In this article I show that rabbinic reasoning, in its mature Talmudic form, rests on a foundation of five presuppositions, or axioms, including the comprehensiveness and non-redundancy of Scripture, and is guided by two formulas. The first formula is the formula of bijection, A∼B, which establishes a one-to-one correspondence between A, the textual elements of the Torah and B, the propositions of law comprising the system of halakhah; the second is the formula of adequate justification, ∃fx ( fx ⊃L ), (...) which states that there is a feature fx that serves as adequate justification for the application of a law L. The ‘Thirteen Rules of Rabbi Yišma’el (Ishmael)’ are analysed in terms of these formulas. An outline of stages in the evolution of rabbinic interpretation and reasoning in the Talmudic period sets the Thirteen Rules in their historical context as a third-century attempt, subsequently refined, to systematise rabbinic scriptural interpretation and legal reasoning. (shrink)

In this article, the author attempts to explicate the notion of the best known Talmudic inference rule called qal wa-omer. He claims that this rule assumes a massive-parallel deduction, and for formalizing it, he builds up a case of massive-parallel proof theory, the proof-theoretic cellular automata, where he draws conclusions without using axioms.