본문 바로가기
KERD
논문KCI 등재

베르나이스와 공리적 방법

Bernays and the Axiomatic Method

박우석
한국논리학회 (Korean Association For Logic)|2011.06|논리연구 (Korean Journal of Logic)|제14권 제2호|pp. 1-37|DOI 10.22860/kafl.2011.14.2.1

0

조회

0

다운로드

3

인용

0

참고문헌

키워드

카르납Carnap공리적 방법힐버트토대의 심화Hilbert베르나이스수학의 적용BernaysAxiomatic methodDeepening the foundationsApplication of mathematics
주제분류철학

초록

베르나이스는 국내외를 막론하고 그의 업적에 상응하는 집중적 관심의 대상이 되지 못했다. 극히 최근에 이르러 베르나이스의 저작의 재출간을 비롯하여 그의 철학에 대한 재조명이 시작되고 있다. 본 논문은 이러한 흐름에 발맞춰 공리적 방법을 초점으로 베르나이스의 사상을 힐버트의 사상으로부터 섬세하게 가려내는 시도를 시작해보고자 한다. 우선 힐버트가 자신의 공리적 방법에 대해 대단한 자부심을 지녔었다는 점을 전거를 제시해가며 부각시킨다.그리고 힐버트의 공리적 방법이 공리적 방법의 역사 전체 안에서 어떤 위치를 지니는지에 관한 베르나이스의 견해를 정리해볼 것이다. 또한 중전기 베르나이스와 후기 베르나이스가 이 문제에 관하여 상당히 다른 입장을 취하는 것으로 보인다는 점에 착안하여, 중전기 베르나이스의 견해와 후기 베르나이스의 견해를 대조해 보일 것이다. 그리하여 공리적 방법에 관하여 가장 뚜렷하게 부각되는 힐버트와 베르나이스의 견해의 차이가 공리적 방법의 제일성의 문제에서 찾아진다는 점을 보여줄 것이다. 같은 맥락에서 1950년대 중반 이후 과학철학에서의 카르납의 프로젝트가 공리적 방법의 제일성에 대한 힐버트의 신념을 계승하려는 것으로 보고, 후기 베르나이스의 카르납 비판을 논의할 것이다.

Abstract

Bernays has not drawn scholarly attention that he deserves. Only quite recently, the reevaluation of his philosophy, including the projects of editing, translating, and reissuing his writings, has just started. As a part of this renaissance of Bernays studies, this article tries to distinguish carefully between Hilbert’s and Bernays’ views regarding the axiomatic method. We shall highlight the fact that Hilbert was so proud of his own axiomatic method on textual evidence. Bernays’ estimation of the place of Hilbert’s achievements in the history of the axiomatic method will be scrutinized. Encouraged by the fact that there are big differences between the early middle Bernays and the later Bernays in this matter, we shall contrast them vividly. The most salient difference between Hilbert and Bernays will shown to be found in the problem of the uniformity of the axiomatic method. In the same vein, we will discuss the later Bernays’ criticism of Carnap, for Carnap’s project of philosophy of science in the late 1950’s seems to be a continuation and an extension of Hilbert's faith in the uniformity of the axiomatic method.

참고문헌 (82)

