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Fuzzy Concepts and Fuzzy Logic in Historical and Genetic Epistemology

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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 325))

Abstract

This paper discusses epistemology in two variations: Genetic and Historical Epistemology. Historical Epistemology combines research in history and philosophy of science to study developments in scientific research whereas Genetic Epistemology is the study of the cognitive development in childhood. We consider Kuhn’s theory of scientific paradigms and paradigm changes on the one hand and Piagest’s Genetic Epistemology of cognitive development on the other. We present parallels of these two structuralist approaches and we introduce “unsharp concepts” into these views. Then the paper throws a glance at their fuzzy extensions. Because of these “fuzzifications” we make an argument for using fuzzy instead of crisp concepts in Genetic and Historical Epistemology.

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Notes

  1. 1.

    This is a quotation of Lotfi Zadeh’s paper [56] that appeared in 1962—three years before he founded the theory of fuzzy sets!

  2. 2.

    In later times Kuhn used the term “disciplinary matrix” instead of “paradigm”.

References

  1. Belohlavek, R., Klir, G.J. (eds.): Concepts and Fuzzy Logic. The MIT Press, Cambridge (2011)

    MATH  Google Scholar 

  2. Anele, D.I.O.: Development in Thomas Kuhn’s theory of perception of similarity relationships in science. Lumina 22(1), 1–25 (2011)

    Google Scholar 

  3. Balzer, W., Moulines, C.U., Sneed, J.D.: An Architectonic for Science. The Structuralist Program. Reidel, Dordrecht (1987)

    Book  MATH  Google Scholar 

  4. Bird, A.: “Thomas Kuhn”. Stanford Encyclopedia of Philosophy. Metaphysics Research Lab at Stanford University. First published Fri Aug 13, 2004; substantive revision Thu Aug 11, (2011). http://plato.stanford.edu/entries/thomas-kuhn/, Accessed February 19, 2015

  5. Bourbaki, N (pseudo.): Elements of Mathematics: Theory of Sets, Addison-Wesley, Reading (1968)

    Google Scholar 

  6. Dizikes, P.: 3 Questions: David Kaiser on Thomas Kuhn’s paradigm shift. Scholars mark 50th anniversary of ‘The Structure of Scientific Revolutions’, MIT News Office, December 6, (2012). http://newsoffice.mit.edu/2012/3-questions-david-kaiser-on-thomas-kuhns-paradigm-shift-1206 Accessed February 19, 2015

  7. Ellington, J.W.: The Unity of Kant’s Thought in his Philosophy of Corporeal Nature, Philosophy of Material Nature. Hackett Publishing Company, Indianapolis (1985)

    Google Scholar 

  8. Fölsing, A.: Heinrich Hertz. Hoffmann und Campe, Hamburg (1997)

    Google Scholar 

  9. Frege, G.: Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens, Halle a. S.: Louis Nebert, 1879. Translated as Concept Script, a formal language of pure thought modelled upon that of arithmetic, by S. Bauer-Mengelberg in J. van Heijenoort (ed.) From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931, Harvard University Press, Cambridge (1967)

    Google Scholar 

  10. Frege, G.: Funktion und Begriff, 1891. In: Patzig, G. (ed) Frege, G.: Funktion, Begriff, Bedeutung, Vandenheoeck & Ruprecht, Göttingen, pp. 18–39 (1986)

    Google Scholar 

  11. Frege, G.: Grundgesetze der Arithmetik, vol. 2, Jena: Hermann Pohle, 1893–1903, Bd. II. English translation: Basic Laws of Arithmetic, translated and edited with an introduction by Ebert, P.A., Rossberg, M., Oxford University Press, Oxford (2013)

    Google Scholar 

  12. Frege, G.: Nachgelassene Schriften. Meiner, Hamburg (1969)

    MATH  Google Scholar 

  13. Freud, S.: Three Essays on the Theory of Sexuality VII, 1905, 2nd edn. Hogarth Press (1955)

    Google Scholar 

  14. Goguen, J.A.: Categories of fuzzy sets: applications of a non-cantorian set theory. Ph.D. Thesis. University of California at Berkeley, June 1968

