Peirce recognized the triadic nature of logic already in his youth (W 1:304; 2:57), and in the course of his life he proposed several names for the three branches of this science. This is particularly true concerning the third subdivision of his logic. He named it speculative, universal, general, and pure rhetoric, as well as objective logic and methodeutic. The plurality of names and descriptions regarding this science cannot but be a stimulus for the interpreter to clarify what was going on in Peirce’s thought. Thus, the concern of this chapter is to highlight what Peirce was trying to identify under these labels and to clarify a very important distinction needed to understand his intentions: the distinction between a general study of the conditions of interpretation, which we can indicate with the term speculative rhetoric, and a study of the purposeful development of knowledge, a narrower interest with principles of its own, which is well designated by the term methodeutic. Speculative rhetoric and methodeutic will thus be revealed to be the branches of logic where purposefulness becomes semiotically relevant. After this distinction has been drawn, I will try to clarify in depth Peirce’s methodeutic through the analysis of one of its applications, namely its utility in furthering mathematical discoveries. I will then identify the principles of this science as rooted in practical methods of thinking and show how a methodeutical clarification of the steps of scientific inquiry, especially abduction, can enhance our understanding of inquiry as a whole. As a result, methodeutic will be revealed to be a study attempting to improve our capacity to gain knowledge by means of a clarification of the principles that are guiding the development of our thinking and that are already working in our everyday and scientific practices. Therefore, I will maintain that the epistemological value of methodeutic lies more in the identification of the principles that govern the attainment of knowledge than in the justification of the latter. In the last section, I will analyze a manuscript that has been used by commentators for establishing the relationship between speculative rhetoric and methodeutic, and I will propose my interpretation of it.