In this paper we study the relations between the fragment L of classical logic having just conjunction and disjunction and the variety D of distributive lattices, within the context of Algebraic Logic. We prove that these relations cannot be fully expressed either with the tools of Blok and Pigozzi's theory of algebraizable logics or with the use of reduced matrices for L. However, these relations can be naturally formulated when we introduce a new notion of model of a sequent calculus. (...) When applied to a certain natural calculus for L, the resulting models are equivalent to a class of abstract logics (in the sense of Brown and Suszko) which we call distributive. Among other results, we prove that D is exactly the class of the algebraic reducts of the reduced models of L, that there is an embedding of the theories of L into the theories of the equational consequence (in the sense of Blok and Pigozzi) relative to D, and that for any algebra A of type (2,2) there is an isomorphism between the D-congruences of A and the models of L over A. In the second part of this paper (which will be published separately) we will also apply some results to give proofs with a logical flavour for several new or well-known lattice-theoretical properties. (shrink)

In a series of publications, Robert Stalnaker and Hartry Field have undertaken a dispute about what is the correct way to explain intentionality naturalistically. Field wishes to assimilate mental intentionality to linguistic intentionality and to explain both kinds of intentionality using Tarskian truth theory plus the causal theory of reference. Stalnaker wishes to subsume mental intentionality under the notion of indication and to explain it on the model of measurement theory, leaving linguistic intentionality to be explained derivatively. I attempt to (...) adjudicate their dispute, paying particular attention to the question whether Tarskian truth theory has a role to play in explaining intentionality naturalistically. ;The first half of the dissertation examines Tarski's theory. I argue that Field and Stalnaker are incorrect when they agree that Tarski's reduction of the notion of truth is defective and I explain Tarski's 'structural' notion of truth. In the second half of the dissertation, I argue that Stalnaker's criticisms of Field mostly do not stand up to scrutiny, but that Field's theory is unsatisfactory nonetheless; I also argue that certain criticisms of Stalnaker do more damage than he thinks. I conclude that neither has solved 'the problem of intentionality', but that Stalnaker is right that truth theory as such will not have a role in the correct solution. (shrink)