Translations on the dispute between Logical Pluralism and Monism

• Grant number: 23/02114-5
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: June 01, 2023
• End date: October 31, 2023
• Field of knowledge: Humanities - Philosophy - Logic
• Principal Investigator: Itala Maria Loffredo D'Ottaviano
• Grantee: Sofia Abelha Meirelles
• Host Institution: Instituto de Filosofia e Ciências Humanas (IFCH). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The use of translations between logics is quite appropriate to analyze how different logics are related and how they can be interpreted in each other. A classic example of this are the relative consistency proofs of classical logic in relation to intuitionistic logic, which represents an important milestone in the history of logic. The possibility of finding a common ground to discuss different logics is advantageous both from a formal point of view, about which are the theorems and how validity is constructed, and from a philosophical point of view, since we can compare the meaning of different logical inferences in the case of classical and intuitionistic logic, it is possible to compare and discuss why the tertium non datur (law of excluded middle) and the double negation are no longer valid intuitionistically. Our motivation is to employ translations between logics in the popular discussion about logical pluralism, i.e., the thesis that there is more than one correct logic, as opposed to logical monism, which claims that there is only one true logic. Our aim is to circumvent the meaning-variance thesis, initially proposed by Quine 1986, through translations in order to allow meaningful variants of logical pluralism. For this purpose, we start from the concept of conservative translations as a safe framework that eliminates the incommensurability between logics and, consequently, allows the rigorous discussion of objections to logical pluralism, such as the already mentioned meaning-variance