Is Judaic logic used in the Talmud for inferring Judaic laws analytic? Is it a priori?
Judaism differs considerably from other theistic religions. One of the main features is that Jewish religious laws are not dogmatic but based on specific legal reasoning. This reasoning was already used by the first Judaic commentators of the Bible (Tannaim) for inferring Judaic laws from the Pentateuch. Hence, Judaic logic that was aimed to be a methodology for deducing religious laws has been developed in Judaism. Rambam claimed that this logic was invented by nobody, but it is a part of the Torah. Indeed, this logic differs from other formal systems (Stoic propositional logic, Aristotelean syllogistic, etc.). On the one hand, Judaic logic is analytic as well as other systems. On the other hand, it contains so many ad hoc rules that we may ask whether it is a prpiori in fact?
The paper by Curtis Franks http://www.nd.edu/~cfranks/frankssacredinference.pdf considers cases when we may not draw an inference from something which itself has been inferred. Under these circumstances, we could assume that Judaic logic is analytic a posteriori. The status of analytic a posteriori was grounded first by Saul Kripke and Stephen Palmquis. Also, we could attempt to answer, whether the Lord is analytic a posteriori? As we know, in Kant’s opinion, the Lord is a construction a priori. This means that God exists just in our thoughts and nowhere else. According to modern logicians, there is analytic a posteriori. Perhaps the Lord is analytic a posteriori, too? This means that we could investigate His Will logically, i.e. analytically, and at the same time He is in reality, i.e. a posteriori.