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매디의 수학적 자연주의의 존재론적 퇴보

Ontological Regress of Maddy's Mathematical Naturalism

박우석
한국논리학회 (Korean Association For Logic)|2006.08|논리연구 (Korean Journal of Logic)|제9권 제2호|pp. 117-175

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참고문헌

키워드

콰인괴델Quine수학적 실재론필수불가결성 논증mathematical realismindispensability argument수학적 자연주의매디과학과 수학의 유비mathematical naturalismMaddyanalogy of science and mathematicsGoedel
주제분류철학

초록

이 논문은 매디가 왜 수학적 실재론을 포기하고 그녀 특유의 수학적 자연주의를 표방하게 되었는지를 탐구하려 한다. 이 문제에 관하여 널리 받아들여지고 있는 한 가설에 따르면, 매디의 입장 변화는 콰인-퍼트남 필수불가결성 논증을 비판하고 포기함으로써 야기되었다. 필자는 이 가설이 지닌 설득력을 인정하지만, 그것만으로는 실재론의 포기의 충분한 이유가 될 수 없다고 생각하며, 그 대신 과학과 수학의 유비 문제가 매디의 입장 변화를 이해하는 데 더 나은 조망을 제공한다는 점을 보여주고자 한다. 이를 위해서는 콰인과 괴델에 크게 빚졌던 실재론자 시절 매디의 사유가 얼마만큼 수학과 과학의 유비에 지배되었는지를 살펴보아야 하는 동시에, 왜 매디가 이 유비를 포기함으로써 실재론을 포기하게 되는지를 이해하여야 한다. 아울러 이 유비의 포기에 대한 다소의 비판적 검토를 통해 매디의 수학적 존재론의 지적 여정을 왜 필자가 존재론적 퇴보라 믿는지에 대한 몇 가지 이유가 시사될 것이다.

Abstract

This paper is an attempt to probe the question as to why Maddy gave up mathematical realism and moved to her own version of mathematical naturalism. According to one widespread hypothesis, Maddy’s change of mind was brought up by her criticism of Quine-Putnam indispensability argument. Though quite convincing, it is not good enough to explain why one has to give up mathematical realism. The analogy of science and mathematics will instead be shown to be the better perspective to fathom Maddy’s changing beliefs. For this purpose, we have to understand to what extent Maddy's thought in her realist years, which was strongly influenced by Quine and Goedel, was governed by the analogy of science and mathematics. Also, we have to understand why Maddy gave up the analogy, and thereby gave up mathematical realism. Finally, some criticisms against Maddy's abandonment of the analogy will be examined so as to hint at reasons why I believe Maddy's intellectual journey in mathematical ontology is rather regress than progress.

참고문헌 (57)

