LINGUA CHARACTERICAANDCALCULUS RATIOCINATOR: THE LEIBNIZIAN BACKGROUND OF THE FREGE-SCHRÖDER POLEMIC

Abstract

AbstractAfter the publication ofBegriffsschrift, a conflict erupted between Frege and Schröder regarding their respective logical systems which emerged around the Leibnizian notions oflingua charactericaandcalculus ratiocinator. Both of them claimed their own logic to be a better realisation of Leibniz’s ideal language and considered the rival system a merecalculus ratiocinator. Inspired by this polemic, van Heijenoort (1967b) distinguished two conceptions of logic—logic as language and logic as calculus—and presented them as opposing views, but did not explain Frege’s and Schröder’s conceptions of the fulfilment of Leibniz’s scientific ideal.In this paper I explain the reasons for Frege’s and Schröder’s mutual accusations of having created a merecalculus ratiocinator. On the one hand, Schröder’s construction of the algebra of relatives fits with a project for the reduction of any mathematical concept to the notion of relative. From this stance I argue that he deemed the formal system ofBegriffsschriftincapable of such a reduction. On the other hand, first I argue that Frege took Boolean logic to be an abstract logical theory inadequate for the rendering of specific content; then I claim that the language ofBegriffsschriftdid not constitute a completelingua charactericaby itself, more being seen by Frege as a tool that could be applied to scientific disciplines. Accordingly, I argue that Frege’s project of constructing alingua charactericawas not tied to his later logicist programme.