Foundations and principles of Frege's logical objects

• Grant number: 14/27057-5
• Support type: Scholarships in Brazil - Doctorate
• Effective date (Start): May 01, 2015
• Effective date (End): March 01, 2019
• Field of knowledge: Humanities - Philosophy - Epistemology
• Cooperation agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
• Principal researcher: Marco Antonio Caron Ruffino
• Grantee: Vincenzo Ciccarelli
• Home Institution: Instituto de Filosofia e Ciências Humanas (IFCH). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated scholarship(s): 16/15742-0 - The notion of content and Frege's logical objects, BE.EP.DR

Abstract

The alleged conception of logic as a topic neutral subject, whose propositions are nothing but uninterpreted strings of symbols, was challenged in the second half of XIX century by the work of Gottlob Frege. Specifically, his investigations on the foundation of the concept of natural number, lead to a position historically known as logicism, according to which arithmetic - and secondly the entire edifice of mathematics - is derivable from "basic laws of pure thought". In other words Frege inaugurated a turn in the very conception of logic, with the main consequence that objects such as numbers, classes (here intended as extensions of concepts) and truth values are precisely "logical", namely their existence and their distinctive features are grounded on first principles of the analytical a priori knowledge. After being undermined by Russell's discovery of his set-theoretical paradox, this view returned under debate in the second half of XX century, when scholars like Parson, Boolos, Wright and Hale tried to fix the fregean theory of numbers. In this project I am aimed at investigating the notion of logical object in virtue of his central role in Frege's and neo-fregean's theories. My point is that by characterizing the differences between extensions of concepts and sets as unconditioned collections, numbers defined through Hume's Principle and their set-theoretical expressions, truth values as objects and truth value as properties of statements, the characteristic marks of logical objects will be unearthed and therefore the logico-ontological hierarchy of such objects will be made explicit. Moreover I will deal with the introduction procedure of logical objects into second-order logic, by analyzing the logico-epistemological status of the abstraction principle. As outcome of my research activity I expect to spell out the genealogy of the notion of logical objects from the axioms and the principles of second-order propositional calculus, thus highlighting main epistemological, logical and ontological assumptions of every logicist theory so far arisen and preparing the ground for a unified theory of logical objects. (AU)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

CICCARELLI, Vincenzo. Uma explicação do procedimento de re-modelização de conteúdo em Frege. 2019. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Filosofia e Ciências Humanas Campinas, SP.