A pragmatic logic for expressivism

This article aims to show that the incompatibility between the application of logic to norms and values and the expressive conception of these notions – basically summed up by the Frege–Geach problem – can be overcome. To this end, a logic is constructed for the expressive conception of norms and values which provides a solution to the Frege–Geach problem and is not affected by the limitations that occur in some previous attempts. More specifically, a pragmatic language LP is introduced which is an extension of the language L of standard propositional logic, obtained by adding two categories of logical-pragmatic signs to the vocabulary of L: the signs of pragmatic mood ((Formula presented.), (Formula presented.), (Formula presented.), standing for assertion, obligation and approval, respectively) and the pragmatic connectives (∼, ∩, ∪, ⊃, ≡, standing for pragmatic negation, conjunction, disjunction, implication and bi-implication, respectively). The notions of pragmatic validity, consistency (satisfiability), compatibility, equivalence and inference are then defined, and some criteria of pragmatic validity are given. It is thus possible to carry out in LP inferences on norms and values expressively understood, adequately formalizing Geach's problematic inferences.