Logical Theory-Choice: The Case of Classical Logic and Temporal Logic

Abstract

We investigate to what extent the abductive method can be applied to the choice between logical theories, taking as a case study the dispute between classical logic and temporal logic. Typically, examples of the application of the abductive method focus on disputes between classical logic and non-classical logics. We believe, however, that there are also relevant disagreements between classical logic and logics that extend it without rejecting its principles, such as temporal logic. These disagreements do not arise from the relation of logical consequence (what follows from what), but involve assumptions about the nature of time and language. By recovering this historical perspective on the clash between logical theories, we show that the limitations of abductivism are not restricted to disputes between classical and non-classical logics, but also manifest in debates concerning logics that present themselves as extensions of the classical.