Russell's paradox and the beginnings of mereology

Abstract

The discovery of the title paradox probably took place around 1901. It was published by Russell in 1903 in his book "Principles of Mathematics". Russell’s paradox concerns distributive classes (as extensions of concepts), analyzed by Frege in "Grundgesetze der Arithmetik". This paradox directly indicated that the theory adopted by Frege was contradictory. When Frege learned of this from Russell’s letter, he stated in the afterword to his book that the logical foundations of arithmetic that he had assumed were “shaken.”