  1. 리드, "힐베르트" (2005), 사이언스북스
  2. 박우석, "제르멜로와 공리적 방법", 논리연구, 11(2), pp.1~57 (2008), 한국논리학회
  3. 전영삼, "공간론에서 힐버트와 카르납", 과학철학, 11(2), pp.1~34 (2008), 한국과학철학회
  4. 최원배, "흄의 원리와 암묵적 정의", 논리연구, 10(2), pp.25~46 (2007), 한국논리학회
  5. 최원배, "존재와 일관성을 둘러싼 프레게", 힐버트 논쟁, 2009, pp.99(99), 127~148[DOI]
  6. Bar-Hillel, Y., "Essays on the Foundations of Mathematics, dedicated to A. A. Fraenkel on his Seventieth Anniversary" (1966), Magnes Press, The Hebrew University
  7. Bernays, Paul, "Über die Bedenklichkeiten der neueren Relativitätstheorie", Abhandlungen der Fries'schen Schule, 4(3), pp.459~482 (1913)
  8. Bernays, Paul, "Die Bedeutung Hilberts fṻr die Philosophie der Mathematik, In Die Naturwissenschaften", pp.189~197 (1998), Die Naturwissenschaften
  9. Bernays, Paul, "Zur mathematischen Grundlegung der kinetischen Gastheorie", Mathematische Annalen, 85, pp.242~255 (1922)
  10. Bernays, Paul, "Uber Nelsons Stellungnahme in der Philosophie der Mathematik", Die Naturwissenschaften, 16, pp.142~145 (1928)
  11. Bernays, Paul, "Die Philosophie der Mathematik und die Hilbertsche Beweistheorie", pp.234~265 (1998), English translation in Mancosu
  12. Bernays, Paul, "Review of Max Steck, 'Ein unbekannter Brief von Gottlob Gregeṻber Hilberts erste Vorlesungṻber die Grundlagen der Geometrie", Journal of Symbolic Logic, 7(2), pp.92~93 (1942)
  13. Bernays, Paul, "Zur Rolloe der Sprache in erkenntnistheoretischer Hisicht", Synthese, 13, pp.185~200 (1961)
  14. Bernays, Paul, "Scope and Limits of Axiomatics, In Lecture at the Delaware Seminar in the Foundations of Physics", pp.188~191 (1967), Springer Verlag
  15. Bernays, Paul, "Abhandlungen zur Philosophie der Mathematik" (1976), Wissenschaftliche Buchgesellschaft
  16. Bernays, Paul, "Selected Essays in the Philosophy of Mathematics, In Chicago and La Salle, Ill.: Open Court"
  17. Beth, E., "Carnap's Views on the Advantages of Constructed Systems Over Natural Languages in Analytic Philosophy", pp.469~502 (1963)
  18. Bohnert, H. G., "Carnap's Logicism", pp.183~216 (1975)
  19. Carnap, R., "The Logical Syntax of Language" (1937), Kegan Paul
  20. Carnap, R., "The Methodological Character of Theoretical Concepts, In Minnesota Studies in the Philosophy of Science, Vol. I: The Foundations of Science and the Concepts of Psychology and Psychoanalysis", pp.38~76 (1956), University of Minnesota Press
  21. Carnap, R., "Observational Language and Theoretical Language", pp.75~85 (1975), Dialectica
  22. Carnap, R., "Theoretical Concepts in Science", pp.158~172 (2000), Psillos
  23. Carnap, R., "On the Use of Hilbert’s e-operator in Scientific Theories, In Essays on the Foundations of Mathematics", pp.156~164 (1961), The Magnus Press
  24. Carnap, R., "Replies and Systematic Expositions", pp.859~1013 (1963), Schillp
  25. Carnap, R., "An Introduction to the Philosophy of Science" (1974), Basic Books
  26. Carson, Emily, "Intuition and the Axiomatic Method" (2006), Kluwer
  27. Corry, L., "David Hilbert and the Axiomatization of Physics (1898-1918)" (2004), Kluwer
  28. Ewald, William Bragg, "From Kant to Hilbert. A Source Book in the Foundations of Mathematics, vol. 2" (1996), Oxford University Press
  29. Feferman, S., "Lieber Herr Bernays!, Lieber Herr Gödel! Gödel on Finitism, Constructivity, and Hilbert's Program", Dialectica, 62(2), pp.179~203 (2008)
  30. Franchella, M., "Paul Bernays' Philosophical Way", Grazer philosophische Studien, 70, pp.47~66 (2005)
  31. Franks, C., "The Autonomy of Mathematical Knowledge: Hilbert's Program Revisited" (2009), Cambridge University Press
  32. Friedman, M., "Carnap and A Priori Truth", pp.47~60 (1992)
  33. Friedman, M., "Geometry, Convention, and the Relativized A Priori", pp.59~70 (1999), Reprinted in Friedman
  34. Friedman, M., "Reconsidering Logical Positivism" (1999), Cambridge University Press
  35. Friedman, M., "Dynamics of Reason" (2001), CSLI Publications
  36. Friedman, M., "Geometry as a Branch of Physics: Background and Context for Einstein's ‘Geometry and Experience’", pp.193~229 (2002)
  37. Friedman, M., "Wissenschaftslogik: the role of logic in the philosophy of science", Synthese, 164, pp.385~400 (2008)
  38. Friedman, M., "Carnap on Theoretical Terms: Structuralism without Metaphysics", Synthese, 180, pp.249~263 (2011)
  39. Friedman, M., "The Cambridge Companion to Carnap" (2007), Cambridge University Press
  40. George, A., "Mathematics and Mind" (1994), Oxford University Press
  41. Giere, R. N., "Origins of Logical Empiricism, Minnesota Studies in the Philosophy of Science, Vol. XVI" (1996), University of Minnesota Press
  42. Gödel, K., "Collected Works, Vol. 1-5" (1986), Oxford University Press
  43. Hahn, H., "Logic, Mathematics, and Knowledge of Nature", pp.24~45 (1987)
