Frege's attempt to solve Russell's Paradox and its logical insufficiency

• Grant number: 23/03920-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2023
• End date: March 31, 2024
• Field of knowledge: Humanities - Philosophy - Logic
• Principal Investigator: Anderson Luis Nakano
• Grantee: Pedro Navarro Artoni
• Host Institution: Faculdade de Filosofia, Comunicação, Letras e Artes. Pontifícia Universidade Católica de São Paulo (PUC-SP). São Paulo , SP, Brazil

Abstract

In his work Begriffsschrift, Gottlob Frege builds, for the first time in history, a formal system (and the very notion of formal system) that will intend, some years later, to be able to give foundation to arithmetic. His formal system intended to be capable of formalizing all the arithmetic notions of his time, based solely and exclusively on basic laws of logic - an attempt that became historically known as logicism. As is known, however, this project - presented for the first time in his work The Foundations of Arithmetic - failed, as shown in a paradigmatic way by Russell's Paradox pointed out by Bertrand Russell in a letter to Frege in June 1902. Frege, however, in an attempt to save the logicist program, outlines a solution attempt to escape the paradox in the appendix of his work Grundgesetze der Arithmetik. This solution, however, turns out to be unsatisfactory. The aim of our research is, therefore, to investigate why this solution does not prove itself satisfactory, both for technical reasons and for reasons internal to Frege's thought.