Truth is not fundamental
Traditionally, truth is considered a fundamental notion and logical consequence is considered less fundamental because it can be defined as truth-transmission. What is often forgotten is that things could also be presented the other way around: with logical consequence as fundamental and truth as derived from it. (This, I think is one of the important consequences of the work of Mike Dunn on algebraic methods for philosophical logic and David Lewis’ later work on the metaphysics of set theory). Perhaps the main difference between logical consequence and truth is that the first one is a homogenous relationship, that is a relation between things of the same sort – propositions or sets of propositions, while truth is considered either not a relation or a heterogenous one – if one thinks of truth as truth-in-a-world, that is, a relation between things of different ontological kinds: a proposition and a world. So the first step in defining truth in terms of logical consequence...