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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985955%3A_____%2F21%3A00544080" target="_blank" >RIV/67985955:_____/21:00544080 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1017/S175502031900025X" target="_blank" >https://doi.org/10.1017/S175502031900025X</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1017/S175502031900025X" target="_blank" >10.1017/S175502031900025X</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

60301 - Philosophy, History and Philosophy of science and technology

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Review of Symbolic Logic

ISSN

1755-0203

e-ISSN

1755-0211

Svazek periodika

14

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

36

Strana od-do

411-446

Kód UT WoS článku

000673319400005

EID výsledku v databázi Scopus

2-s2.0-85091819812