Frege’s Critique of Formal Arithmetic in Grundgesetze der Arithmetik Cover Image
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Fregego krytyka arytmetyki formalnej w Grundgesetze der Arithmetik
Frege’s Critique of Formal Arithmetic in Grundgesetze der Arithmetik

Author(s): Ryszard Miszczyński
Subject(s): Philosophy, Epistemology, Logic, Analytic Philosophy
Published by: Uniwersytet Warszawski - Wydział Filozofii i Socjologii, Instytut Filozofii
Keywords: formal arithmetic; meaningful arithmetic; radical formalists; Heine; Thomae; Frege; arithmetic as playing chess

Summary/Abstract: The author discusses Frege’s critique of the so-called formal arithmetic. It is included in the second volume of Grundgesetze der Arithmetik. This study has been the main source of knowledge about the views of radical formalists (such as Heinrich Eduard Heine and Carl Johannes Thomae). For them, arithmetic is like playing chess: writing mathematical formulas according to arbitrarily adopted rules. Formulas, like chess pieces, do not carry any meaning, do not indicate anything. By contrast, Frege supports traditional mathematics: formulas have meanings and applications. He believes that formalists failed to reduce mathematics to a game of formulas — in fact, they based their views on meaningful science. Frege’s conclusion was that formal mathematics should be supplemented with its metatheory.

  • Issue Year: 23/2015
  • Issue No: 4 (92)
  • Page Range: 89-101
  • Page Count: 13
  • Language: Polish