The abundance of the future: A paraconsistent approach to future contingents

Supervaluationism holds that the future is undetermined, and as a consequence of this, statements about the future may be neither true nor false. In the present paper, we explore the novel and quite different view that the future is abundant: statements about the future do not lack truth-value, but may instead be glutty, that is both true and false. We will show that (1) the logic resulting from this "abundance of the future" is a non-adjunctive paraconsistent formalism based on subvaluations, which has the virtue that all classical laws are valid in it, while no formula like φ & - φ is satisfiable (though both φ and - φ may be true in a model); (2) The peculiar behaviour of abundant logical consequence has an illuminating analogy in probability logic; (3) abundance preserves some important features of classical logic (not preserved in supervaluationism) when it comes to express those important retrogradations of truth which are presupposed by the argument de praesenti ad praeteritum. © Nicolaus Copernicus University (Toruń) 2013.