Lingua characterica and calculus ratiocinator: The Leibnizian background of the Frege-Schröder polemic

0544080 - FLÚ 2022 RIV GB eng J - Journal Article
Bertran-San Millán, Joan
Lingua characterica and calculus ratiocinator: The Leibnizian background of the Frege-Schröder polemic.
Review of Symbolic Logic. Roč. 14, č. 2 (2021), s. 411-446. ISSN 1755-0203. E-ISSN 1755-0211
Grant - others:AV ČR(CZ) AP1602
Program: Akademická prémie - Praemium Academiae
Institutional support: RVO:67985955
Keywords : Frege * Schröder * Leibniz * lingua characterica * calculus ratiocinator * concept-script * algebra of logic
OECD category: Philosophy, History and Philosophy of science and technology
Impact factor: 1.217, year: 2021
Method of publishing: Limited access
https://doi.org/10.1017/S175502031900025X

After the publication of Begriffsschrift, a conflict erupted between Frege and Schröder regarding their respective logical systems which emerged around the Leibnizian notions of lingua characterica and calculus ratiocinator. Both of them claimed their own logic to be a better realisation of Leibniz’s ideal language and considered the rival system a mere calculus 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 mere calculus 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 of Begriffsschrift incapable 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 of Begriffsschrift did not constitute a complete lingua characterica by 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 a lingua characterica was not tied to his later logicist programme.
Permanent Link: http://hdl.handle.net/11104/0321141