![]() Second, Boole intended to derive the laws of logic from the laws of the operation of the human mind, and to show that these laws were valid of algebra and of logic both, when applied to a restricted domain. Boole’s motivation is, first, to address issues in the foundations of mathematics, including the relationship between arithmetic and algebra, and the study and application of differential equations (Durand-Richard, van Evra, Panteki). In his 1854 work An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, Boole argues that the laws of thought acquire normative force when constrained to mathematical reasoning. Logicians in the New Analytic tradition were influenced by the work of Immanuel Kant, and by the German logicians Wilhelm Traugott Krug and Wilhelm Esser, among others. George Boole emerged from the British tradition of the “New Analytic”, known for the view that the laws of logic are laws of thought. And I will scrutinize his philosophical references so as to precise how his enterprise answered these issues, relating to necessary reasoning, and to probable reasoning as well. Clearly, Boole wanted to stand out from empiricism, and from metaphysics as well, and to maintain an absolute meaning to formal sciences. 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. 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. In this chapter, 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. However, the known Boole’s algebra is not the one Boole produced. After more than twenty centuries where logic was associated to the analysis of language, it was handled for the first time with mathematical symbols. ![]() 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. ![]() ![]() ![]() 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. ![]()
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