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Kriterion: Revista de Filosofia

versión impresa ISSN 0100-512Xversión On-line ISSN 1981-5336

Resumen

NAKANO, Anderson Luis. WITTGENSTEIN, FORMALISM, AND SYMBOLIC MATHEMATICS. Kriterion [online]. 2020, vol.61, n.145, pp.31-53.  Epub 18-Mayo-2020. ISSN 1981-5336.  https://doi.org/10.1590/0100-512x2020n14502aln.

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.

Palabras clave : Wittgenstein; formalism; symbolic mathematics; applicability; autonomy of arithmetic.

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