix, "The infinite in mathematics" 1978

      4 Hilbert, D, "Sur l'infini, dans J. Largeault (dir.), Logique mathématique. Textes, A. Colin"

      5 Descartes, R, "Principes de la philosophie, in Œuvres et lettres de Descartes, Bibliothèque de la Pléiade, Gallimard"

      6 Cavailles, J, "Philosophie des mathématiques" Herman 1962

      7 Sierpinski Waclaw, "Leçons sur les nombres transfinis"

      8 Leibniz G.W.F, "Lettre à Jean Bernoulli. in Mathematische Schriften" 535 (535): 1698

      9 Bolzano, B, "Les paradoxes de l'infini"

      10 Badiou Alein, "Le Nombre et les nombres" Seuil 1990

      11 Belna, J. P, "La notion de nombre chez Dedekind, Cantor, Frege" Vrin 1996

      12 Gilbert Thérèse, "La notion d'infini" ellipses 2001

      13 Poincare, H, "La logique de l'infini, in Logique et fondements des mathématiques" 393-415, 1909

      14 Delahaye J.P, "L'infini est-il paradoxal en mathématiques? In Pour la science n°278, décembre 2000"

      15 Charraud, N, "Infini et Inconscient" Anthropos 1994

      16 Monnoyeur, F, "Infini des mathématiciens et infini des philosophes" Belin 1992

      17 Cantor, G, "Fondements d'une théorie générale des ensembles. Leibzig, Teubner. Trad. Milner in Cahiers pour l'Analyse 10"

      18 Cantor, G, "Correspondance Cantor-Dedekind:Philosophie des mathématiques" Paris, Hermann 179-250, 1962

      19 Lauria Philippe, "Cantor et le transfini" L'Harmattan 2004

      20 Belna, J. P, "Cantor" 2000

      21 Guillen, M, "Bridges to infinity" Jeremy P. Tarcher, Inc 1983

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      2016 0.19 0.19 0.23
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