Czy matematyka jest składnią języka? Kurta Gödla argument przeciwko formalizmowi

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.