Filosofía de las Matemáticas

Naturalismo: El Debate Contemporáneo

Posgrado en Filosofía de la Ciencia

 

I.                               El Fantasma de Quine: La Ontología Naturalizada

Textos en discusión:

Mark Colyvan, “The Quinean Backdrop”. segundo capítulo de The Indispensability of Mathematics (Oxford 2001)

W.v.O. Quine, “Five Milestones of Empiricism”, en Theories and Things, (Harvard 1981) Originalmente publicado en 1975.

 

Bibliografía Secundaria:

Azzoni, Jody, (1998) “On “On what there is””, Pacific Philosophical Quarterly, vol. 79, No. 1

Burgess, John (2004) “Quine Analyticity and Philosophy of Mathematics”, The Philosophical Quarterly, vol. 54, no. 214, pp.38-55

Dyson, Freeman J.  (2004) “One in a Million”, New York Review of Books, v. 51, no. 5, Marzo 25.

Hersh, Reuben (1997) What is Mathematics, Really? New York: Oxford University Press.

Quine, W.v.O. (1951) “On what there is” en Paul Benacerraf y Hilary Putnam (eds.), Philosophy of Mathematics, Selected Readings, Cambridge: Cambridge University Press, 1983 y en From a Logical Point of View, segunda edición, Cambridge, MA: Harvard University Press, pp. 1-19. Original de 1948.

                     (1980) “Two Dogmas of Empiricism”, en From a Logical Point of View, segunda edición, Cambridge, MA: Harvard University Press, pp. 20-46. Original de 1951.

                     (1976), “Posits and Reality” en The Ways of Paradox, editción revisada, Cambridge, MA: Harvard University Press, pp. 246-254. Original de 1955.

Ivonne Raley, (2005) “Ontological Naturalism”, Pacific Philosophical Quarterly, vol. 86, no. 2, pp. 284-294

Yablo, Stephen (1998), “Does ontology rest on a mistake?” Proceedings of the Aristotelian Society, supplement. vol. 72, 229-261

 

 

II.                            El Naturalismo de Maddy

Textos en discusión:

Dieterle, J. M. (1999) “Mathematical, Astrological, and Theological Naturalism”, Philosophia Matemática (3), vol. 7, pp. 129-135

Maddy, Penélope (1997) Naturalism in Mathematics, New York: Oxford University Press.

(2001), “Naturalism: Friends and Foes” en James E. Tomberlin (ed.), Metaphysics, Philosophical Perspectives, no. 15, suplemento de  Noěs, vol. 35, pp. 37-67(31)

Tennant, Neil (2000) “What is Naturalism in Mathematics, Really?”, Philosophia Mathematica, vol. 8, no. 3, pp.316-338

 

Bibliografía Secundaria

Balaguer, Mark (1994) “Against (Maddian) Naturalized Platonism”, Philosophia Matemática, vol. 2, no. 3, pp. 97-108

Barceló, Axel, (2004), “Revisionismo en la Filosofía de las Matemáticas”, Signos Filosóficos, vol. 6, no. 12, pp. 149-154.

Leng, Mary, (1999), ReseĖa de Naturalism in Mathematics de  Penelope Maddy, International Studies in the Philosophy of Science, vol. 13, no. 2, pp. 195-197

Maddy, Penelope (1997) Realism in Mathematics, New York: Oxford University Press.

                     (2004) “Three Forms of Naturalism” en S. Shapiro (ed.), Handbook of Philosophy of Logic and Mathematics, Oxford.

Rosen, Gideon, (1999), Estudio Crítico de Naturalism in Mathematics de  Penelope Maddy, British Journal for the Philosophyof Science

Una bibliografía más completa sobre la obra de Penelope Maddy se encuentra en http://sun3.lib.uci.edu/eyeghiay/Philosophy/Faculty/maddy.html

 

 

III.                         La Crítica de Gideon y Rosen al Nominalismo

Textos en discusión:

Rosen, Gideon y John P. Burgess, (2005) “Nominalism Reconsidered” en S. Shapiro, (ed.), Handbook for the Philosophy of Mathematics, Oxford University Press.

                     (1997) A Subject with No Object: Strategies for Nominalist Reconstrual in Mathematics, Oxford University Press.

John P. Burgess, (2004), ReseĖa de  Deflating existential consequence: a case for nominalism de Jody Azzouni, Bulletin of Symbolic Logic, vol. 10, pp. 573-4

 

Bibliografía Secundaria:

Azzouni, Jody (2004), Deflating Existential Consequence: A Case for Nominalism, New York: Oxford University Press.

Chihara, Charles (1990) Constructibility and Mathematical Existence, Oxford: Oxford University Press.

Colyvan, Mark, (2001), “The Eleatic Principle” en The Indispensability of Mathematics, Oxford University Press

Field, Hartry (1980). Science Without Numbers. Oxford: Blackwell.

(1989). Realism, Mathematics and Modality. Oxford: Blackwell.

Hellman, Geoffrey, (1989), Mathematics without Numbers, Oxford: Oxford University Press.

(2001), “On Nominalism”, Philosophy and Phenomenological Research, vol. 62, pp. 691—705.

Katz, Jerrold, (1998) “Philosophical Preliminaries”, primer capítulo de Realistic Rationalism, Boston: MIT Press.

Maddy, Penelope (2005), “Mathematical Existence”, Bulletin of Symbolic Logic, vol. 11, no. 3, pp. 351–376

Una bibliografía más completa sobre el Nominalismo en Matemáticas se encuentra en: http://weka.ucdavis.edu/~ahwiki/bin/view/Arche/MathNominalism

 

Sesiones Efectivas

Presentador

Texto en discusión

Agosto

25:

Karla

Mark Colyvan, “The Quinean Backdrop”

Septiembre

1

Dalia

W.v.O. Quine, “Five Milestones of Empiricism”

8

Juan Carlos

Maddy, Penélope (1997), Capítulos 1-3, de la  sección III “Naturalism” de Naturalism in Mathematics, pp. 161-182

Octubre

6

Marco

Maddy, Penélope (1997) III.4 “Mathematical Naturalism”, en Naturalism in Mathematics, pp. 183-205

13

Axel

Dieterle, J. M. (1999) “Mathematical, Astrological, and Theological Naturalism” & Tennant, Neil (2000) “What is Naturalism in Mathematics, Really?”

20

Marco

Maddy, Penélope (2001), “Naturalism: Friends and Foes”

27

Miguel

Rosen, Gideon y John P. Burgess, (1997) A Subject with No Object: Strategies for Nominalist Reconstrual in Mathematics, pp. 3-25

Noviembre

10

Karla

Rosen, Gideon y John P. Burgess, (1997) A Subject with No Object: Strategies for Nominalist Reconstrual in Mathematics, pp.25-66

24

Héctor

Rosen, Gideon y John P. Burgess, (1997) Conclusiones de A Subject with No Object: Strategies for Nominalist Reconstrual in Mathematics.

Diciembre

1

Alejandro

Rosen, Gideon y John P. Burgess, (2005) “Nominalism Reconsidered” &

John P. Burgess, (2004), ReseĖa de  Deflating existential consequence: a case for nominalism

8

 

Conclusiones Finales