Inconsistency, Paraconsistency and omega-inconsistency

BRUNO DA RE

Seminario; wip; 2017

In this talk I explore the relation between omega-inconsistency and plain inconsistency, in the context of theories that intend to capture semantic concepts. In particular, I'll focus on two very well known inconsistent but non-trivial theories of truth: LP and STTT. Both have the interesting feature of being able to handle semantic and arithmetic concepts, maintaining the standard model. However, it can be easily shown that both theories are omega-inconsistent. Although usually a theory of truth is generally expected to be $\omega$-consistent, all conceptual concerns don't apply to inconsistent theories. Finally, I'll explore if it's possible to have an inconsistent, but omega-consistent theory of truth, restricting my analysis to substructural theories.