Frege y los números como objetos auto-subsistentes

Abstract

This paper argues that Frege is not the metaphysical platonist about mathematics that he is standardly taken to be. It is shown that Frege's project has two distinct stages: the identification of what is true of our ordinary notions, and then the provision of a systematic account that shares the identified features. Neither of these stages involves much metaphysics. The paper criticizes in detail Dummett's interpretation of §§55-61 of Grundlagen. These sections fall under the heading 'Every number is a self-subsistent object' and are described by Dummett as containing the worst arguments put forward by Frege. It is argued that essentially all of Dummett's interpretive points are mistaken. Finally, I show that Frege's claims about the independence of mathematics from humans and their activities does not commit him to any particularly metaphysical position either.

Keywords:

Dummett

Frege

Grundlagen

independencia de las Matemáticas

platonismo metafísico

Dummett

Frege

Grundlagen

independence of Mathematics

metaphysical platonism

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References

BEANEY, M. (1996). Frege: Making Sense. London: Duckworth.

________. (2004). “Carnap’s conception of explication: from Frege to Husserl?” In: AWODEY, S. & KLEIN, C. (Eds.). Carnap Brought Home: The View from Jena (pp.117-150). Chicago and La Salle, IL: Open Court.

BURGE, T. (2005). Truth Thougt Reason: essays on Frege. Oxford & New York: Oxford University Press.

DEMOPOULOS, W. (1993). “Critical notice of Michael Dummett’s ‘Frege”. In: Philosophy of mathematics’ Canadian Journal of Philosophy, vol. 23, no. 3, p. 477-496.

DUMMETT, M. (1991). Frege: Philosophy of Mathematics. Cambridge, MA: Harvard University Press.

________. (1993). “Frege as a realist”. In: SLUGA, H. (Ed.). Meaning and Ontology in Frege’s Philosophy, Vol. 3 of The Philosophy of Frege. (pp. 109-122). New York & London: Garland.

FREGE, G. (1967). The Basic Laws of Arithmetic: Exposition of the System. Edited and translated by Montgomery Furth. Berkeley and Los Angeles: University of California Press.

________. (1979). “Logic in mathematics”. In: HANS HERMES, F. K. & KAMBARTEL, F. (Ed.). Poshumous Writings. (pp. 203-250). Oxford: Basil Blackwell.

________. (1980). The Foundations of Arithmetic. 2d. ed. Evanston, IL: Northwstern University Press.

________. (1984a). “Review: Husserl, philosophy of arithmetic”. In: McGUINNESS, B. (Ed.). Collected Papers on Mathematics, Logic and Philosophy. (pp. 293-340). Oxford: Basil Blackwell.

________. (1984b). “On the foundations of geometry: second series”. In: McGUINNESS, B. (Ed.). Collected Papers on Mathematics, Logic and Philosophy. (pp. 293-340). Oxford: Basil Blackwell.

RECK, E. H. (1997). “Frege’s infuence on Wittgenstein: reversing metaphysics versus the context principle”. In: TAIT, W. W. (Ed.). Early Analytic Philosophy: Frege, Russell, Wittgenstein. (pp. 123-85). Chicago and La Salle, IL: Open Court.

________. (2007). “Frege on thruth, judgement, and objectivity”. In: Grazer Philosophische Studien, vol. 75, no. 1, p. 149-173.

RICKETTS, T. (1986). “Objectivity and objecthood: Frege’s metaphysics of judgement”. In: HAAPARANTA, L. & HINTIKKA, J. (Eds.). Frege Synthesized. (pp. 65-95). Dordrecht: Reidel.

________. (1996). “Frege on logic and truth”. In: Proceedings of the Aristotelian Society Supplement, vol. 70, p. 121-140.

WEINER, J. (2007). “What’s in a numeral? Frege’s answer” In: Mind, vol. 116, no. 463, p. 677-716.

WRAY, K. B. (1995). “Reinterpreting section 56 of Frege’s The Foundations of Arithmetic”. In: Auslegung: A Journal of Philosophy, vol. 20, no. 2, p. 76-82.