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Inference of Opposites as Halachic process
In the Talmudic discussion of the Sotah ritual, the halacha is derived that, because part of the ritual requires uncovering the woman's hair, the obligation would otherwise be to keep the hair covered.
As explained in Ketuvot 72a (via dafyomi.co.il)
Question: Uncovered hair is mid'Oraisa!
- (Tana d'Vei R. Yishmael): "He will uncover her hair" warns (married) Benos Yisrael that they should not go out with uncovered hair.
Similarly (though I know it isn't identical) when an Eishet Yefat To'ar is captured, the lets her nails grow -- but I learned that she either cuts them or lets them grow depending on the societal convention of beauty: whichever is desirable (short or long) she does the opposite.
In each of these cases, the law we follow is derived by establishing an opposite of the biblical position. I also know that there are 13 hermeneutic principles that we use to derive law from text.
Which of R. Yishma'el's 13 would "derive the opposite by inference" be? I know that his set of 13 is not the only such list (I have heard of longer ones) but his is the one that is codified in daily prayer.
If this method of intuiting an opposite is one of the 13, then that's great and I appreciate being pointed to the right one. If not:
a) how can the sages make that derivation and encode it into law? b) why wouldn't R. Yishma'el have included it, especially if the statement from Ketuvot is from the House of R. Yishma'el?
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