Matematica e filosofia della matematica: presente e futuro

Carlo Cellucci

La Matematica nella Società e nella Cultura. Rivista dell'Unione Matematica Italiana (2010)

  • Volume: 3, Issue: 2, page 201-234
  • ISSN: 1972-7356

Abstract

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In this paper it is claimed that in the future mathematics will develop along lines essentially different from those in which it has developed since the second half of the nineteenth century. This will require a change in the philosophy of mathematics on which such development has been based. Therefore in the paper an alternative philosophy of mathematics is outlined.

How to cite

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Cellucci, Carlo. "Matematica e filosofia della matematica: presente e futuro." La Matematica nella Società e nella Cultura. Rivista dell'Unione Matematica Italiana 3.2 (2010): 201-234. <http://eudml.org/doc/290646>.

@article{Cellucci2010,
abstract = {In questo articolo si sostiene che in futuro la matematica si svilupperà lungo linee sostanzialmente differenti da quelle secondo cui si è sviluppata a partire dalla seconda metà dell'Ottocento. Questo richiederà un cambiamento nella filosofia della matematica che è stata alla base di tale sviluppo. Perciò nell'articolo si propone una filosofia della matematica alternativa.},
author = {Cellucci, Carlo},
journal = {La Matematica nella Società e nella Cultura. Rivista dell'Unione Matematica Italiana},
language = {ita},
month = {8},
number = {2},
pages = {201-234},
publisher = {Unione Matematica Italiana},
title = {Matematica e filosofia della matematica: presente e futuro},
url = {http://eudml.org/doc/290646},
volume = {3},
year = {2010},
}

TY - JOUR
AU - Cellucci, Carlo
TI - Matematica e filosofia della matematica: presente e futuro
JO - La Matematica nella Società e nella Cultura. Rivista dell'Unione Matematica Italiana
DA - 2010/8//
PB - Unione Matematica Italiana
VL - 3
IS - 2
SP - 201
EP - 234
AB - In questo articolo si sostiene che in futuro la matematica si svilupperà lungo linee sostanzialmente differenti da quelle secondo cui si è sviluppata a partire dalla seconda metà dell'Ottocento. Questo richiederà un cambiamento nella filosofia della matematica che è stata alla base di tale sviluppo. Perciò nell'articolo si propone una filosofia della matematica alternativa.
LA - ita
UR - http://eudml.org/doc/290646
ER -

