Archivo | octubre, 2013

Sesión XXII: A Pictorial Aspect of Mathematical Notation in Wittgenstein

2 Oct

Hi y’all.

Llega curso nuevo y con él más sesiones del SFC. Arrancamos con Jakub Mácha (Masaryk University, Brno) que nos presentará A Pictorial Aspect of Mathematical Notation in Wittgenstein: Generality, numbers and proofs porque sabemos que tenemos mucho aficionado a Wittgenstein y las matemáticas entre nosotros. Aquí os dejo el abstract:

The core in Wittgenstein’s conception of mathematics can be summed up in the motto that “arithmetical rules are statements of internal relations.” (PPO, p. 390) I am going to focus on Wittgenstein’s insistence on a certain pictorial aspect of mathematical notation, which is, of course, his Tractarian heritage. Mathematical notation must always be capable to depicture a state of affairs. This is true of numbers, but also of mathematical proofs. Numbers and proofs are for Wittgenstein a sort of prototypes of certain activities. (1) This finitistic conception of mathematics is threatened by general arithmetical propositions. Do they picture some general characteristics of numbers? (2) The pictorial aspect of numerals is expressed in the key definition of a cardinal number: “A cardinal number is an internal property of a list.” (PR, p. 140) Wittgenstein’s concrete and finitistic approach takes numeral for concrete objects as opposed to Frege-Russell’s approach based on abstract sets. The decisive advantage of Wittgenstein’s conception of numbers over Frege and Russell’s is that numbers are rooted in our primitive activities like children’s finger counting or counting with the abacus. (3) Mathematical propositions are statements of internal relations as well. A proof of a mathematical proposition aims to picture or rather lay down its internal relatedness to a system of other mathematical rules. We may say that “the completely analysed mathematical proposition is its own proof.” (PR, p. 192) Proof is so a picture of an experiment, even more “it can be thought of as a cinematographic picture” (RFM, p. 159).

La sesión tendrá lugar el próximo lunes 21 de octubre a las 16,00 en la sala 324 de la Facultad de Filosofía de la UNED (Edif. Humanidades – Pº Senda del Rey 7). Aquí queda el texto de referencia, así como en nuestra nutrida sección de materiales.

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Esperamos veros a todos por allí.

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