Czy matematyka jest składnią języka? Kurta Gödla argument przeciwko formalizmowi

Abstract

I S M ATHEMATICS S YNTAX OF L ANGUAGE ? K URT G ÖDEL ’ S A RGUMENT AGAINST F ORMALISM 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 rele-vance 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.