Rabbi Ishmael's Thirteen Hermeneutic Rules as a Kind of Logic

Since the Middle Ages, Judaic hermeneutics, containing certain rules of inference, called middot in Hebrew, has been regarded as a kind of logic. For example, Maimonides argued this assertion. In the 19th century, some rabbis with a good German philosophical background attempted for the first time to formalize the most important middot logically. These attempts have been continued into the 21st century. However, the question arises to what extent the early applications of the middot by Hillel and Rabbi Ishmael in their historicalcultural contexts can be assessed as a kind of logic in the modern sense. In this paper, I argue that a simple formalization of Rabbi Ishmael's thirteen middot, which is consonant with his examples and intuitions, is consistent but incomplete. This allows us to consider the system of these rules as a kind of logic in a broad sense.