Scientific Objectivity and the Community of Inquirers: C.S. Peirce on Mathematics

By exploring Peirce’s view of mathematics, I investigate the relationship between the objectivity of mathematics as a science, and therefore the status of its “scientific” objects, and the role accorded by Peirce to intersubjectivity in mathematics and mathematical practice. In a nutshell, how can Peirce combine the ‘objective side’ of this very peculiar science, with its subjective, or inter-subjective side? To reach this goal, the paper is divided into three parts: (i) the first one introduces Peirce’s definition and characterization of mathematics, which according to him is the only science that does not depend on philosophy, but the other way around philosophy must depend on it; (ii) the second underlines the indispensable role of intersubjectivity in science, and try to understand whether or not this intersubjective dimension is essential and required in both mathematical practice and “mathematical knowledge”; (iii) the third part analyzes Peirce’s peculiar realism in mathematics, which actually overcome the common, contemporary dichotomy between realism and idealism in philosophy of mathematics, by relying upon Peirce’s pragmatic principle.