New Logic and the Seeds of Analytic Philosophy

Abstract

Simplistic accounts of its history sometimes portray logic as having stagnated in the West completely from its origins in the works of Aristotle all the way until the nineteenth century. This is of course nonsense. The Stoics and Megarians added propositional logic. Medievals brought greater unity and systematicity to Aristotle’s system and improved our understanding of its underpinnings (see e.g., Henry 1972), and important writings on logic were composed by thinkers from Leibniz to Clarke to Arnauld and Nicole. However, it cannot be denied that an unprecedented sea change occurred in the nineteenth century, one that has completely transformed our understanding of logic and themethods used in studying it. This revolution can be seen as proceeding in two main stages. The first dates to the mid-nineteenth century and is owed most signally to theworkofGeorgeBoole (1815–1864). The seconddates to the latenineteenth century and the works of Gottlob Frege (1848–1925). Both were mathematicians primarily, and their work made it possible to bring mathematical and formal approaches to logical research, paving theway for the significantmeta-logical results of the twentieth century. Boolean algebra, the heart of Boole’s contributions to logic, has also come to represent a cornerstone of modern computing. Frege had broad philosophical interests, and his writings on the nature of logical form, meaning and truth remain the subject of intense theoretical discussion, especially in the analytic tradition. Frege’s works, and the powerful new logical calculi developed at the end of the nineteenth century, influenced many of its most seminal figures, such as Bertrand Russell, Ludwig Wittgenstein and Rudolf Carnap. Indeed, Frege is sometimes heralded as the “father” of analytic philosophy, although he himself would not live to become aware of any such movement.