Origins of Boolean Algebra in the Logic of Classes: George Boole, John Venn and C. S. Peirce

Abstract

This Primary Source Project (PSP) is based on excerpts from works written in the 19th century by three mathematicians: George Boole, John Venn, and Charles Saunders Peirce. Without explicitly introducing modern notation, it develops a modern understanding of set operations and their basic properties within the context of the trio’s early efforts to develop a symbolic algebra for logic. While the project focuses on what would now be called ‘introductory set theory,’ it also lays the groundwork for a more abstract discussion of Boolean algebra as a discrete axiomatized structure. Project questions further prompt students to explore a variety of other mathematical themes, including the notion of an inverse operation, issues related to mathematical notation, and standards of rigor and proof. Beyond a certain level of mathematical maturity commensurate with a typical Calculus I background, however, there are no prerequisites for this PSP. Strong students at a pre-calculus level could also complete the earlier sections of the project.

This PSP is designed for use in an introductory or intermediate course in discrete or finite mathematics that includes a study of elementary set theory. Additionally, it may be used in any course that considers Boolean algebra from either a mathematical or computer science perspective, either alone or as a companion to one or both of the following PSPs:

• Boolean Algebra as an Abstract Structure: Edward V. Huntington and Axiomatization
• Applying Boolean Algebra to Circuit Design: Claude Shannon

Either or both of these companion PSPs could also be used independently of the current (Boole-Venn-Peirce) project, or as a preliminary to or as a follow-up to the other companion project.