Deontic Tense Logic With Historical Necessity, Frame Constants, and a Solution to the Epistemic Obligation Paradox (The “Knower”)

Abstract

AbstractIn an earlier paper by the author, Åqvist (1999), I presented an approach to the logic of historical necessity, or inevitability, in the sense of a “two‐dimensional” combination of tense and modal logic for worlds, or histories, with the same time order, known as T × W logic. Distinctive features of that approach were, apart from its two‐dimensionality, its being based on discrete and finite time, and its use of so‐called systematic frame constants in order to enable us to indicate longitudes (x‐values) and latitudes (y‐values) of any points in the co‐ordinate systems under consideration. This led us to study and axiomatize an infinite hierarchy HTWxy of two‐dimensional modal tense logics with the characteristic operators for historical necessity and possibility added to the original basic vocabulary. The main purpose of the present paper is then twofold: (A) to extend the logics HTWxy to the interesting branch of philosophical logic constituted by deontic logic as combined with tense (or temporal) logic; and (B) to deal with a curious puzzle known as the so‐called epistemic obligation paradox – a well known stumbling‐block in this area of research in philosophical logic. We argue for a solution to both these problems, which appeals to a new infinite hierarchy DHTWxym of extensions of the HTWxy in the sense of logics combining dyadic deontic modalities with temporal ones such as those for historical necessity and other two‐dimensional modalities.