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  • -BOURBAKI-* . **

    20 ' - ( ). . (), ' , Bourbaki, . , , Bourbaki . , 40 . * ..., . . . 5-7-2002. ** . . ,

  • , , , , (structuralism = , ) 20 . . . 1. . , , , 2, . 19 20 Ferdinand de Saussure (1857-1913) . 1916 "(Course in general linguistics) 3. Lucien Levy Bruhl (1857-1939) . (Les fonctions mentales dans les socits infrieures) 19224. , , Ernst Cassirer (1874-1945) (Substanzbegriff und Funktionsbegriff) 1910 5. , , o Jean Piaget (1896-1980)

    1 , ..-, .. :" ", . , , 1986, 5, . 97. 2 (, , ). , , . . , : , , ." . . ", 5, .99. 3 , : " Ferdinand de Saussure", , 42, 1985, . 325-337 4 ". . ", 3, . 204. 5 Cassirer, Ernst: " Substance and function and Einstein's theory of Relativity ", Dover Publications, 1953, .93.

    2

  • . (1947) . 6. Levy-Bruhl . Claude Levi Strauss (. 1908), , Levy Bruhl. 1 2 (1958 1973) . Levi Strauss 7. , , 20 , Noam Chomsky (.1928) (1957) 8. , . OULIPO (Ouvroir de Literature Potentielle = ) 1960. 9. , ,

    Jean Piaget

    6 " - ", 8, , 1988, . 263-264. 7 Aubin, David: "The withering immortality of Nicolas Bourbaki", Science in Context, vol. 10, 2, 1997, . 301-302. 8 Chomsky, Noam: " ", . , 1992, . 9 Aubin (1997), . 320-321.

    3

  • . , . , . . , . . . : 10. . : 1) , , 2) 3) 11. ( ) 12. , , , - 13. 14. , . . . Piaget . :

    10 , : " ", . ., , 1989, . 148-149 11 , : " : ", V, , , 1987, . 107 12 Piaget, Jean: "", . ., , , 1972, . 32. 13 www.Britannica.com/structuralism. 14 Cerisy-la-Salle 1959 "Dictionnaire Terminologique de sciences socials" ( ) . Aubin (1997), . 314-315

    4

  • , 15. , .. Lucien Goldman, Piaget. Goldman, , 16. 17. 18. . A. Cicourel , , , , Chomsky. 19. , , . . Rene Thom 20. . , .

    15 Piaget (1972), . 31. 16 Goldman, Lucien: " ", , 1986, . ., .134. 17 Bruner, S.Jerome: " ", , , 1960, .23. 18 (1987), V, .108. 19 Craib, I. :" . ", , 1998, . 206-207. 20 Thom, Ren: " ", . . , 1985, .206.

    5

  • . , , . : " "", "". , , . ' "21. . Q = { ( a1, a2) : a1/a2, a1Z, a2Z, a2 0}22 . . , . < 1 23. , 24. . , ' , . Martin Ohm (1792-1872) 1828 " "(Versuch eines vollkammen consequenten systems der Mathematik) 25. , . , George Peacock (1791-1850) 21 Tymoczko, Thomas: "Structuralism and post- Modernism in the philosophy of mathematics", Palmer Press, 1994, .49. 22 , .: "", , , 1993, .98-99. 23 , : " ", ', , 1996, .7. 24 (1996), .8. 25 Nov, Lubs: "Origins of modern algebra", Noordhoff International Publishing, Leyden, 1973, .83 &89.

    6

  • " "( Report on the recent progress and the present state of certain branches of analysis)26. O Evariste Galois (1811-1832).

    Evariste Galois

    O Galois . , Galois , , 27. , . Richard Dedekind (1831-1916)28. 1872 . Felix Klein (1849-1925) " " (Erlangen Programme) . , 29. , , 19 David Hilbert (1862-1943). 26 Nov(1973), .190 & 199. 27 Wussing, H.:''The genesis of the abstract Group concept'', The MIT press, London, 1984, .102 & 111. 28 ''Companion Encyclopedia of the history of Philosophy'', vol.1, I.Grattan-Guinness, UK, 1994, .752. 29 Wussing (1984), .28.

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  • Hilbert 1900 " , " 30. Hilbert, Paul Bernays, Hilbert . " " 31. Hilbert , , " " (Grundlagen der geometrie) 1899, , "" 1920 32. Hilbert Elie Cartan "" " " 189433. Elie Cartan Henri Cartan Bourbaki. Bourbaki 34.

