Babbage and Boole: the laws of symbolical calculus

In the first half of the XIXth century, Charles Babbage (1791-1871) designed his "analytical engine", which today is identified as a mechanical computer with an external program. Prior to that, George Boole (1815-65) produced the first mathematical writing of logic which, since Aristotle, had been linked with the analysis of language. The aims of this paper are to show that these two authors whose works are not generally associated, belong to the same English algebraical network, and to situate their achievement within the conceptual and institutional effects of the Industrial Revolution. Although these algebraists moved within the framework of Locke's empiricism and philosophy of language, they cannot be identified in a constructivist perspective. As Anglican reformers, they assigned the necessity of mathematics to a radically primary symbolical calculus, making explicit the operations of mind, independently of contingent interpretations. They introduced a radical separation, within a hierarchical relationship, between the operativity and the meaning of symbolical calculus.