Title: History of logic as a tool for exploring the plurality of logical frameworks

Abstract:

I will outline another type of logical pluralism than the one now famously proposed by Beall and Restall (2006). I will argue that in addition to paying attention to particular logics, such as classical, intuitionnistic, relevance logics, etc., it is important to study the different frameworks in which these particular logics are expressed, such a model-theoretic, proof-theoretic, or game-theoretic frameworks. This provides a different kind of logical pluralism, namely a pluralism for logical frameworks. It is a dimension to take into account when studying logics from different cultures, which should be of particular interest to feminist or decolonial approaches to logic, but also when studying logics from different times, and I will focus on this point, taking Aristotle’s logic as a case study.
By comparing different modern formalizations of Aristotle’s assertoric syllogistic, I will highlight the fact that the choice of logical framework injects within a particular logic (syllogistic in this case) the basic principles constitutive of this framework. In this fashion, an uncritical formalization of an ancient logic risks injecting in the ancient texts the modern logician’s preconceptions regarding what logic is, inherited from their preferred logical framework. I will present the dialogical reconstruction of syllogistic I worked out in my PhD dissertation (2021) in order to show that different logical paradigms are embedded in logical frameworks, and can completely change the meaning of logic, even when the logical result stay the same.