    David Hilbert

    30 Aubin (1997), .305. 31 The Encyclopedia of Philosophy: Hilbert, David by Paul Bernays, The Macmillan Company and the Free Press, NY, 1967, .497. 32 Corry, Leo:''The origins of eternal truth in mathematics: Hilbert to Bourbaki and beyond'', Science in Context, is.10, vol.2, .256. 33 Aubin (1997), .341. 34 Ren Thom, o Benot Mandelbrot Michael Resnik. Aubin (1997), .330.

    8

  • , , . 35. 36. . . . , , : -. , , . 37. " " Bourbaki. ' , , .

    35 : , , Piaget (1972), .43. 36 (1987), .107-108. 37 Rickart, Charles: ''Structuralism and Mathematical thinking'', The nature of mathematical thinking, ed. Lawrence Erlbaum Associates, NJ, 1996, .290.

    9

  • BOURBAKI - Bourbaki38. Bourbaki ( B.) , . . 39. ' , , . . ' .

    Bourbaki . Bourbaki40 1934 , Andr Weil Henri Cartan, . 41 .

    38 Corry, Leo: "Nicolas Bourbaki and the concept of mathematical structure", . Synthse, is.92, Kluwer Academic Publishers, 1992, .315. 39 Aubin (1997), .299. 40 Nicholas Bourbaki Ecole Normale, . . . . . . Beaulieu, Liliane: "A Parisian caf and ten proto-Bourbaki meetings (1934-1935)", . The Mathematical Intelligencer, vol.15, no.1, 1993, New York, .29. 41 , , ' . Aubin (1997), .304.

    10

  • 10 1934 Bourbaki. Weil, Cartan, Jean Dieudonn, Paul Delsarte, Claude Chevalley Ren de Possel. . Samuel Eilenberg, Jean Pierre Serre Alexander Grothendieck42.

    . . ' , . , ' . . . . . . , . 50 . 43.

    Bourbaki 1939: S.Weil, Ch. Pisot, A. Weil, J. Dieudonn, C. Chobauty, Ch. Ehresmann, J. Delsarte

    , , . . van der Waerden .

    42 Corry (1992), .318-319. 43 Dieudonne, Jean: " . Bourbaki", , 7, 1977, . 65-68.

    11

  • ' , " " "". . , , . , , . , ., . , , , , , , Lie, , , , , , , , . , , , , , , , , 44. . " " . , , . . , , . , . . , , . . 1939 . , " Mode d' emploi de ce trait" (Elments de Mathematiques), " ". 10. " " . "" . " " R, Rn C. " " Taylor. " "

    44 Dieudonne (1977), .61-62.

    12

  • " " Lie". modules , , 45. 1949 . . '70 . .

    45 Bos, J. M. Henk: Lectures in t1991, .149 46 Corry (1992), .320

    lments Bourbaki

    Hilbert. " "Commutative Algebra" . 1973. 1948 " " " " 46.

    .

    , . , . , ,

    he istory of athematics, American Mathematical Society,

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  • BOURBAKI KAI , , . Bourbaki , : Bourbaki Bourbaki ; . , . , , , , Bourbaki 47. Bourbaki . Bourbaki 184048. 1900. , Bourbaki - LArc (1965) LEsprit (1963,1967)49. . , Bourbaki 47 Jean Piaget . 1955 L'Enseignement des Mathematiques, 11-33, . Neuchatel . 1968 Que je sais? Structuralism Piaget . , Claude Levi Strauss . , Jacques Ronband Le grand incendie de Londres, Paris : Seuil, 1989, . 148, Bourbaki>>. 48 Dieudonn, Jean : The difficult birth of mathematical structures , 1979, .9 49 Aubin (1997) . 316

    14

  • . . Bourbaki 30 . , . , 50. Bourbaki , . . . Bourbaki . Bourbaki 51. , Bourbaki . (Elements de Mathematiques) 1939 (mother structures) Bourbaki. (.. ), (.. , ) (.. , ). . . . . . ..52. Bourbaki , .

    50 Bourbaki, Nicholas: The architecture of Mathematics, . ., . , 1 (1994), . 21-37. 51 Aubin (1997), . 326-327. 52 , :

    , . , 1 (1994), . 14-15.

    15

  • Bourbaki53. Bourbaki . Bourbaki , . Bourbaki . , , , . , 1960, , , 54. Bourbaki , , . , Bourbaki .

    53 . . Galois, Erlangen Klein , (1994), . 14-15. 54 Aubin (1997), . 327-328.

    16

  • (Bourbakism) Bourbaki, . ., , . , . , . . 55. . . . . . 56. , , ., -Bourbakism. - (.. , , ..) . , .57, . . 1960 . , " " () . "" ;

    55 Corry, Leo "Nicolas Bourbaki and the concept of Mathematical structure", . Synthse, . 92, . 315-348, 1992, Kluwer Academic Publishers, . 318-319. 56 - . . 57 , .: " ", . , 1997, . 60.

