A pragmatic logic for the expressive conception of norms and values and the Frege-Geach problem

Abstract: In this paper I intend to overcome the incompatibility -basically expressed by the Frege-Geach problem- between the expressive conception of norms and values and the applicability of logic to them, as well as the widespread scepticism about a possible "logic of attitudes" (Hale). To this end, I present a logic for the expressive conception of norms and values providing a solution to the Frege-Geach problem, that is immune to the ambiguities affecting two previous attempts by Blackburn (1984 and [1988] 1993). In particular, I use and extend a pragmatic language Lp, that is an extension of the language of standard propositional logic L, which is obtained by adding two categories of logical-pragmatic signs to the vocabulary of L: the signs of pragmatic mood („¥, O and H, standing for 'assertion', 'obligation' and 'approval', respectively) and the pragmatic connectives (~, ∩, ∪, ⊃, ≡). The wffs of L are called radical formulas (rf) of Lp. By applying the signs of pragmatic mood to the rfs, we obtain elementary sentential formulas (sf) (assertive, normative, evaluative) of Lp, that can be connected by means of the pragmatic connectives, so obtaining complex sfs. Every rf of Lp has a truth value and every sf has a justification value, which is defined in terms of the intuitive notion of proof and which depends on the truth value of its radical subformulas. In this language, the notions of pragmatic validity, compatibility, satisfiability and inference are defined and some criteria of pragmatic validity are given. Therefore, in Lp, it is possible to carry out inferences between norms and values expressively understood and, thus, to adequately formalize Geach's problematic inferences.