PARACONSISTENCY ON THE ROCKS OF DIALETHEISM

Can one be a non-dialetheic paraconsistentist? I will show that on a standard model-theoretic approach to consequence the answer to this question depends on the philosophical motivation behind the models. If the models are interpretations of the formal language, the answer to the question is "No", but if the models are representations of how things are, the answer is less clear. That different approaches to semantic characterisations of consequence come apart in this way demonstrates that attention should be paid, especially by paraconsistentists, to the motivations behind the theories.