    17

  • 58. . . , . '50 '60, 59. . . . . . , , . . - , 60. . (absolutist view) . . , "status". . . , , 58 Kneebone, G.T.: "Philosophy and the foundations of Mathematics", D.Van Nostrand company limited, 1963, . 328-329. 59 Corry (1992), . 319 60 , : " " . Gutenberg, 1994, . 93.

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  • , . , , . , . 61. . . . Weintramb-Mirowski :"The pure and the Applied: Bourbakism comes to Mathematical Economics" Israel "Un Aspetto Ideologico della Mathematica Contemporanea: Il Bourbakismo"62. . . . . , . 20 .

    61 , (1994) .94. 62 : Israel, G.: "Un Aspetto Ideologico della Mathematica Contemporanea: Il Bourbakismo" , Mathematica e Fisica: Cultura e Ideologia, De Donato Editore, Bari, 1977, . 35-70 Weintramb, E. Roy-Mirowski, Philip: "The Pure and the Applied: Bourbakism comes to Mathematical Economics" . Science in Context, vol. 7, no. 2, 1994, . 245-272, Cambridge University Press.

    19

  • BOURBAKI 1940-1970 , : , Bourbaki, ; , . . , , . , ., , 1934 '70, , . . , . , Raymond Queneau, . Bourbaki , . Jean Piaget, . "" "" ' 63. ' J. Dieudonn 1952 ' Melun, 64. Claude Levi-Strauss, " " (Elementary Structure of Kinship). ' Andr Weil, Levi-Strauss . Raymond Queneau, , Franois Le Lionnais , Ren de Possel. OULIPO (Ouvroir de Literature Pottentielle= ). , Oulipo, , ""

    63 Piaget, Jean: "" .112 (1972). 64 Beth, Evert-Piaget, Jean: "Mathematical Epistemology and Psychology", D. Reidel Publishing Company, 1966, Dordrecht, Holland, . 168.

    20

  • OULIPO Ouvroir de Literature Pottentielle=

    . Oulipo "" . . Queneau "Hundred Thousand Billion Poems" 1961, 65. ' . " " (cultural connectors). . . . ., , , ' , 66. Bourbaki ' . "" . . . . ""

    65 Aubin (1997), . 321-322. 66 Aubin (1997), . 299-330.

    21

  • 67. ' , . . '40-'70 , ' . . . . . .. . . . , . ' , Hilbert van der Waerden , , , . ' "", , 1900. , "" 1930 25 30 . , , . 68. , , . , . , , ' . . . . "" . "". , '70. (catastrophe) Ren Thom fractals Benot Mandelbrot 69. , 30 . , , . . ' . , . . 67 Aubin(1997), . 301-302. 68 Dieudonn, Jean : " . Bourbaki", . , 7, .-.-. 1977, . 56-57. 69 Aubin(1997), . 330-333.

    22

  • BOURBAKI , Bourbaki , . ' . . ' , Bourbaki , . , , . 1960 . . . ...., 1959, Jean Dieudonn Bourbaki Bourbaki . 196070. 1960 " " . Bourbaki71. 1 - 1960 . Jean Dieudonn ( .) (" ")72. . . " " 73. 4

    70 , 9, .161-166 & 206-212, 1960 71 , : " ", , - 1, 1-2, 1960, 2, . 1-4. 72 - , . . . , 1960, . 96. 73 . ., - 7, 1-2, 1966, 1, . 224.

    23

  • 1971 . "" . . "" "Hyperanneaux Fonctions Multivoques"74. "" (1960) 75. 1980, , , , . " " " "76. . 1 .. . . 77. ' . 20 . '59 '62 . . , . . "" . . , 78. , , . , , 79. ' ,

    74 4 . .. , 1971, . 192-195. 75 ... , 1960, . 328. 76 , : " " ", ." " , 1980, . 40-48. 77 1 , 1984, . 259-260 . 139-165. 78 Revuz Andr: "La prise de consience bourbakiste, 1930-1960" Les sciences au lyce: Un sicle de reformes des mathematiques et de la physique en France et a l' tranger, ed. Librairie Vuibert, 1996, Paris, . 74. 79 Revuz (1996), . 70.

    24

  • . . . " ; . ; ". . . " " (mathematiques bourbachiques)80. . , , , 81. ' 1963 . , , : "... ..."82. " ". " " . , , . . . ', ' ' . . , ' 83. - . , 80 Revuz (1996), .74-75. 81 , " ". 82 (1980) .44. 83 , .: " ", , 1997 . 68-80.

    25

  • , 84. , , . . '60, , . . , , '67 85. ******************************** . - , ' , ' '80 . . , .

    84 , (1997), . 81. 85 , (1997),.60.

    26

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