Abstrakt
Paradoxes in mathematics such as the casus irreducibilis (Cardano 1545), the paradoxes of the calculus (Berkeley 1734) or Russell's paradox (Russell 1903) show surprisingly many common features. It is possible to see these paradoxes as linguistic phenomena occurring at a specific stage in the development of the particular theory.
It seems that even though each paradox taken in isolation is well understood, the paradoxes as a general phenomenon still lack sufficient historical analysis. 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 characterizes that stage as the stage when in the language we begin to construct representations of representations.
It argues that the paradoxes exhibit the expressive boundaries of the language of mathematics as introduced in (Kvasz 2008). That is why these paradoxes exhibit several common features-they correspond to the same epistemological phenomenon, namely expressive boundaries of language.