conceptual

Reconstructing Batens' argument: Hypothesis to reduce: Monism, i.e., there is one TRUE logic that is normative and universal, in so far as it provides us with the standard of correctness for reasoning about every domain, to any community, at any historical circumstance. In order for it to be universal, it must take ALL logical possibiltiies in consideration. In order for it to be normative, it must at least make a distinction between good and bad arguments, i.e., it must not trivialize the logical consequence relation. Taking all logical possibiltiies in consideration entails logical nihilism: nothing follows logically from nothing Nihilism trivializes the logical consequence relation (against 3) Ergo, monism is false.

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...