Charles S. Peirce (1839–1914) was first and foremost a logician. In his mature writings, he used to divide logic into three main branches or departments, a division which was fashioned after the medieval trivium of artes sermocinales: grammatica, dialectica, rhetorica. The three departments of Peirce’s logic are “speculative grammar,” “logical critics,” and “methodeutic.” The central department, logical critics, consists in the study of arguments, in the distinction of valid from invalid arguments, and in the classification of valid arguments into essentially distinct kinds. The first department, speculative grammar, is the study and classification of the parts of arguments (propositions and terms) and of other logical forms that are needed in logical critics. The third department, methodeutic, is the study of the methods of scientific inquiry. Logical critics is the “critic” of arguments (the study of the conditions of their validity); speculative grammar is the “physiology” of arguments (the study of their meaning, structure, components, and functioning); methodeutic is the “methodology” of arguments (the study of their general utility and value in conducting an inquiry). The three departments are ordered: methodeutic presupposes logical critics (utility presupposes validity), and logical critics presupposes speculative grammar (validity presupposes meaningfulness).