Analysis of truth conditions and existential requirements in axiomatizations of arithmetic

Author(s)

Edgar Luis Bezerra de Almeida

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Filosofia e Ciências Humanas
• Defense date: 2017-12-11

Examining board members

Itala Maria Loffredo D'Ottaviano; Alexandre Fernandes Batista Costa Leite; Edelcio Gonçalves de Souza; Hugo Luiz Mariano; Giorgio Venturi

• Advisor: Itala Maria Loffredo D'Ottaviano; Rodrigo de Alvarenga Freire

Abstract

This Thesis aims to contribute to the understanding of two important subjects to the philosophy of mathematics. The notion of truth for mathematical propositions and the notion of existence in arithmetic. To pursue this target two original contributions are presented, one for each of these subjects. With regard to the notion of truth, we explore the consequences of adopting a normative framework to fix the truth value of arithmetic propositions. This normative framework is instituted by mathematical practice. The analysis will establish in what sense the standard model of arithmetic - and hence the truth value of arithmetic sentences - is fixed by the analysis' hypothesis. In addition, a strategy to fix the truth of arithmetical sentences based on the normative paradigm is outlined and we will argue that we can avoid some of the main difficulties faced by the realism and formalism with regard to the assignment of truth value to arithmetical sentences. Concerned with the notion of existence, a proposal is made to evaluate the existential requirements of arithmetic sentences. This evaluation is based on the assumption that the existential import of these sentences is an attribute of the truth conditions of arithmetic propositions. The analysis of this assumption motivates a precise and well-founded definition, in the arithmetical context, to the concept of existence axiom in arithmetical context. In addition, the analysis fosters a criterion of differentiation between the axioms of theories that are, from the perspective of interpretations, indistinguishable (AU)

• FAPESP's process: 13/01011-6 - Existence axioms in subtheories of ZFC and related axiomatic systems
• Grantee: Edgar Luis Bezerra de Almeida
• Support Opportunities: Scholarships in Brazil - Doctorate