Antonio Negro

Proposition 5.122 of Wittgenstein’s Tractatus has been the source of much puzzlement among interpreters, so much so that no fully satisfactory account is yet available. This is unfortunate, if only because the containment account of logical consequence has a venerable tradition behind it. Pasquale Frascolla’s interpretation of proposition 5.122 is based on a valid argument and one true premise. However, the argument explains sense containment only in an indirect way, leaving some crucial questions unanswered. Besides, Frascolla does not address the issue of how to make sense containment notationally perspicuous, an essential theme in Wittgenstein’s reflections. In this paper, we elaborate on Frascolla’s account by looking at the issue through the Tractarian notion of logical space. Our analysis shows that, for containment to be fully appreciated, one should adopt a negative perspective on the notion of sense, in line with the exclusionary theory of conceptual content, as labelled by Ian Rumfitt. Besides this, we introduce and discuss two methods—one envisaged by Wittgenstein himself—for making sense containment notationally perspicuous.

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 (,,, 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.