In 1879, Frege published his first book Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens (Concept Notation: A formula language of pure thought, modelled upon that of arithmetic) and was promoted to außerordentlicher Professor (Extraordinarius Professor) at Jena.  Although the Begriffsschrift constituted a major advance in logic, it was neither widely understood nor well-received. Some scholars have suggested that this was due to the facts that the notation was 2-dimensional instead of linear and that he didn’t build upon the work of others but rather presented something radically new (e.g., Mendelsohn 2005, 2).  Though our discussion below is framed primarily with an eye towards the system Frege developed in his two-volume work of 1893/1903 (Grundgesetze der Arithmetik), the principal elements of this later system can be found already in the Begriffsschrift of 1879.