Implication and Peirce's philosophy of logic

Peirce claims that there is but one primary logical relation, that of illation or logical consequence. The present paper is devoted to show the influence of this viewpoint in Peirce's conception of logic. After a brief presentation of the Peirce's membership in the tradition of language as calculus, it examines his pioneering work in modal logic and other systems of logic. The last section attempts to summarize his doctrine of logic as a normative science.