The Illocutionary Foundation of Mathematical Social Constructivism

• Grant number: 23/17906-4
• Support Opportunities: Scholarships in Brazil - Master
• Start date: June 01, 2025
• End date: February 28, 2026
• Field of knowledge: Humanities - Philosophy - Metaphysics
• Principal Investigator: Marco Antonio Caron Ruffino
• Grantee: Pedro Daher Novo
• Host Institution: Instituto de Filosofia e Ciências Humanas (IFCH). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The traditional perspective of the philosophy of mathematics, typically attributed to the thought of Gottlob Frege, characterizes mathematical objects as abstract entities. According to this perspective, known as platonic realism, since statements about mathematical entities are true, we must assume the existence of objects that are referred to by terms and expressions that operate as proper names. However, after the arrival of arguments based on the requirement of causal connection of Paul Benacerraf and Hartry Field, several alternative theories to platonic realism emerged that sought to recover the intuitive characteristics of mathematical entities, such as their objectivity, their metaphysical necessity and their timelessness, without the necessity of admiting the problematic ontological commitments of platonic realism. Julian Cole's social constructivism stands out among alternative approaches once it sustains the classical abstract properties of mathematical truths, preserving the dependence of mathematical facts on their institutional practice. Cole's current perspective on institutional reality is based on a refinement of John Searle's social ontology, adding a different kind of function, which does not assign a status, but delimits and characterizes the transition between domains of deontic powers. In turn, institutions impose functions on reality in virtue of the linguistic capacity of human beings to generate new aspects of reality through declarative speech acts. Thus, the main objective of this project is to analyze the theoretical advantages and disadvantages in characterizing declarations as the foundation of mathematics.