Boolean Algebra as an Abstract Structure: Edward V. Huntington and Axiomatization

Abstract

This Primary Source Project (PSP) is based on a 1904 paper in the study of axiomatizations of Boolean Algebra by the American postulate theorist Edward V. Huntington. This paper fully encapsulated the formal rigor that became a hallmark of 20th-century mathematics. In it, Huntington introduced various postulate sets for what is now called a Boolean Algebra and illustrated the use of models to establish the independence and consistency of a postulate set. While the project assumes some (minimal) familiarity with the set operations of union and intersection and their representation by Venn diagrams, that prerequisite material may be introduced by completing the companion Boole-Venn-Peirce project listed below, through reading a standard textbook treatment of elementary set operations, or via a short class discussion/lecture.

This PSP is primarily designed for use in an introductory or intermediate course in discrete or finite mathematics that considers Boolean algebra from either a mathematical or computer science perspective. The following PSPs are further available as potential companion projects in such a course, where either or both of these companion projects could also be used independently of the Huntington project, or as a preliminary to or as a follow-up to the other companion project.

• “Origins of Boolean Algebra in the Logic of Classes: George Boole, John Venn and C. S. Peirce”
• “Applying Boolean Algebra to Circuit Design: Claude Shannon”

Given its treatment of axiomatization (e.g., consistency, independence), some or all of the current (Huntington) project could also be used in a course on abstract algebra or model theory.