Abstract

George Boole is widely regarded as the founder of symbolic logic. He initiated the revolution that transformed logic from the mold in which it had been set in ancient times into the dramatically growing mathematical form it has acquired in more recent times. However, Boole viewed himself not as a revolutionary but as completing a project undertaken by Aristotle two millennia earlier. He saw himself as reformulating traditional logic into a branch of mathematical analysis, thus refining and extending it. His orientation simultaneously blinded him to many of the shortcomings of his logic and led him to many original contributions transforming the field. In this dissertation I assess Boole's philosophy of logic while tracing its origins to the philosophies underlying the two main traditions that influenced it: Aristotelian logic and the field of mathematics then called mathematical analysis. ;Boole's orientation led him to view logic as a branch of mathematics about which mathematical results could be proved and not as the study of proofs themselves---especially proofs in mathematics---as had been done traditionally. For example, Boole completely ignored the indirect proof, so frequently encountered in mathematics. He viewed the logically perfect language as consisting of algebraic equations and the proper form of the propositions studied by logic as equational. In order to do this he viewed 'All Ss' in 'All Ss are Ps' as denoting the class of Ss and simultaneously, for the first time, he expanded the subject-matter of mathematics to include nonquantitative domains. ;Boole saw the central problem of logic not as the attempt to determine of a given premise-conclusion argument whether or not it was valid but as the attempt to find solutions to given equational "premises". This view led him to commit the fallacy of confusing a solution of an equation with a consequence of the equation but simultaneously, for the first time, to raise the Boolean summarization problems. His orientation prevented the expression of negation in his language; however, it simultaneously led him to the attempt, for the first time, to axiomatize logic, thus codifying infinitely many tautological forms, and also to use mathematical techniques to find metatheorems about his system, including decision procedures