Ladislav Kvasz:
How mathematics confronts its paradoxes

Abstract

How mathematics confronts its paradoxes

Paradoxes in mathematics show surprisingly many common features. The paper analyzes the historical development of the language of the particular mathematical theory (i.e., algebra, calculus, and predicate logic, respectively) and argues that the paradoxes occur at a particular phase of the historical development of the language. It argues that the paradoxes exhibit the expressive boundaries of the language of mathematics.

Language: english

Keywords: paradox; language of mathematics