    Google Scholar 

  15. Goguen, J.A.: The Logic of Inexact Concepts. Synthese 19, 325–373 (1969)

    Article  MATH  Google Scholar 

  16. Kant, I.: Critic of Pure Reason, Chapter III. The Architectonic of Pure Reason, The Cambridge Edition of the Works of Immanuel Kant, Cambridge University Press: 1998). http://www.philosophy-index.com/kant/critique_pure_reason/ii_iii.php. Accessed 9.2.2015

  17. Kuhn, T.S.: The road since structure: Philosophical essays, 1970–1993. In: Conant, J., Haugeland, J., (eds.) Chicago: University of Chicago Press (2000)

    Google Scholar 

  18. Kuhn, T.S.: The Structure of Scientific Revolutions, 1st edn, University of Chicago Press (1962)

    Google Scholar 

  19. Kuhn, Thomas S.: The Copernican Revolution: Planetary Astronomy in the Development of Western Thought, Cambridge. Harvard University Press, Massachusetts (1957)

    Google Scholar 

  20. Kuhn, ThS: The Essential Tension, pp. 297–308. The University of Chicago Press, Chicago (1977)

    Google Scholar 

  21. Lakoff, G.: Hedges: a study in meaning criteria and the logic of fuzzy concepts. J. Philos. Logic 2, 458–508 (1972)

    MathSciNet  Google Scholar 

  22. Loftus, G., et al.: Introduction to Psychology, 15th Edn, London, Cengage, (2009)

    Google Scholar 

  23. Machery, E.: Concepts are not a natural kind. Philos. Sci. 72, 444–467 (2005)

    Article  Google Scholar 

  24. MacIsaac, D.: The Pedagogical Implications of Parallels between Kuhn’s Philosophy of Science and Piagets’ Model of Cognitive Development. http://physicsed.buffalostate.edu/danowner/kuhnpiaget/KP1.html

  25. Margolis, E., Lawrence, S.: “Concepts”. Stanford Encyclopedia of Philosophy. Metaphysics Research Lab at Stanford University. First published Mon Nov 7, 2005; substantive revision Tue May 17, (2011). Accessed February 19, 2015

    Google Scholar 

  26. Merton, R.: Science, Technology and Society in Seventeenth Century England. Osiris IV(2), 360–632 (1938)

    Article  Google Scholar 

  27. Piaget, J., Garcia, R.: Psychogenesis and the History of Science. (H. Fieder, Trans.). Columbia University Press, New York (1988). (Original published in 1983)

    Google Scholar 

  28. Piaget, J.: Les notions de mouvement et de vitesse chez l’enfant, Paris (1946)

    Google Scholar 

  29. Piaget, J.: The Child’s Conception of Causality, transl. by M. Gabain, London (1930)

    Google Scholar 

  30. Rheinberger, H.-J.: “Gene”, Stanford Encyclopedia of Philosophy. Available at: http://plato.stanford.edu/entries/gene/. Accessed 10.2.2015

  31. Rheinberger, H.-J.: Experimental complexity in biology: some epistemological and historical remarks. Philosophy of science. In: Proceedings of the 1996 Biennial Meeting of the Philosophy of Science Association, Supplement to, vol. 64(4), pp. 245–254 (1997)

    Google Scholar 

  32. Rheinberger, H.-J.: Gene Concepts. Fragments from the perspective of molecular biology. In: Beurton, P., Falk, R., Rheinberger, H.-J. (eds.) The Concept of the Gene in Development and Evolution. pp. 219–239, Cambridge, Cambridge University Press (2000)

    Google Scholar 

  33. Rosch, E.: Natural categories. Cogn. Psychol. 4, 328–350 (1973)

    Article  Google Scholar 

  34. Sadegh-Zadeh, K.: Handbook of Analytical Philosophy of Medicine. vol. 113, Springer, Dordrecht (2012). (Philosophy and Medicine)

    Google Scholar 

  35. Sadegh-Zadeh, K.: The fuzzy revolution: goodbye to the Aristotelian Weltanschauung. Artif. Intell. Med. 21, 1–25 (2001)

    Article  Google Scholar 

  36. Santrock, J.W.: Life-Span Development, 9th edn. McGraw-Hill College, Boston (2004)

    Google Scholar 

  37. Santrock, J.W.: A Topical Approach To Life-Span Development, pp. 211–216. McGraw-Hill, New York (2008)

    Google Scholar 

  38. Seising, R.: Between empiricism and rationalism: a layer of perception modeling fuzzy sets as intermediary in philosophy of science. In: Melin, P. et al. (eds.) Theoretical Advances and Applications of Fuzzy Logic and Soft Computing. Proceedings of the IFSA 2007 World Congress Theory and Applications of Fuzzy Logic and Soft Computing,Cancun Mexico, 2007. Berlin, Springer (Advances in Soft Computing 42, LNCS, vol. 4529), pp. 101–108 (2007)

