On Conditions of Set-Theoretic Paradoxes

A unified explanation of set-theoretic paradoxes, capable of determining their necessary and sufficient conditions, remains an open problem for philosophy of mathematics, and philosophy of logics. The paper contributes to a solution of this problem. A number of set-theoretic paradoxes are examined, namely Russell’s, Burali-Forti’s, Ramsey’s, Richard’s, Konig’s and Berry’s paradoxes. The aim of the paper is determining their necessary and sufficient conditions. The paradoxes in question can be divided into two types: ones using set-theoretical notions only, and ones using also some linguistic notions. Russell showed that necessary conditions of paradoxes of both types are self-reference and derivability of contradiction. The paper shows that the paradoxes of the second type demand, in addition, some linguistic premises. It is also shown that Ladov’s claim that using a negative property is sufficient for all paradoxes in question except Burali-Forti’s paradox is erroneous.