References

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  1. ACERBI, F. (2000), Plato: Parmenides 149 a7-c3. A proof by complete induction?, Archive for History of Exact Sciences, vol. 55, pp. 57-76. Zbl0960.01005MR1780443DOI10.1007/s004070000020
  2. ASPRAY, W. e KITCHER, P. (a cura di) (1988), History and philosophy of modern mathematics, University of Minnesota Press, Minneapolis. Zbl1367.00029MR945464
  3. BOURBAKI, N. (1962), L'architecture des mathématiques, in F. Le Lionnais (ed.), Les grands courants de la pensée mathématique, Blanchard, Paris, pp. 35-47. MR35980
  4. BOURBAKI, N. (2006), Théorie des ensembles, Springer, Berlin. MR65611
  5. BOURBAKI, N. (2007), Éléments d'histoire des mathématiques, Springer, Berlin. (Trad. it., Feltrinelli, Milano1963). 
  6. CARTIER, P. (1997), Vie et mort de Bourbaki. Notes sur l'histoire et la philosophie des mathématiques I, Institut des Hautes Etudes Scientifiques, Paris. 
  7. CELLUCCI, C. (1998), Le ragioni della logica, Laterza, Bari. 
  8. CELLUCCI, C. (2002), Filosofia e matematica, Laterza, Bari. Zbl1067.03001MR2098863
  9. CELLUCCI, C. (2007), La filosofia della matematica del Novecento, Laterza, Bari. Zbl0169.29401MR2098863
  10. CELLUCCI, C. (2008 a), Perché ancora la filosofia, Laterza, Bari. 
  11. CELLUCCI, C. (2008 b), Why proof? What is a proof?, in R. Lupacchini e G. Corsi (eds.), Deduction, computation, experiment. Exploring the effectiveness of proof, Springer, Berlin, pp. 1-27. Zbl1197.00016MR2464826DOI10.1007/978-88-470-0784-0_1
  12. CELLUCCI, C. (2008 c), The nature of mathematical explanation, Studies in History and Philosophy of Science, vol.39, pp. 202-210. 
  13. CELLUCCI, C. (2009), Indiscrete variations on Gian-Carlo Rota's themes, in E. Damiani, O. D'Antona, V. Marra e F. Palombi (eds.), Combinatorics to philosophy. The legacy of G.C. Rota, Springer, NewYork2009, pp. 211-228. Ristampato in M. Pitici (a cura di), The best writings on mathematics2010, Princeton University Press, Princeton, di prossima pubblicazione. MR2777703
  14. CLEARY, J.J. (1995), Aristotle and mathematics: aporetic method in cosmology and metaphysics, Brill, Leiden. MR1467480DOI10.1163/9789004320901
  15. CORFIELD, D. (2003), Towards a philosophy of real mathematics, Cambridge University Press, Cambridge. Zbl1089.00003MR1996199DOI10.1017/CBO9780511487576
  16. CURRY, H. B. (1951), Outlines of a formalist philosophy of mathematics, North-Holland, Amsterdam. Zbl0043.00601MR44471
  17. CURRY, H. B. (1977), Foundations of mathematical logic, Dover, New York. Zbl0396.03001MR434751
  18. DAVIS, P. J. e HERSH, R. (1980), The mathematical experience, Birkhäuser, Boston. (Trad. it., Edizioni di Comunità, Milano1985). MR601591
  19. DEDEKIND, J. W. R. (1932), Was sind und was sollen die Zahlen?, in J. W. R. Dedekind, Gesammelte mathematische Werke, vol. III, Vieweg, Braunschweig, pp. 335-391. (Trad. it. in Dedekind 1982, pp. 79-128). Zbl36.0087.04MR106846
  20. DEDEKIND, J. W. R. (1974), Lettera a Keferstein, 27 febbraio 1890, in M.-A. Sinaceur, L'infini et les nombres, Revue d'Histoire des Sciences, vol. 27 (1974), pp. 251-278. (Trad. it. in Dedekind 1982, pp. 154-156). MR1129633DOI10.3406/rhs.1990.4165
  21. DEDEKIND, J. W. R. (1982), Scritti sui fondamenti della matematica, a cura di F. Gana, Bibliopolis, Napoli. 
  22. DE L'HOSPITAL, G. (1716), Analyse des infiniment petits pour l'intelligence des lignes courbes, Montalant, Paris. 
  23. DEVLIN, K. (2008), What will count as mathematics in 2100?, in B. Gold e R. A. Simon (a cura di), Proof and other dilemmas. Mathematics and philosophy, The Mathematical Association of America, Washington, pp. 292-311. MR2452085
