Talk 1: Boole’s Algebra of Logic: A Modern Version, and A Modern Adaptation of the Original Version

George Boole (1815-1864), an English mathematician, revolutionized logic in the 19th century by applying methods from the then emerging field of symbolical algebra to logic. Boole’s algebra of logic, however, was not perfect and received much criticism. Yet, the system seemed, by and large, to work just as Boole claimed it would. In these lectures, I will present: (a) historical factors that influenced Boole’s thinking during (1847-1854), (b) the criticisms pointing to the weaknesses of Boole’s Logic, (c) a rigorous modern version of Boole’s theorems, based in good part on Vol. I and II of Schroeder’s Algebra der Logik, published in the 1890s, and (d) a rigorous modern presentation of Boole’s original algebra of logic (time permitting). These lectures will be mostly based on the recent (unpublished) joint work with Professor Stanley Burris, and Professor Burris’s article, George Boole, in Stanford Encyclopedia of Philosophy.