Peirce’s use of the “scroll” as a graphical syntax for implication continued to raise many questions at this point in the Peirce List reading. I think a lot of what bothers people has more to do with general misunderstandings about material implication than anything peculiar to Peirce’s graphs. I suggested a way of reading the “scroll” that makes it crystal clear to me, namely, “not a without b”, and then I added the following comment.
Peirce’s approach in these lectures appeals to the line of thinking that takes implications and the corresponding subject-predicate form as basic, but that is not the only possible basis for a system of logical syntax and not the only basis that Peirce himself took up in his many syntactic experiments. In relating logical signs to logical objects it normally proves best to remain flexible and to consider the object of logic that is common to all its avatars.