Boole’s Symbolized Laws of Thought Facing Empiricism

Overview & Synopsis

George Boole (1815-1864) is rightly known as a logician, the author of an algebra of logic, even if he did not conceive it quite in the same way as we know it. The calculus on classes and the calculus of propositions, that he set out to be equivalent, were at the core of his algebra of logic. After more than twenty centuries where logic was associated to the analysis of language, it was handled for the first time with mathematical symbols. However, the known Boole's algebra is not the one Boole produced. In this paper, I would like to move apart from the classical recurring approach to history-often referred to as Whiggist-, and to contextualize Boole's work so as to brighten the main trends which guided this renewal of how to deal with logic. Boole was also a mathematician, and since his Mathematical Analysis of Logic (1847), his work was very close to the symbolical way of thinking algebra, as it was developed in Cambridge by "The Analytics" in order to found usual algebraic practices. An Investigation on the Laws of Thought (1854) enunciated a more systematic view of this project for logic, devised as a whole system, facing what was at stake for the theory of knowledge with the strong rise of experimental sciences. Clearly, Boole wanted to stand out from empiricism, and from metaphysics as well, and to maintain an absolute meaning to formal sciences. And I will scrutinize his philosophical references so as to precise how his enterprise answer these issues, relating to necessary reasoning, and to probable reasoning as well.