DIAGONALIZATION, THE LIAR PARADOX, AND THE INCONSISTENCY OF THE FORMAL SYSTEM PRESENTED IN THE APPENDIX TO FREGE’S GRUNDGESETZE: VOLUME II

Abstract

The Liar Paradox is constructed within Frege’s Grundgesetze using a variant of Gödel’s diagonalization lemma. The particular instance of Basic Law V that triggers the Liar paradox is identified, and it is observed that this is exactly the principle that Frege himself identified as the root of Russell’s paradox in the appendix to Volume II of the Grundgesetze. This suggests that a re-examination of Frege’s work might shed new light onto both paradoxes, and the interconnections between them.