Impossible Truths: A Non-dialetheist Paraconsistent Approach to Paradoxes

In this paper, I intend to offer a non-dialetheist semantics for a modal treatment of both negation and conditional that represents the Transparency of Truth. I shall argue that to evaluate paradoxical self-referential sentences (extensional and hyper-intensional ones) we need to consider inconsistent situations, even if we are evaluating these sentences in a consistent situation. This is a good point pro paraconsistency but does not force us into Dialetheism. I offer here a paracomplete paraconsistent logical consequence (LIT—The Logic of Impossible Truths) based on structures that preserve intuitions behind non-vacuism about counterpossibles, and non-dialetheism about semantic paradoxes. One of the main important results in this framework is that worlds are impossible (inconsistent) fictional situations. This result mirrors inside my framework the indefinite extensibility of situations and truth, what I take to be one of the main lessons we should learn from paradoxes.