The Algebra of Boole Is Not Boolean Algebra - Math Foundations

Explore the intricacies of George Boole's original algebra in this 27-minute lecture from the Math Foundations series. Delve into the arithmetic over the bifield B_2={0,1} and its applications to vector spaces and algebra. Learn how to reformulate Aristotle's syllogistic construction using Boole's algebra and prove syllogisms through simple algebraic methods. Examine the complexities of third figure syllogisms, such as Darapti, and understand the concept of "existential import" in logical reasoning. Conclude by distinguishing between the Algebra of Boole and modern Boolean algebra used in circuit analysis and set theory. Gain valuable insights into the foundations of mathematical logic and its historical development.

Introduction
Aristotles Square of Opposition
Syllogisms
Existential import
Boolean algebra