Rethinking Talmudic Temporal Logic I. Legal Analysis Functions without Parallel Histories

This paper explores the underlying logical framework of a legal approach to backwards causation in Talmudic (ancient Jewish) law. The Talmudic cases involve legal constructions such as purchases, marriages, or divorces, whereby the action is stipulated to be conditional upon a future occurrence (or non-occurrence) of an event. The Talmud accepts the principle of future causation, though there are different approaches that appear to involve different metaphysical and logical philosophies. One approach takes a future state of affairs to be considered an objective fact in the present moment. On this approach the future-condition is fulfilled (or not) as soon as it is made, although the facts remain epistemically inaccessible to the agents themselves until the later time. A second approach takes future facts to be non-facts until they become true. On this approach, when the later event occurs it causes a contrary-to-time effect to take place. Although we briefly discuss the second approach, our primary focus is the former approach. We analyse and elaborate upon the Abraham-Gabbay-Schild Talmudic language L, which is an executable temporal language, flexible enough to handle reference to absolute moments in time, and also to the subjective present as it changes for agents travelling through time. We then critically assess their Parallel-histories model for the approach that takes future facts to be present facts. In this paper we raise an alternative to the Parallel-Histories approach. We argue that to truly represent the Talmudic position, there is a need for a function F that is not a part of the language L, but operates at a meta-level, permitting or cancelling the conditional statements. We argue that once this function is introduced, then the potency of the language L makes the need for Parallel-Histories redundant (though we accept that it may serve as a useful heuristic). We argue further that the Parallel-Histories applied to paradoxical cases (temporal loops) does not have sufficient resources to fully unravel the loop alone, whereas the language L augmented by the function F indeed has the resources to diffuse such paradoxical constructions.