The arithmetic paradigm: conceptual relations between logic and arithmetic

• Grant number: 14/04749-9
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: June 01, 2014
• End date: August 11, 2015
• Field of knowledge: Humanities - Philosophy - Logic
• Agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
• Principal Investigator: Itala Maria Loffredo D'Ottaviano
• Grantee: Leandro Oliva Suguitani
• Host Institution: Centro de Lógica, Epistemologia e História da Ciência (CLE). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 10/51038-0 - Logical consequence, reasoning and computation - LOGCONS, AP.TEM

Abstract

George Boole ushered the study of "mathematical logic" establishing, as far as possible, the relations between logic and arithmetic so that the latter could be applied as a formal tool for investigating logical inferences upon a certain category of propositions.This unique perspective Boole - we call it "arithmetic paradigm" of logic - was dropped early, perhaps because of the criticism it received at that time and also by the successfull development of logic under the so-called "algebraic paradigm", established by the successors of Boole, and the "linguistic paradigm", whose main precursors are G. Frege and B. Russel. However, we believe that there are still many results in logic, potentially, to be explored from its interrelations with arithmetic. In this Research Project, we aim at reconstructing the original scenery of mathematical logic with modern logic-algebraic tools in order to clarify/establish some conceptual relationships between logic and arithmetic so that we can restore the arithmetic paradigm, under which we hope to obtain interesting results for logic. (AU)