From Counterfactual Conditionals to Temporal Conditionals

Abstract

AbstractAlthough it receives less attention, (Lewis in Noûs 13:455–476, 1979. https://doi.org/10.2307/2215339) admitted that the branching-time(-like) model fits a wide range of counterfactuals, including (Nix) ‘If Nixon had pressed the button, there would have been a nuclear war’, which was raised by (Fine in Mind 84:451–458, 1975). However, Lewis then claimed that similarity analysis is more general than temporality analysis. In this paper, we do not scrutinise his claim. Instead, we re-analyse (Nix) not only model-theoretically but also proof-theoretically from the ‘meaning-as-use’ and ‘inferentialist’ points of view. Then, we re-formalise (Nix) in a natural extension of hybrid tense logic, which we refer to as hybrid tense logic for temporal conditionals (HTL$$_{TC}$$ TC ). Consequently, we find that not only among counterfactuals, but also among indicatives, there is a wide range of conditionals whose formalisation in HTL$$_{TC}$$ TC is appropriate. We refer to these conditionals as temporal conditionals. This suggests a new logical generality that temporality analysis has but similarity analysis does not, from which emerges a new logical perspective on conditionals in general: temporal ones and others.