WITTGENSTEIN, FORMALISM, AND SYMBOLIC MATHEMATICS
Palabras clave:
Wittgenstein, formalism, symbolic mathematics, applicability, autonomy of arithmeticResumen
In a recent essay, Sören Stenlund tries to align Wittgenstein’s approach to the foundations and nature of mathematics with the tradition of symbolic mathematics. The characterization of symbolic mathematics made by Stenlund, according to which mathematics is logically separated from its external applications, brings it closer to the formalist position. This raises naturally the question whether Wittgenstein holds a formalist position in philosophy of mathematics. The aim of this paper is to give a negative answer to this question, defending the view that Wittgenstein always thought that there is no logical separation between mathematics and its applications. I will focus on Wittgenstein’s remarks about arithmetic during his middle period, because it is in this period that a formalist reading of his writings is most tempting. I will show how his idea of autonomy of arithmetic is not to be compared with the formalist idea of autonomy, according to which a calculus is “cut off” from its applications. The autonomy of arithmetic, according to Wittgenstein, guarantees its own applicability, thus providing its own raison d’être.
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DURING, E. “Ni ‘pure’ ni ‘appliquée’: les usages de la géométrie chez Wittgenstein et Poincaré”. Revue de métaphysique et de morale, 46 (2), 2005, pp. 197-214.
FRASCOLLA, P. “Wittgenstein’s Philosophy of Mathematics”. London, New York: Routledge, 1994.
FREGE, G. “Grundgesetze der Arithmetik”. Band II. Jena: Hermann Pohle, 1903.KLEIN, J. “Greek mathematical thought and the origin of algebra”. 2nd ed. trans. by E. Brann, 1992. Cambridge: MIT Press, 1968.
MEDINA, J. “The Unity of Wittgenstein’s Philosophy: Necessity, Intelligibility, and Normativity”. Albani: State University of New York Press, 2002.
MÜHLHÖLZER, F. “Braucht die Mathematik eine Grundlegung? Ein Kommentar des Teils III von WittgensteinsBemerkungen über die Grundlagen der Mathematik”. Frankfurt: Vittorio Klostermann, 2010.
NARBOUX, J-P. “Aspects de l’arithmétique”. Archives de Philosophie, 3, 2001, pp. 569-591.
RODYCH, V. “Wittgenstein on Mathematical Meaningfulness, Decidability, and Application”. Notre Dame Journal of Formal Logic, 38 (2), 1997, pp. 195-225.
SHAPIRO, S. “Thinking about Mathematics”. Oxford: Oxford University Press, 2000.
STENLUND, S., 2015. “On the Origin of Symbolic Mathematics and Its Significance for Wittgenstein’s Thought”. Nordic Wittgenstein Review, 4 (1), pp. 7-92.
WITTGENSTEIN, L. (1921) “Tractatus Logico-Philosophicus”. Trans. D. F. Pears and B. F. McGuinness. London: Routledge & Kegan Paul, 1969.
____________. [PG] “Philosophical Grammar”. R. Rhees (ed.). Trans. A. J. P. Kenny. Oxford: Blackwell, 1974.
____________. [PR] “Philosophical Remarks”. 2nd ed., R. Rhees (ed.), trans. R. Hargreaves and R. White. Oxford: Blackwell, 1975.
____________. [RFM] “Remarks on the Foundations of Mathematics”. 3rd ed., G. H. von Wright, R. Rhees and G. E. M. Anscombe (eds.), trans. G. E. M. Anscombe. Oxford: Blackwell, 1978.
____________. [WWK] “Ludwig Wittgenstein and the Viena Circle: Conversations Recorded by Friedrich Waismann”. B. McGuinness (ed.), trans. J. Schulte and B. McGuinness. Oxford: Blackwell, 1979.
____________. [LWL] “Wittgenstein Lectures, Cambridge, 1930-1932: From the Notes of John King and Desmond Lee”. D. Lee (ed.). Totowa, New Jersey: Rowman and Littlefield, 1980.
____________. [Wi2] “Wiener Ausgabe”. Band 2. Philosophische Betrachtungen, Philosophische Bemerkungen. Hg. von Michael Nedo. Wien, New York: Springer, 1994.
____________. [BT] “The Big Typescript: TS 213”. German/English Scholar's Edition, trans. C. Grant Luchart and M. E. Aue. Oxford: Wiley-Blackwell, 2012.
