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LINGUA CHARACTERICA AND CALCULUS RATIOCINATOR: THE LEIBNIZIAN BACKGROUND OF THE FREGE-SCHRÖDER POLEMIC

Part of: Philosophical aspects of logic and foundations Mathematical Logic and Foundations History of mathematics and mathematicians

Published online by Cambridge University Press:  29 June 2020

JOAN BERTRAN-SAN MILLÁN
JOAN BERTRAN-SAN MILLÁN*
Affiliation:
INSTITUTE OF PHILOSOPHY CZECH ACADEMY OF SCIENCES JILSKÁ 1 110 00PRAGUECZECH REPUBLICE-mail: sanmillan@flu.cas.cz
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Abstract

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.

Keywords

FregeSchröderLeibnizlingua charactericacalculus ratiocinatorconcept-scriptalgebra of logic

MSC classification

Primary: 01A55: 19th century
Secondary: 03-03: Historical (must also be assigned at least one classification number from Section 01) 03A05: Philosophical and critical
Type
Research Article
Information
The Review of Symbolic Logic , Volume 14 , Issue 2 , June 2021 , pp. 411 - 446
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© Association for Symbolic Logic, 2020

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