  In the present paper we aim to provide a thoughtful and exegetical account of
the fundamental ideas at the basis of Boole's theory, with the goal of
developing our investigation strictly within the conceptual structure
originally introduced by Boole himself. In particular, we will focus on the
meaning and the usefulness of the methods of the developments. We will also
consider a slight variation of it that will allow us to to present in a new
light some important and ingenuous aspects of Boole's calculus examined by the
author in his work. Finally, a large attention is devoted to the analysis of
the 'neglected' logical connective of division.
