The basis of Boole's logical calculus

TL;DR

This paper provides a detailed analysis of Boole's logical calculus, exploring its fundamental ideas, methods, and a novel perspective on the logical connective of division, within Boole's original conceptual framework.

Contribution

It offers an exegetical reinterpretation of Boole's theory, including a new view on the logical connective of division and its methodological implications.

Findings

Clarifies the meaning and usefulness of Boole's methods.

Introduces a variation of Boole's calculus for new insights.

Analyzes the neglected logical connective of division.

Abstract

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.