A substructural analysis of embedded conditionals

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 (which rejects the validity of weakening and splits the connectives into two) as presented in Paoli (2002, 2007). 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 (2005) gives to McGee’s paradoxes of the Modus Ponens. © 2020, Springer Nature B.V