ABSTRACT My aim in this paper is to present a pluralist thesis about the inferential role of logical constants, which embraces classical, relevant, linear and ordered logic. That is, I defend that a logical constant c has more than one correct inferential role. The thesis depends on a particular interpretation of substructural logics' vocabulary, according to which classical logic captures the literal meaning of logical constants and substructural logics encode a pragmatically enriched sense of those connectives. The paper is divided (...) into four parts: first, I introduce the motivation for the pluralist thesis of the paper; second I introduce the calculus for the different logics endorsed in the pluralist thesis; third, I motivate how the different behaviors of the logical vocabulary of these logics can be pragmatically interpreted, and fourth, I motivate how the different inferential roles that each substructural logic attribute to logical constants can coexist, and how we should reason with a logical constant c given this plurality. (shrink)

A detailed analysis of joint-contribution of premises and conclusions in classically valid sequents is presented in terms of hypergraphs. In (Saint-Germier, P., Verdée, P., & Villalonga, P. T. (2024). _Relevant entailment and logical ground. Philosophical Studies_ (pp. 1–43). https://doi.org/10.1007/s11098-024-02101-1 ), this idea of joint-contribution is introduced and motivated as a method for characterizing four kinds of relevant validity, in the sense of selecting the relevantly valid sequents among the classically valid sequents. The account in (Saint-Germier, P., Verdée, P., & Villalonga, (...) P. T. (2024). _Relevant entailment and logical ground. Philosophical Studies_ (pp. 1–43). https://doi.org/10.1007/s11098-024-02101-1 ) is built on a calculus, called \(\textsf{GLK}^{\hbox {a}}\), which proves grounding claims for (enthymematically) valid sequents. In the present paper an adequate representation of \(\textsf{GLK}^{\hbox {a}}\) is given in terms of hypergraphs. The hypergraphs are a kind of diagrammatic proofs for Classical Propositional Logic, entirely based on the grounds of premises and conclusions. The hypergraphs and their visualization provide insights into the relations between premises and conclusions and into the way validity is produced by the binding of premises and conclusions via their partial grounds. They visualize the network of elements of the sequent that contribute to its logical validity. Non-contributing (i.e. irrelevant) premises and conclusions are then specified to be those that are disconnected from the network, however one constructs the graphs. (shrink)

The aim of this paper is to give a general solution to the paradoxes of the material conditional, including the paradoxes generated by embedded conditionals. The solution consists in a pragmatic reinterpretation of the formal languages of classical logic LK and relevant logic LR as presented in Paoli. In particular I argue that the material conditional in the classical logic LK captures the truth conditions of “if...then”, but ignores certain pragmatic enrichments that are associated to it, while relevant logic LR (...) can give a systematic diagnostic of the cases in which a conditional is pragmatically enriched and those cases in which it is not. This diagnostic shows the reason why the paradoxes seem unacceptable and why they are, nevertheless, truth-preserving. This reinterpretation will also cover the solution that Paoli gives to McGee’s paradoxes of the Modus Ponens. (shrink)