Definite totalities and determinate truth in conceptual structuralism

This article investigates the connection and dependence between the definiteness of the totalities involved in mathematical structures and the determinateness of statements about that structure. From a logical perspective, we investigate whether logical principles expressing the definiteness of totalities license the use of classical logic. From a philosophical perspective, this article provides a reconstruction of Solomon Feferman’s claim that the definiteness of the natural number conception implies the determinateness of arithmetical statements and therefore justifies the adoption of classical logic for arithmetical theories.