Abstract

The standard account of the history of logic, in its crudest outline, runs as follows. Logic as a discipline was invented by Aristotle with his creation of syllogistic theory, which, despite the emergence of propositional logic in the work of the Stoics, refinements by mediæval logicians, and Leibniz's sketches of a characteristica universalis, dominated philosophy until the middle of the nineteenth century, when Boole's work on the "algebra of logic" and Frege's Begriffsschrift finally absorbed it into a larger framework. Boolean and Fregean logic were rivals until the beginning of the twentieth century, when the superior power of the Fregean system, as developed by Peano and Russell, won the day, and modern logic as we know it began to exert its hegemony. However, as with any crude account, there are glaring omissions and anomalies that threaten its usefulness even as a first approximation, and Peirce's role in the story has perhaps been the most seriously underplayed of all. Whilst rooted in the Boolean tradition, Peirce also—admittedly slightly later, but nevertheless independently of Frege—invented a notation for quantifiers: a notation, indeed, that influenced modern notation to a far greater extent than Frege's own cumbersome two-dimensional script. Furthermore, Peirce's logic of relations was a significant development in its own right, and both this and the stirrings of the model-theoretic approach in his work was to feed into the mainstream tradition through the work of Schröder, Löwenheim, Skolem, and Tarski, in particular.