 Boole’s The Mathematical Analysis of Logic presents many interesting logic novelties: It was the beginning of nineteenth-century mathematization of logic and provided an algorithmic alternative (via a slight modification of ordinary algebra) to the catalog approach used in traditional logic (even if reduction procedures were developed in the latter). Instead of a list of valid forms of argument, the validity of arguments were determined on the basis of general principles and rules. Furthermore, it provided an effective method for proving logical laws on the basis of a system of postulates. As Boole wrote later, it was a proper “science of reasoning”, and not a “mnemonic art” like traditional Syllogistics (Boole 1997: 136).  Three-quarters of the way through this book, after finishing his discussion of syllogistic logic, Boole started to develop the general tools that would be used in his Laws of Thought (1854) to greatly extend traditional logic by permitting an argument to have many premises and to involve many classes. To handle the infinitely many possible logical arguments of this expanded logic, he presented theorems that provided key tools for an algorithmic analysis (a catalog was no longer feasible).