Do Christian or Muslim theologians use the same rules as Rabbinate teachers do, when they interpret their respective holy scriptures?
I'm particularly interested in the '13-methods to infer from holy scriptures'.
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At the seminary I graduated from, we were taught the rules in Dr. Hernanado's Hermeneutics class as part of the history of interpretation. In Dr. Nunnally's Jewish backgrounds to the NT class, we were drilled in them again. They both showed us places in the New Testament where the writers used the rules in their own interpretation. However, we were not expected to use them on our own. We could do so but were not required.
Christian hermeneutics use similar rules. For example, "from the minor to the major" is very similar to qal v'khomer ("minor to major" also appears in a lot of philosophy arguments--it's far from Christian only). Gezerah Shavah (without calling it that), the fact that a similar case gave a certain verdict therefore the present case should render a similar verdict, will also appear frequently in Christian writings. Ka-yotze bo mi-makom acher and Davar ha-lamed me-inyano both rely on context to determine the meaning of a passage and solving difficulties between two passages. Every good Christian interpreter uses these last two.
You can almost certainly find some Christian interpreters using the other rules listed and other Jewish methods that are not part of the list of 13. I have seen Christians use gematrias and let us not forget the Christians who used the Bible Code, which relies on Akiva's belief that "nothing superfluous exists in the Torah." Rabbi Ishmael disagreed (Sifre, Numbers 112).