  44. Hallett, Michael, "Hilbert and Logic, In Quebec Studies in the Philosophy of Science I", pp.135~187 (1995), Kluwer
  45. Hallett, Michael, "Hilbert's Axiomatic Method and the Laws of Thought", pp.158~200 (1994)
  46. Heidelberger, M., "History of Philosophy and Science" (2002), Kluwer
  47. Heinzmann, G., "Henry Poincare: Science and Philosophy" (1996), Akademie Verlag
  48. Hendricks, V. F., "Interactions: Mathematics, Physics and Philosophy, 1860-1930" (1996), Springer
  49. Hendricks, V. F., "Proof Theory" (2000), Kluwer
  50. Hilbert, David, "Grundlagen der Geometrie, Teubner, Leibzig; English Translation of the Tenth German edition, Foundations of Geometry" (1899), Open Cour
  51. Hilbert, David, "Ueber den Zahlbegriff", pp.1089~1096 (1996), English translation in Ewald
  52. Hilbert, David, "Ueber die Grundlagen der Logik und der Arithmetik", pp.129~138 (1967), English translation in van Heijenoort
  53. Hilbert, David, "Axiomatisches Denken", pp.1105~1115 (1996), English translation in Ewald
  54. Hilbert, David, "Naturerkennen und Logik", pp.1157~1165 (1996), English translation in Ewald
  55. Hilbert, David, "Gesammelte Abhandlungen, vol. 3" (1935), Springer
  56. Hilbert, David, "Grundlagen der Mathematik, vol. 1" (1934), Springer
  57. Hilbert, David, "Grundlagen der Mathematik, vol. 2" (1939), Springer
  58. Hintikka, J., "Rudolf Carnap, Logical Empiricist" (1975), Reidel
  59. Hoffmann, M. H. G., "Activity and Sign ― Grounding Mathematics Education" (2005), Springer
  60. Jahnke, H. N., "Hilbert, Weyl, and the Philosophy of Mathematics", pp.215~228 (2005)
  61. Logica Studia Paul Bernays Dedicata, "Editions du Griffon, Neuchatel, Suisse", ~ (1959)
  62. Majer, U., "The Axiomatic Method and the Foundations of Science: Historical Roots of Mathematical Physics in Göttingen (1900-1930)", pp.11~33 (2001), Redei and Stöltzner
  63. Majer, U., "Hilbert's Program to Axiomatize Physics (in Analogy to Geometry) and its Impact on Schlick, Carnap and Other Members of the Vienna Circle", pp.213~224 (2002)
  64. Majer, U., "Hilbert's Axiomatic Approach to the Foundations of Science ― a Failed Research Program", pp.154~184 (2006), Hendricks
  65. Malament, D. B., "Reading Natural Philosophy: Essays in the History and Philosophy of Science and Mathematics" (2002), Open Court
  66. Mancosu, Paolo, "From Brouwer to Hilbert. The Debate on the Foundations of Mathematics in the 1920s" (1998), Oxford University Press
  67. Mancosu, Paolo, "Hilbert and Bernays on Metamathematics", pp.149~188 (1998), Mancosu
  68. Mṻller, G. H.,, "Sets and Classes: On the Work by Paul Bernays" (1976), North-Holland Publishing Company
  69. Park, W., "Friedman on Implicit Definition: In Search of the Hilbertian Tradition in Philosophy of Science", Erkenntnis (2011)
  70. Parsons, C.,, "Paul Bernays' Later Philosophy of Mathematics, In Lecture Notes in Logic 28, Associations for Symbolic Logic" (2006), Cambridge University Press
  71. Psillos, S., "Scientific Realism: How Science Tracks Truth" (1999), Routledge
  72. Psillos, S., "Rudolf Carnap's ‘Theoretical Concepts in Science’", Studies in History and Philosophy of Science, 31, pp.151~172 (2000)
  73. Redei, M., "John von Neumann and the Foundations of Quantum Physics" (2001), Kluwer
  74. Reichenbach, H., "The Theory of Relativity and A Priori Knowledge" (1965), University of California Press
  75. Salmon, W., "Logic, Language, and the Structure of Scientific Theories" (1994), University of Pittsburgh Press
  76. Schlick, M., "General Theory of Knowledge" (1985), Open Court
  77. Schilpp, P. A., "The Philosophy of Rudolf Carnap" (1963), Open Court
  78. Specker, E., "Paul Bernays, In Logic Colloquium 78" (1979), North-Holland Publishing Company
  79. Stöltzner, M., "How Metaphysical Is Deepening the Foundations? Hahn and Frank on Hilbert's Axiomatic Method", pp.245~262 (2002)
  80. Stöltzner, M., "The Principle of Least Action as the Logical Empiricist's Shibboleth", Studies in History and Philosophy of Modern Physics, 34, pp.285~318 (2003)
  81. Weyl, H., "Axiomatic versus Constructive Procedures in Mathematics", The Mathematical Intelligencer, 7(4), pp.10~17 (1985)
  82. Zach, R., "Completeness before Post: Bernays, Hilbert, and the Development of Propositional Logic", The Bulletin of Symbolic Logic, 5(3), pp.331~366 (1999)

관련 논문AI추천

제르멜로와 공리적 방법박우석한국논리학회 · 논리연구2008 · 제11권 제2호힐버트와 형식주의최원배한국수학사학회 · 한국수학사학회지2011 · 제24권 제4호프레게와 힐버트 – 메타이론적 증명박준용한국동서철학회 · 동서철학연구2017 · 제86호비트겐슈타인과 힐베르트 프로그램박정일한국논리학회 · 논리연구2012 · 제15권 제1호프레게의 인식론과 수리철학심철호범한철학회 · 범한철학2004 · 제33권 제2호흄의 원리와 암묵적 정의최원배한국논리학회 · 논리연구2007 · 제10권 제2호

이 간행물의 다른 논문 (3건)

직관주의적 유형론에서의 명제와 판단정인교pp. 39-75무지에의 호소 다시 보기최훈pp. 77-103존재 예화 규칙과 보편 조건문화 규칙선우환pp. 105-120
원문 보기