Philosophy of notation’s main concern are the signs that better represent logic and mathematics. Notation is the clothing or the medium by means of which logicians want to express their ideas. Therefore, philosophy of notation must be a part of semiotics. For Peirce, semiotics has three branches: speculative grammar or syntax; critics or semantics; and speculative rethorics or pragmatics. Although notation is mostly related to grammar or syntax of logic because notation is concerned with the elements through which logic must be expressed, philosophy of notation is at the bottom a question of rethorics, because the the third branch of semiotics has the purpose or telos of logic, it has the whole view of logics, and therefore, it can have the most important questions and demands to make to syntax. 

RFERENCES

Colapietro, V. (2007). C. S. Peirce’s Rhetorical Turn. En: Transactions of the Charles S. Peirce Society. Vol. 43, No. 1

Liszka, J. J. (2000). Peirce's New Rhetoric. En: Transactions of the Charles S. Peirce Society, Vol. 36, No. 4, pp. 439-476. https://www.jstor.org/stable/40320810

Peirce, C.S. (1904). "Ideas, Stray or Stolen, about Scientific Writing." MS 774, EP 2 325-330.