C. S. Peirce was both a logician and a philosopher of logic. Strangely, these two approaches have not been much compared. This present paper intends to explicitly raise the question of the relation between logical formalism and the philosophical conceptions of logic that Peirce supported. The problem we consider is simply whether there is any connection between Peirce’s advances in logic and how he conceived of logic, that is, between logical theory and logical practice. Is logic philosophically neutral or does it involve at least a certain conception of itself? We answer that Peirce’s semiotic, iconic, relational, dialogical, inquiry-based formalism, that is, the pragmaticist conception of logic, stresses the insufficiency of deductive logic. Being mostly inductive and abductive, the inquiry cannot be expressed through formal logics. It shows that the contemporary meaning of logic cannot be separated from its Peircian use: Logic and philosophy of science come together, and it may paradoxically be this faith which motivated most of the formal advances of Peirce’s logic.