An investigation of logical pluralism and b-entailment

Abstract

Logical pluralism has recently been given much attention, with numerous authors contesting its nature. In a broad sense, logical pluralism is the view that there are more than one correct or legitimate logic, which can be articulated in different ways. The present study participates in this debate by exploring the framework of 𝐵-entailment in the context of several of varieties of pluralism. 𝐵-entailment is a logical consequence relation, which may express different consequence relations, such as those of many-dimensional logics. In particular, this study examines four different takes on pluralism: Shapiros’s eclectic pluralism, Beall and Restall’s GTT pluralism, Hjortland’s intra-theoretic pluralism and Restall and Paoli’s pluralism based on proof-theory. It will be shown how 𝐵-entailment fits into these varieties of pluralism, and a discussion is presented on how 𝐵-entailment falls short is some aspects. The aim is to contribute to the discussion on logical pluralism as well as to expand the discussion about 𝐵-entailment and consequence relations of this sort.