  24. DIEUDONNÉ, J. (1964), Recent developments in mathematics, The American Mathematical Monthly, vol. 71, pp. 239-248. MR1532579DOI10.2307/2312178
  25. DIEUDONNÉ, J. (1988), Pour l'honneur de l'esprit humain. Les mathématiques aujourd'hui, Hachette, Paris. MR1023602
  26. DIRAC, P. (1958), The principles of quantum mechanics, Oxford University Press, Oxford. Zbl0080.22005MR23198
  27. FERREIROS, J. (1999), Labyrinth of thought, Birkhäuser, Boston. Zbl0934.03058MR1726552DOI10.1007/978-3-0348-5049-0
  28. FERREIROS, J. e GRAY, J. J. (a cura di) (2006), The architecture of modern mathematics. Essays in history and philosophy, Oxford University Press, Oxford. Zbl1089.00004MR2258016
  29. GILLIES, D. (a cura di) (1992), Revolution in mathematics, Oxford University Press, Oxford. Zbl0758.01019MR1192351
  30. GÖDEL, KURT (1986-2002), Collected works, a cura di Solomon Feferman et al., Oxford University Press, Oxford. (Trad. it., Bollati Boringhieri, Torino1999-2009). MR831941
  31. GÖWERS, T. (a cura di) (2008), The Princeton companion to mathematics, Princeton University Press, Princeton. 
  32. GRIFFITHS, P. A. (2000), Mathematics at the turn of the millennium, The American Mathematical Monthly, vol. 107, No. 1, pp. 1-14. Zbl0994.01012MR1745565DOI10.2307/2589372
  33. GROSHOLZ, E. (2007), Representation and productive ambiguity in mathematics and the sciences, Oxford University Press, Oxford. Zbl1209.00016MR2343928
  34. GROSHOLZ, E. e BREGER, H. (a cura di) (2000), The growth of mathematical knowledge, Kluwer, Dordrecht. Zbl0937.00005MR1895942DOI10.1007/978-94-015-9558-2_6
  35. HADAMARD, J. (1954), The psychology of invention in the mathematical field, Dover, Mineola, NY. (Trad. it., Cortina, Milano1993). Zbl0056.00101MR11665
  36. HARDY, G. H. (1929), Mathematical proof, Mind, vol. 38, pp. 1-25. Zbl55.0030.03
  37. HARDY, G. H. (1992), A mathematician's apology, Cambridge University Press, Cambridge. (Trad. it., Garzanti, Milano1989). Zbl0025.19301MR1148590DOI10.1017/CBO9781139644112
  38. HERSH, R. (1997), What is mathematics, really?, Oxford University Press, Oxford. (Trad. it., Baldini Castoldi Dalai, Milano2001). Zbl0913.00010MR1462890
  39. HERSH, R. (1998), Some proposals for reviving the philosophy of mathematics, in T. Tymoczko (ed.), New directions in the philosophy of mathematics, Princeton University Press, Princeton, pp. 9-28. MR1664604
  40. HERSH, R. (a cura di) (2006), 18 unconventional essays on the nature of mathematics, Springer, New York. Zbl1081.00005MR2145193DOI10.1007/0-387-29831-2
  41. HILBERT, D. (1926), Über das Unendliche, Mathematische Annalen, vol. 95, pp. 161-190. (Trad. it. in Hilbert 1985, pp. 233-266). MR1512272DOI10.1007/BF01206605
  42. HILBERT, D. (1929), Probleme der Grundlegung der Mathematik, Mathematische Annalen, vol. 102, pp. 1-9. (Trad. it. in Hilbert 1985, pp. 291-300). Zbl55.0031.01MR1512566DOI10.1007/BF01782335
  43. HILBERT, D. (1931), Die Grundlegung der elementaren Zahlenlehre, Mathematische Annalen, vol. 104, pp. 485-494. (Trad. it. in Hilbert 1985, pp. 313-323). Zbl57.0054.04MR1512682DOI10.1007/BF01457953
  44. HILBERT, D. (1985), Ricerche sui fondamenti della matematica, a cura di V. M. Abrusci, Bibliopolis, Napoli. MR850261
  45. HUET, S. (1998), Bourbaki est mort, CQFD, Liberation, 28 aprile. 
  46. KAC, M., ROTA, G.-C. e SCHWARTZ, J. T. (1986), Discrete thoughts. Essays on mathematics, science, and philosophy, Birkhäuser, Boston. Zbl0597.00034MR890747DOI10.1007/978-1-4899-6667-4
