The ontological implications of neo-Fregeanism

  1. María de Ponte 1
  1. 1 Universidad de Sevilla, España
Zeitschrift:
Daimon: revista internacional de filosofía

ISSN: 1130-0507,  1989-4651

Datum der Publikation: 2016

Nummer: 69

Seiten: 159-174

Art: Artikel

DOI: 10.6018/DAIMON/221831 DIALNET GOOGLE SCHOLAR

Andere Publikationen in: Daimon: revista internacional de filosofía

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Zusammenfassung

Neo-Fregeanism is a combination of two ideas: logicism, according to which arithmetic can be derived from logic plus definitions, and Platonism, according to which there are mathematical objects (which are abstract). Neo-Fregeans propose a new interpretation of Frege’s principles of abstraction (mainly the so-called Hume’s Principle) and of the role of reconceptualization and implicit definition for the introduction of numbers into our ontology. I analyze the ontological implications of neo-Fregeanism, not only for mathematics, but for abstract entities in general. After briefly introducing some of the main elements of neo-Fregeanism, I present two possible readings of its ontological implications and I argue that none of them gives the desired results.

Bibliographische Referenzen

  • Balaguer, M. (1998) Platonism and Anti-Platonism in Mathematics.
  • Boolos, G. (1990) “The Standard Equality of Numbers”, reprinted in Boolos (1998) Logic, Logic and Logic. Harvard University Press, pp.202-220.
  • Cook, R.T. (2009) “New waves on an Old Beach: Fregean Philosophy of Mathematics Today”, in O. Bueno & O. Linnebo (eds) (2009) New waves in philosophy of mathematics. Palgrave Macmillan, pp.13-34.
  • Eklund, M. (2006) “Neo-Fregean Ontology”, Philosophical Perspectives, 20, Metaphysics: 95-121.
  • Field, H. (1989) Realism, Mathematics and Modality. Oxford: Blackwell.
  • Frege, G. (1884) Die Grundlagen der Arithmetik. W. Koebner, Breslau. English translation by J.L Austin (1950) The Foundations of Arithmetics. Oxford: Blackwell.
  • Hale, B. and Wright, C. (2001) The Reason’s Proper Study Oxford: Oxford University Press.
  • Hale, B. and Wright, C. (2002) “Benacerraf’s Dilemma Revisited”, European Journal of Philosophy, 10: 101-29.
  • Hawley, K. (2007) “Neo-Fregeanism and Quantifier Variance”, Proceedings of the Aristotelian Society, Supplementary Volume 81 (1): 233-249.
  • Heck, R. (2000) “Syntactic Reductionism”, Philosophia Mathematica 8 (3): 124-149.
  • Lowe, E.J. (1995) “The Metaphysics of Abstract Objects”, The Journal of Philosophy 92 (10): 509-520.
  • MacBride, F. (2003) “Speaking with Shadows: A Study of Neo-Logicism”, British Journal of Philosophy of Science 54: 103-163.
  • Putnam, H. (2004) “Sosa on Internal Realism and Conceptual Relativity”, in Greco, J (ed) Ernest Sosa and His Critics. Oxford: Blackwell, pp. 233-248.
  • Quine, W.V. (1948) “On What There Is”, Review of Metaphysics 2: 21-38.
  • Sider, T. (2007) “Neo-Fregeanism and Quantifier Variance”, Proceedings of the Aristotelian Society, Supplementary Volume 81 (1): 201-232.
  • Sosa, E. (1999) “Existential Relativity” Midwest Studies in Philosophy 23 (1): 132-143.
  • Wright, C. (1983) Frege’s Conception of Numbers as Objects. Aberdeen University Press.
  • Wright, C. (1997) “On the Philosophical Significance of Frege’s Theorem”. Reprinted in Hale and Wright 2001, pp. 272-307..
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