Plebani: Sull'ontologia della matematica

Plebani, Matteo:
Sull'ontologia della matematica
La Matematica nella Società e nella Cultura. Rivista dell'Unione Matematica Italiana Serie 1 7 (2014), fasc. n.3 —Matematica e filosofia. Contributi al dialogo interdisciplinare, p. 319-342, (Italian)
pdf (325 Kb), djvu (212 Kb). | MR 3363738 | Zbl 1391.03014

Referenze Bibliografiche

BENACERRAF, P. (1965), `What numbers could not be', Philosophical Review, vol. 74, pp. 47-73. | MR 171702

BENACERRAF, P. (1973), `Mathematical truth', Journal of Philosophy, vol. 70, pp. 661-80. | fulltext (doi) | MR 485124

BERTO, F. e PLEBANI, M. (2015), Ontology and Metaontology: A Contemporary Guide, Bloombsury Academic, London e New York.

BLACK, M. (1952), `The identity of indiscernibles', Mind, vol. 61, pp. 153-64 (trad. it. `L'identità degli indiscernibili', in A. C. Varzi (a cura di), Metafisica. Classici contemporanei, Laterza, Roma-Bari, 2008).

BOOLOS, G. (1975), `On second-order logic', Journal of Philosophy, vol. 72 , pp. 509-527.

BOOLOS, G. (1984), `To be is to be a value of a variable (or to be some values of some variables)', Journal of Philosophy, vol. 81, pp. 430-49. | fulltext (doi) | MR 755478

BOOLOS, G. (1985), `Nominalist platonism', Philosophical Review, vol. 94, pp. 327-44.

BURGESS, J. (2005), Fixing Frege, Princeton University Press, Princeton (NJ). | MR 2157847 | Zbl 1089.03001

BURGESS, J. e ROSEN, G. (1997), A subject with no object, Oxford University Press, Oxford. | MR 1468985 | Zbl 0871.03002

BURGESS, J. (2008), `Cats, dogs, and so on', in D. Zimmerman (a cura di), Oxford Studies in Metaphysics, Oxford University Press, Oxford, pp. 4-56.

CHIHARA, C. (2005), `Nominalism', in Shapiro (2005), pp. 483-514.

FIELD, H. (1980), Science without numbers: A defence of nominalism, Blackwell, Oxford. | Zbl 0454.00015

FIELD, H. (1989), Realism, mathematics and modality, Blackwell, Oxford. | Zbl 1098.00500

FIELD, H. (2001), Truth and the absence of fact, Oxford University Press, Oxford. | Zbl 0984.03003

HALE, B. e WRIGHT, C. (2001), The reason's proper study. Essays towards a neo-Fregean philosophy of mathematics, Oxford University Press, Oxford. | Zbl 1005.03006

HELLMAN, G. (2005), `Structuralism', in Shapiro (2005), pp. 536-62.

HODES, H. (1984), `Logicism and the ontological commitments of arithmetic', Journal of Philosophy, vol. 81, pp. 123-49.

HOFWEBER, T. (2005), `Number determiners, numbers, and arithmetic', Philosophical Review, vol. 114, pp. 179-225.

KERÄNEN, J. (2001) `The identity problem for realist structuralism', Philosophia Mathematica, vol. 9, 308-30.

LEITGEB, H. e LADYMAN, J. (2008), `Criteria of identity and structuralist ontology', Philosophia Mathematica, vol. 16, pp. 388-96. | Zbl 1162.03306

LIGGINS, D. (2014), `Abstract expressionism and the communication problem', British Journal for the Philosophy of Science, vol. 65, pp. 599-620. | Zbl 1319.00011

LOLLI, G. (2002), Filosofia della matematica. L'eredità del Novecento, il Mulino, Bologna.

MACBRIDE, F. (2005), `Structuralism reconsidered', in Shapiro (2005), pp. 563-89.

MACBRIDE, F. (a cura di) (2006), Identity and modality, Oxford University Press, Oxford.

MCDANIEL, K. (2009), `Ways of being', in D. Chalmers, D. Manley e R. Wasserman (a cura di), Metametaphysics. New essays on the foundations of ontology, Clarendon Press, Oxford, pp. 290-319.

MCGEE, V. (1997), `How we learn mathematical language', Philosophical Review vol. 106, pp. 35-68.

PANZA, M. e SERENI, A. (2010), Il problema di Platone, Carocci, Roma.

PANZA, M. e SERENI, A. (2013), Plato's problem: An introduction to mathematical platonism, Palgrave Macmillan, London e New York. | fulltext (doi) | MR 3115057 | Zbl 1277.00026

PEDERSEN, N. J. L. L. e ROSSBERG, M. (2010), `Open-endedness, schemas and ontological commitment', Noûs, vol. 44, pp. 329-39.

PLEBANI, M. (2001), Introduzione alla filosofia della matematica, Carocci, Roma.

POINCARÉ, H. (1968), La science et l'hypothèse, Flammarion, Paris (trad. it. La Scienza e l'Ipotesi, Bompiani, Milano, 2003).

QUINE, W. V. O. (1948), `On what there is', Review of Metaphysics, vol. 2, pp. 21-38 (trad. it. `Su ciò che vi è', in A. C. Varzi (a cura di), Metafisica. Classici contemporanei, Laterza, Roma-Bari, 2008).

QUINE, W. V. O. (1969), `Existence and quantification', in J. Margolis (a cura di), Fact and Existence, Basil Blackwell, Oxford, pp. 1-17 (trad. it. `Esistenza e quantificazione', in Quine, La relatività ontologica e altri saggi, Armando, Roma, 1986).

RAYO, A. (di prossima pubblicazione), `Nominalism, trivialism, logicism', Philosophia Mathematica.

ROSEN, G. (2012) `Abstract Objects', The Stanford Encyclopedia of Philosophy (Spring 2012 Edition), Edward N. Zalta (ed.) URL = <http://plato.stanford.edu/archives/spr2012/entries/abstract-objects/>.

SHAPIRO, S. (2000), Thinking about mathematics, Oxford University Press, Oxford. | MR 1999744 | Zbl 0990.00005

SHAPIRO, S. (a cura di) (2005), The Oxford handbook of philosophy of mathematics and logic, Oxford University Press, Oxford. | fulltext (doi) | MR 2118373 | Zbl 1081.03001

SHAPIRO, S. (2008), `Identity, indiscernibility, and ante rem structuralism: The tale of i and -i', Philosophia Mathematica, vol. 16, pp. 285-309. | fulltext (doi) | MR 2516018 | Zbl 1162.03308

TURNER, J. (2010), `Ontological pluralism', Journal of Philosophy, vol. 107, pp. 5-34.

VAN INWAGEN, P. (1998), `Meta-ontology', Erkenntnis, vol. 48, pp. 233-50.

YABLO, S. (2002). `Abstract objects: A case study', Philosophical Issues, vol. 12, pp. 220-40. | fulltext (doi) | MR 1953819 | Zbl 1366.03154

bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

Referenze Bibliografiche