Rethinking Talmudic Temporal Logic II: Two-Dimensional Perspectival Logic in place of Dual-time

In the field of Talmudic Temporal logic, an important question has been how to model the approach known in one paper as ‘Shkop logic’ (after the 19th-20th century philosopher of Jewish law, Rabbi Shimon Shkop). Previous suggestions have included a model that involved a ‘Dual-time’ account. In this paper we first analyse the Dual time approach, including the logical language, its motivation and mechanism for diffusing legal contrary-to-time paradoxes. We compare the Dual time approach to a logic whose semantics need not appeal to Dual-time, but that employs a combination of trivalent truth function for the future, together with legal-functions designed to achieve the same conclusion. We show why such an approach would be inadequate, but then claim that a similar objection can be raised against the ‘Dual-time’ account. We then offer our own proposal, which involves a two-dimensional temporal model, thus permitting truth-valuations for events at moments in time to shift relative to other moments without any temporal loops. The language in which the model is expressed is sufficiently context-sensitive to permit a shift in perspective form the antecedent of a condition to its consequent. We argue that such an approach has significant benefits both in terms of being truer to the Talmudic sources, and in terms of its ability to diffuse legal paradoxes. We anticipate criticisms of the approach and argue that it can meet those criticisms. This is a part of a series of papers, and in future papers we intend to demonstrate the potential for this Perspectival 2-D Talmudic Temporal logic to resolve paradoxes such as Liar Paradoxes.