  1. 박우석, "현대 수학철학의 백가쟁명 (잃어버린 과학을 찾아서)", 과학과 철학, 5, pp.327~340 (1994)
  2. 이진희, "수학이 과학에 필요불가결함에 기초한 수학적 실재론 연구", D, 철학과, pp.2005
  3. Baker, Alan, "Maximizing Principles and Mathematical Methodology (Logique et Analyse)", pp.179~281 (2002)
  4. Benacerraf, P, "What Numbers Could Not Be", pp.272~294 (1965)
  5. Benacerraf, "Mathematical Truth", pp.403~420 (1973)
  6. Benacerraf, P, "Philosophy of Mathematics, 2nd edition" (1983), Cambridge: Cambridge University Press
  7. Burgess, John P, "A Subject with No Object" (1997), Oxford: Clarendon Press
  8. Burgess, John P., "Comments on Penelope Maddy's 'Mathematical Existence' (unpublished comment read at Chapel Hill Colloquim ; available at his homepage)" (2004)
  9. Cassou-Noguès, P, "Goedel and ‘the Objective Existence’ of Mathematical Objects", History and Philosophy of Logic, 26, pp.211~228 (2005)
  10. Chihara, Charles S., "A Goedelian Thesis Regarding Mathematical Objects: Do They Exist? And Can We Perceive Them?", Philosophical Review, 91, pp.211~227 (1982)
  11. "Constructibility and Mathematical Existence" (1990), Oxford: Clarendon Press; New York: Oxford University Press
  12. "The Worlds of Possibility" (1998), Oxford: Oxford University Press
  13. "A Structural Account of Mathematics" (2004), Oxford : Oxford University Press
  14. Colyvan, Mark, "In Defence of Indispensability", Philosophia Mathematica, 6, pp.39~62 (1998)
  15. "Review of Maddy", Mind, 108, pp.586~590 (1999)
  16. "The Indispensability of Mathematics" (2001), New York: Oxford University Press
  17. Decock, L, "uine's Weak and Strong Indispensability Argument", Journal of the General Philosophy of Science, 33, pp.231~250 (2003)
  18. Dieterle, Jill M, "Mathematical, Astrological, and Theological Naturalism", Philosophia Mathematica, 7, pp.129~135 (1999)
  19. Field, Hartry H, "Realism, Mathematics and Modality" (1989), Oxford & New York: Blackwell
  20. Gaerdenfors, P., "Knowledge in Flux" (1988), Cambridge, Mass.: MIT Press
  21. Gaerdenfors, P, "Belief Revision (Handbook of Logic in Artificial Intelligence and Logic Programming Vol. 4, Epistemic and Temporal Reasoning)", pp.35~132 (1995), Oxford: Clarendon Press
  22. Goedel, Kurt, "What Is Cantor's Continuum Problem?", pp.470~485 (1944)
  23. Benacerraf, "Russell's Mathematical Logic", pp.447~469 (1947)
  24. Leng, M, "Whats Wrong with Indispensability?", Synthese, 131, pp.395~417 (2002)
  25. Levine, A, "Conjoining Mathematical Empiricism with Mathematical Realism: Maddy's Account of Set Perception Revisited", Synthese, 145, pp.425~448 (2005)
  26. MacCallum, David, "Conclusive Reasons that We Perceive Sets", International Studies in the Philosophy of Science, 14, pp.25~42 (2000)
  27. Maddy, P, "Perception and mathematical intuition", Philosophical Review, 89, pp.163~196 (1980)
  28. "Realism in Mathematics" (1990), Oxford University Press
  29. "Indispensability and practice", Journal of Philosophy, 89, pp.275~289 (1992)
  30. "Does V equal L?", Journal of Symbolic Logic, 58, pp.15~41 (1993)
  31. Prawitz, D, "Taking naturalism seriously (Logic, Methodology and Philosophy of Science IX)", pp.383~407 (1994), Elsevier Science
  32. "Naturalism and Ontology", Philosophia Mathematica, 3, pp.248~270 (1995)
  33. Morton, A, "The legacy of "Mathematical truth" (Benacerraf and his Critics)", pp.60~72 (1996), Oxford: Blackwell, ), pp.60-72.
  34. "Naturalism in Mathematics" (1997), Oxford University Press
  35. Schirn, M, "Naturalizing mathematical methodology (Philosophy of Mathematics Today)", pp.175~193 (1998), Oxford: Oxford University Press
  36. Dales, G, "How to be a naturalist about mathematics (Truth in Mathematics)", pp.161~180 (1998), Oxford: Oxford University Press
  37. Boghossian , P, "Naturalism and the a priori (New Essays on the A Priori)", pp.92~116 (2000), Oxford: Oxford University Press
  38. Tomberlin, J, "Naturalism: friends and foes(Philosophical Perspectives 15, Metaphysics)", pp.37~67 (2001), Madlen, MA: Blackwell
  39. "Some naturalistic remarks on set theoretic method", Topoi, 20, pp.17~27 (2001)
  40. Shapiro, S, "Three forms of naturalism (Oxford Handbook of Philosophy of Logic and Mathematics)", pp.437~459 (2005), Oxford: Oxford University Press
  41. "Mathematical Existence", Bulletin of Symbolic Logic, 11(3), pp.351~376 (2005)
  42. Park, Woosuk, "Belief Revision in Baduk = 바둑학연구", 2(2)통권 : 4, pp.1~11 (2005)
  43. Paseau, A, "Naturalism in Mathematics and the Authority of Philosophy", British Journal for the Philosophy of Science, 56, pp.377~396 (2005)
  44. Peressini, A., "Troubles with Indispensability: Applying Pure Mathematics in Physical Theory", Philosophia mathematica, 5, pp.210~227 (1997)
  45. "Review of Colyvan, The Indispensability of Mathematics", Philosophia mathematica, 11, pp.208~223 (2003)
  46. Pincock, C, "A Revealing Flaw in Colyvan's Indispensability Argument", Philosophy of Science, 71, pp.61~79 (2004)
  47. Putnam, Hilary, "Philosophy of Logic", pp.323~357 (1971)
  48. Putnam, "What Is Mathematical Truth?", pp.60~78 (1975)
  49. "Mathematics, Matter and Method" (1979), Cambridge: Cambridge University Press
  50. Quine, W.V.O., "On What There Is", pp.1~19 (1948)
  51. "From a Logical Point of View, 2nd edition" (1980), Cambridge: Harvard University Press
  52. "Theories and Things" (1981), Cambridge: Cambridge University Press
  53. Resnik, Michael D, "Scientific versus Mathematical Realism: The Indispensability Argument", Philosophia Mathematica, 3, pp.166~174 (1995)
  54. Russell, B, "On ‘Insolubilia’ and Their Solution by Symbolic Logic", pp.190~214 (1906)
  55. Russell, "The Regressive Method of Discovering the Premises of Mathematics", pp.272~283 (1907)
  56. Essays in Analysis, "Lacky, D", London: Allen and Unwin, ~ (1973)
  57. Sober, Elliott, "Mathematics and Indispensability", Philosophical Review, 102, pp.35~57 (1993)

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