 Peirce was probably the first person to discuss rules of transformation in a non-sentential representation system. In the same way that the rules of algebra tell us which transformations of symbols are permitted and which are not, so should the rules of diagram manipulation. Some of Pierce’s six rules needed more clarification and turn out to be incomplete—a problem which Peirce himself anticipated. However, more importantly, Peirce did not have any theoretical tool—a clear distinction between syntax and semantics—to convince the reader that each rule is correct or to determine whether more rules are needed. That is, his important intuition (that there could be transformation rules for diagrams) remained to be justified.