The reasonable effectiveness of mathematics and its cognitive roots

Geometries of Nature, Living Systems and Human Cognition: New Interactions of Mathematics with Natural Sciences and Humanities

Volumn , Issue , 2005, Pages 351-381

  Longo, Giuseppe ^a  

^a ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84967350873     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/9789812700889_0007     Document Type: Chapter

References (49)

1. Bachelard G., La Philosophic du non, Paris, PUF, 1940.
2. Bailly F., "L'anneau des disciplines," special issue of Revue Internationale de systemique, Vol. 5, No. 3, 1991.
3. Berthoz A., Le sens du mouvement, Paris, Odile Jacob, 1997.
4. Boi L., Le probleme mathematique de I'espace. Une quite de I 'intelligible, Berlin and Heidelberg, Springer-Verlag, 1995.
5. Boi L., "The role of intuition and formal thinking in Kant, Husserl and in the modern Mathematics and Physics," Mathesis, 2005.
6. Boole G., The laws of Thought, 1854.
7. Bottazzini U., Tazzioli R., "Naturphilosophie and its role in Riemann's mathematics," Revue d'Histoire des Mathematiques, 1 (1995), 3-38.
8. Connes A., Geometrie non-commutative, Paris, InterEditions, 1990.
9. Dehaene S., The Number Sense, Oxford, Oxford University Press, 1998. (Review/article downloadable from http://www.dmi. ens. fr/users/longo.).
10. Devaney, R. L., An Introduction to chaotic dynamical systems, Addison-Wesley, 1989. Edelman G., The matter of Mind, Naw York, Basic Books, 1992.
11. Frege G., The Foundations of Arithmetic, 1884 (english transl. Evanston, 1980.).
12. Galileo G., Dialoghi sopra i due Massimi Sistemi, U, 1632.
13. Girard J.-Y., "Linear Logic," Theoretical Comp. ScL, 50 (1-102), 1987.
14. Girard J. Y., Lafont Y., Taylor P., Proofs and Types, Cambridge U. Press, 1990.
15. Godel K., Nagel E., Newman J., Girard J.-Y., Le theoreme de Godel, Paris, Seuil, 1989.
16. Harrington L. et al. (eds) H. Friedman's Research on the Foundations of Mathematics, Amsterdam, North-Holland, 1985.
17. Heath T. L., The Thirteen Books of Euclid's Elements, Cambridge, Cambridge University Press, 1908.
18. Hertz J., Krogh A. and Palmer R., Introduction to the Theory of Neural Computation, 1991.
19. Husserl, H., The origin of Geometry, part of Krisis, 1936.
20. Jacob F., La logique du vivant, Paris, Gallimard, 1970.
21. Lakoff, G. and Nunez, R., Where Mathematics Comes From: How the Embodied Mathematics Creates Mathematics, New York: Basic Books, 2000.
22. Lambert D., Structure et Efficacite des interactions recentes entre Mathematiques et Physique, These de Doctorat, Louvain-la-Neuve, 1996.
23. Lanfredini R., Husserl: la teoria dell'Intenzionalita, Roma, Laterza, 1994.
24. Laskar J., "The chaotic behaviour of the solar system," Icarus, 88: 266-291, 1990.
25. Longo G., "Mathematics and the Biological Phenomena" in International Symposium on Foundations in Mathematics and Biology: Problems, Prospects, Interactions, Pontifical Lateran University, Vatican City, November, 1998 (proceedings, Basti ed.).
26. Longo G. "The mathematical continuum, from intuition to logic" in Naturalizing Phenomenology: issues in comtemporary Phenomenology and Cognitive Sciences, (J. Petitot et al, eds) Stanford U. P., 1999c.
27. Longo G., "Mathematical Intelligence, Infinity and Machines: beyond the Godelitis" Invited paper, Journal of Consciousness Studies, special issue on Cognition, vol. 6, 11-12, 1999a.
28. Longo G., "The Constructed Objectivity of Mathematics and the Cognitive Subject" Quantum Mechanics, Mathematics and Cognition (M. Mugur-Schachter ed.), Kluwer, 2001.
29. Longo G., "Memoire et Objectvite en Mathematiques," Le Reel en Mathematique, colloque de Cerisy, 1999 (a paraitre).
30. Longo G., Petitot J., Teissier B. Geometrie et Cognition, research project, downloadable from http://www.dmi. ens. fr/users/longo, 1999.
31. Philosophy of Computer Science, special issue of The Monist (G. Longo ed.), vol. 82, 11, Jan. 1999.
32. Ninio J., L'empreinte des sens, Seuil, Paris, 1991.
33. Piazza M., Intorno ai numeri. Oggetti, proprieta', finzioni utili, Mailand, Mondadori, 2000.
34. Prochiantz A., Les anatomies de la pensee, Odile Jacob, 1997. (Recensione/articolo downloadable da http://www.dmi. ens. fr/users/longo.).
35. Riemann B., "On the hypothesis which lie at the basis of geometry," 1854 (english transl. by W. Clifford, Nature, 1873; trad, italiana di R. Pettoello, Boringhieri, 1999).
36. Shanker S., Godel's Theorem on focus, Croom Helm, 1988.
37. Tazzioli R., Riemann, Le Scienze, Aprile 2000.
38. Thorn R., Stabilite structurelle et Morphogenese, Benjamin, Paris, 1972.
39. Zellini P., Breve Storia dell'Infinito, Adelphi, 1980.
40. Waismann F., Wittgenstein und der Wiener Kreis, Frankfurt a. M., Suhrkamp, 1967 (Waismann's notes: 1929-31). (English translation: Wittgenstein and the Vienna circle: conversations recorded by F. Waismann, Barnes & Noble Books, New York, 1979).
41. Weyl H., "Uber die Definitionen der mathematischen Grundbegriffe," Math, naturwisss. Blatter, 7, 1910.
42. Weyl H., Das Kontinuum, 1918.
43. Weyl H., Raum, Zeit, Materie, 1918.
44. Weyl H., "Comments on Hilbert's second lecture on the foundations of Mathematics." 1927. in van Heijenoort J., From Frege to Goedel, 1967.
45. Weyl H., Philosophy of Mathematics and Natural Science, Princeton, Princeton University Press, 1949.
46. Weyl H., Symmetry, Princeton University Press, 1952.
47. Weyl, H. "Axiomatic Versus Constructive Procedures in Mathematics." (Edited by T Tonietti) The Mathematical Intelligence, Vol. 7, No. 4, 1985.
48. Wigner E., "The unreasonable effectiveness of Mathematics in the Natural Sciences," Comm. Pure Applied Math., XIII, 1-14, 1960.
49. Wittgenstein L., Philosophical Remarks, translated into English by G. E. M. Anscombe, Barnes & Noble, New York, 1968.