  Peirce’s special strength lay not so much in theorem-proving as rather in the invention and developmental elaboration of novel systems of logical syntax and fundamental logical concepts. He invented dozens of different systems of logical syntax, including a syntax based on a generalization of de Morgan’s relative product operation, an algebraic syntax that mirrored Boolean algebra to some extent, a quantifier-and-variable syntax that (except for its specific symbols) is identical to the much later Russell-Whitehead syntax. He even invented two systems of graphical two-dimensional syntax. The first, the so-called “entitative graphs,” is based on disjunction and negation. A version of the entitative graphs later appeared in G. Spencer Brown’s Laws of Form, without anything remotely like proper citation of Peirce. A second, and better, system of graphical two-dimensional syntax followed: the so-called “existential graphs.” This system is based on conjunction and negation. Even though the syntax is two dimensional, the surface it actually requires in its most general form is a torus of finite genus. So, the system of existential graphs actually requires three dimensions for its representations, although the third dimension in which the torus is embedded can usually be represented in two dimensions by the use of pictorial devices that Peirce called “fornices” or “tunnel-bridges” and by the use of identificational devices that Peirce called “selectives.” The existential graphs are essentially a syntax for logic that uses the whole mathematical apparatus of topological graph theory. There are three parts of it: alpha (for propositional logic), beta (for quantificational logic with identity but without functions), and gamma (for modal logic and meta-logic).