    Google Scholar 

  39. Seising, R.: Fuzzy sets and systems and philosophy of science. In: Seising, R., (ed.) Views on Fuzzy Sets and Systems. pp. 1–35, Springer, Berlin (2009)

    Google Scholar 

  40. Seising, R.: Interview with G. Lakoff, August 6, 2002, UC Berkeley, Dwinell Hall

    Google Scholar 

  41. Seising, R.: Interview with L. A. Zadeh, July, 26, 2000,UC Berkeley, Soda Hall, see [40]

    Google Scholar 

  42. Seising, R.: Scientific theories and the computational theory of perceptions: a structuralist view including fuzzy sets. In: Stepnika, M, et al. (eds.) New Dimensions in Fuzzy Logic and Related Technologies. Proceedings of the 5th EUSFLAT Conference, Ostrava, Czech Republic, vol. 1, pp. 401–408 ( 2007)

    Google Scholar 

  43. Seising, R.: The Fuzzification of Systems. The Genesis of Fuzzy Set Theory and Its Initial Applications—Developments up to the 1970s, Springer, Berlin (2007)

    Google Scholar 

  44. Sneed, J.D.: The Logical Structure of Mathematical Physics. Reidel, Dordrecht (1971)

    Book  Google Scholar 

  45. Stegmüller, W.: The Structure and Dynamics of Theories. Springer, New York (1976)

    Book  MATH  Google Scholar 

  46. Steup, M.: “Epistemology”, The Stanford Encyclopedia of Philosophy (Winter 2013 Edition). http://plato.stanford.edu/archives/win2013/entries/epistemology/. Accessed 9.2. 2015

  47. Suppes, P.: A set of independent axioms for extensive quantities (1951). See: http://suppes-corpus.stanford.edu/browse.html?c=mpm&d=1950

  48. Suppes, P.: Some remarks on problems and methods in the philosophy of science (1954). See: http://suppes-corpus.stanford.edu/browse.html?c=mpm&d=1950

  49. Suppes, P.: Introduction to Logic. Van Nostrand, New York (1957)

    MATH  Google Scholar 

  50. Wadsworth, B.: Piaget’s Theory of Cognitive Development: An Introduction for Students of Psychology and Education. David McKay & Company, NewYork (1971)

    Google Scholar 

  51. Wadsworth, B.: Piaget for the Classroom Teacher. Longman, New York (1978)

    Google Scholar 

  52. Wittgenstein, L.: Tractatus logico-philosophicus. Routledge & Kegan Paul, London (1922)

    MATH  Google Scholar 

  53. Wittgenstein, L.: Philosophical Investigations. Blackwell Publishing, Oxford (1953)

    Google Scholar 

  54. Zadeh, L.A.: Autobiographical note, undated type-written manuscript. after 1978

    Google Scholar 

  55. Zadeh, L.A.: Fuzzy Languages and their relation to human and machine intelligence. In: Marois, M, (ed.) Man and Computer. Proceedings of the First International Conference on Man and Computer, Bordeaux, June 22–26 1970. Basel: Karger, S., 1972, pp. 130–165

    Google Scholar 

  56. Zadeh, L.A.: From circuit theory to systems theory. Proc. IRE 50, 856–865 (1962)

    Article  MathSciNet  Google Scholar 

  57. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  58. Zadeh, L.A.: My life and work—a retrospective view. Appl. Comput. Math. 10(1), 4–9 (2011)

    MATH  MathSciNet  Google Scholar 

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Acknowledgments

Work leading to this paper was partially supported by the Foundation for the Advancement of Soft Computing Mieres, Asturias (Spain).

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Seising, R. (2015). Fuzzy Concepts and Fuzzy Logic in Historical and Genetic Epistemology. In: Seising, R., Trillas, E., Kacprzyk, J. (eds) Towards the Future of Fuzzy Logic. Studies in Fuzziness and Soft Computing, vol 325. Springer, Cham. https://doi.org/10.1007/978-3-319-18750-1_17

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