Javid Jafari

What happens if we drop the axiom (K) and the necessitation rule from the usual axiomatic presentation of modal logic T? This system was first introduced by Ivlev (1988, Bull. Sect. Log., 17, 114–121). We show that this logic is a syntactical variant of the well-known paraconsistent logic BK (also known as mbCciw), which belongs to a large family of Brazilian paraconsistent logics known as Logics of Formal Inconsistency (LFIs). Our approach is semantical, as BK can be characterized by a 3-valued non-deterministic matrix (Nmatrix); we show that this Nmatrix can alternatively be axiomatized in a modal vocabulary by more convenient axioms. This result links this family of paraconsistent logics to another line of research aimed at characterizing modal logics without possible worlds, initiated by the works of Kearns (1981, J. Symb. Log., 46, 77–86) and Ivlev (1988, Bull. Sect. Log., 17, 114–121). We will see that the modal logics T and S4 ⁠, as well as their corresponding versions without the necessitation rule, can be characterized with the help of simple refinements of this single Nmatrix. All of this shows that this logic can serve as a base for both modal logics and LFIs.

Carnap (1943) noted that categoricity fails even for propositional logic. He observed that some “non-normal” models exist for classical logical consequence. The immediate reaction to this phenomenon was to strengthen the formal machinery or impose semantical constraints to rule out nonnormal models, and as a result, their very structure was largely overlooked. In this paper, I examine these non-normal models and explore the possibility that they assign non-classical meanings to logical connectives. By relaxing some standards regarding semantics, we will see that these models, in some sense, embed a non-deterministic matrix (Nmatrix) with interesting similarity to the strong Kleene’s 3-valued matrix. Then, I briefly explore its induced logics: two non-compositional counterparts of the well-known logics LP and K3.

According to Thomasson’s Easy Ontology, all existential questions have straightforward answers and are solvable by conceptual and empirical work. So there is no need for traditional metaphysics to solve them. First, I give some counterexamples to this thesis from incomplete and undecidable theories. Then I discuss some possible responses, I consider a wider sense of conceptual analysis and argue that even in this sense Easy ontology is not able to resolve the problem and must sacrifice either easiness or answerability. Finally, I will argue that although traditional metaphysics does not make the undecidable sentences answerable, it can still make sense of them and helps us to understand why there are unanswerable questions at all.