Is Mathematics Syntax of Language? Kurt Gödel’s Argument against Formalism Cover Image

Czy matematyka jest składnią języka? Kurta Gödla argument przeciwko formalizmowi
Is Mathematics Syntax of Language? Kurt Gödel’s Argument against Formalism

Author(s): Maciej Głowacki
Subject(s): Philosophy
Published by: Uniwersytet Warszawski - Wydział Filozofii i Socjologii, Instytut Filozofii
Keywords: Kurt Gödel; formalism; syntactic interpretation of mathematics; Rudolf Carnap; platonism

Summary/Abstract: In this paper, I critically examine Kurt Gödel’s argument against the syntactic interpretation of mathematics. While the main aim is to analyze the argument, I also wish to underscore the relevance of the original elements of Gödel’s philosophical thought. The paper consists of four parts. In the first part, I introduce the reader to Gödel’s philosophy. In the second part, I reconstruct the formalist stance in the philosophy of mathematics, which is the object of Gödel’s criticism. In the third part, I sketch his argument against the syntactic interpretation of mathematics. Finally, I discuss some controversies regarding the argument.

  • Issue Year: 29/2021
  • Issue No: 1(113)
  • Page Range: 43-61
  • Page Count: 19
  • Language: Polish