  47. KITCHER, P. (1983), The nature of mathematical knowledge, Oxford University Press, Oxford. Zbl0519.00022MR692216
  48. KLINE, N. (1980), Mathematics, the loss of certainty, Oxford University Press, Oxford. (Trad. it., Mondadori, Milano1985). Zbl0458.03001MR584068
  49. KLINE, M. (1990), Mathematical thought from ancient to modern times, Oxford University Press, Oxford. (Trad. it., Einaudi, Torino1999). Zbl0784.01048MR472307
  50. LAKATOS, I. (1961), Essays in the logic of mathematical discovery, PhD thesis, Cambridge. 
  51. LAKATOS, I. (1976), Proofs and refutations, a cura di J. Worrall e E. Zahar. Cambridge University Press, Cambridge. (Trad. it., Feltrinelli, Milano1979). MR479916
  52. LEÂVY-LEBLOND, J.-M. (1982), Physique et mathématiques, in Maurice Loi et al., Penser les mathématiques, Editions du Seuil, Paris, pp. 195-210. MR674510
  53. MANCOSU, P. (ed.) (2008), The philosophy of mathematical practice, Oxford University Press, Oxford. Zbl1163.03001MR2590934DOI10.1093/acprof:oso/9780199296453.001.0001
  54. NEEDHAM, T. (1997), Visual complex analysis, Oxford University Press, Oxford. Zbl0893.30001MR1446490
  55. NEWTON, I. (1971), MS Add. 3698, f. 101, in I. B. Cohen, Introduction to Newton's "Principia", Cambridge University Press, Cambridge, pp. 292-294. MR465755
  56. NEWTON, I. (1981), The 1704 De Quadratura Curvarum: final text additions, in The mathematical papers, a cura di D. T. Whiteside, vol. VIII, Cambridge University Press, Cambridge, pp. 122-159. 
  57. POINCARÉ, H. (1908), Science et méthode, Flammarion, Paris. (Trad. it., Einaudi, Torino1997). 
  58. ROTA, G.-C. (1997), Indiscrete thoughts, Birkäuser, Boston. MR1419503DOI10.1007/978-0-8176-4781-0
  59. RUSSELL, B. (1994), Mysticism and logic, Routledge, London. (Trad. it., Newton Compton, Roma1970). 
  60. SENECHAL, M. (1998), The continuing silence of Bourbaki, The Mathematical Intelligencer, vol. 19, pp. 22-28. Zbl0915.01010
  61. SHAPIRO, S. (1997), Philosophy of mathematics. Structure and ontology, Oxford University Press, Oxford. Zbl0897.00004MR1468988
  62. SHAPIRO, S. (2000), Thinking about mathematics. The philosophy of mathematics, Oxford University Press, Oxford. Zbl0990.00005MR1999744
  63. SHAPIRO, S. (2004), Foundations of mathematics: metaphysics, epistemology, structure, The Philosophical Quarterly, vol. 54, pp. 16-37. MR2050637DOI10.1111/j.0031-8094.2004.00340.x
  64. STARIKOVA, I. (2010), Why do mathematicians need different ways of presenting mathematical objects? The case of Cayley graphs, Topoi, vol. 29, pp. 41-51. Zbl1195.00053MR2607524DOI10.1007/s11245-009-9065-4
  65. SUPPES, P. (2002), Representation and invariance of scientific structures, CSLI, Stanford. Zbl1007.03003MR1931576
  66. TURING, A. M. (2001), Mathematical logic, a cura di R. O. Gandy e C. E. M. Yates, North-Holland, Amsterdam. Zbl0986.01023MR1869997
  67. TYMOCZKO, T. (a cura di) (1985), New directions in the philosophy of mathematics, Birkhäuser, Boston. Zbl0891.00005MR1127231DOI10.1007/BF00567746
  68. VAN KERKHOVE, B. e VAN BENGEDEM, J. P. (a cura di) (2007), Perspectives on mathematical practices, Springer, Dordrecht. 
  69. WANG, H. (1996), A logical journey. From Gödel to philosophy, The MIT Press, Cambridge, Mass.. MR1433803
  70. WEISBERG, R. W. (2006), Creativity, Wiley, New York. 
  71. WELTON, J., MONAHAN, A. J., MELLONE, S. H. (1962), Intermediate logic, 4ed. University Tutorial Press, London. 
  72. ZELLINI, P. (1985), La ribellione del numero, Adelphi, Milano. 

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