Comments on Hookway, “The Pragmatic Maxim and the proof of pragmatism (2): after 1903”

In his article published in the current issue of Cognitio, Professor Christopher Hookway addresses the question of Peirce’s proof of pragmaticism after 1903. It is essential to give a clear account of the details of Peirce’s proof, specially of his use of the then newly-discovered logic of Existential Graphs (EG). Hookway’s aim is to answer why Peirce did believe a proof of pragmaticism needed the Existential Graphs. I suggest that Peirce’s proof can still be maintained, since some modifications are made. My question is to twofold: first, given the logical theory of EGs at hand, can the proof itself be reconstructed with it, and, second, if so, how?