 In  §1.1,  we showed that formalizing relations was a key motivation behind Peirce’s new logic—first-order logic. In  §2.1,  we established a connection between Peirce’s own pragmatic maxim and his graphic representation of relations. Peirce did not aim to present a new logic by inventing a graphic system, but rather to present another new notation for the logic carried out by quantifiers and bound variables. He almost took it for granted that a graphic representation of relations helps us observe their consequences in a more efficient way. Hence, the Beta system may be considered to be the final stop of Peirce’s long journey to search for better notation for the logic of relations, which started in 1870 at the  latest.[34]