The rabbis used different hermeneutical methods to expound the Torah in order to derive halakhot. One can find a list of 13 different methods expounding the Torah compiled by Rabbi Yishmael in a traditional prayer book before Pesukai deZimrah. (https://www.sefaria.org/Siddur_Ashkenaz%2C_Weekday%2C_Shacharit%2C_Preparatory_Prayers%2C_Korbanot%2C_Baraita_of_Rabbi_Yishmael?lang=bi)
Dappim TB Zevakhim 50-51
will analyze the interplay between four different methods, hekash-הֶיקֵשׁ, gezarah
shavah-גְזֵירָה
שָוָה,
kal vekhomer-קַל וָחוֹמֶר, binyan av-בִּנְיַן
אָב.
A gezarah shavah- גְזֵירָה שָוָה is a hyperlink. Two different verses use the same word. One word leads to the other in order to learn a common halakha.
A kal vekhomer- וָחוֹמֶר קַלis a conclusion drawn from a minor or lenient law, to a major or more strict one.
A binyan av-אָב בִּנְיַן is when the Torah sets the precedent. Anything that matches the precedent shares the same halakhot. The second case has to be exactly like the precedent. If there is even one difference, then the second case doesn’t fall under the precedent.
Dappim TB Zevakhim 50-51 analyzes the interplay between the above four methodologies. Can you double jump from one methodology to the next methodology. One can go from A to B, but then can one go from B to C? The answer is sometimes yes and sometimes no. Below is a summary whether one can double jump or not.
Starting
with a hekash one cannot apply a second hekash to learn a halakha.
Starting
with a hekash one cannot apply a gezarah shavah to learn a halakha.
Starting
with a hekash one can apply a kal vekhomer to learn a halakha.
Starting with a hekash and then applying a binyan av to learn a halakha is undecided.
Starting
with a gezarah shavah
may one apply a hekash to learn a halakha? Rav Pappa says yes and Mar Zutra says no.
Starting
with a gezarah shavah
one can apply a second gezarah shavah to learn a halakha.
Starting
with a gezarah shavah
one can apply a kal vekhomer to learn a halakha.
Starting with
a gezarah shavah
and then applying a binyan av to learn a halakha is undecided.
Starting
with a kal vekhomer one can apply a hekash to learn a halakha.
Starting
with a kal vekhimer one can apply a gezarah shavah to learn a halakha.
Starting
with a kal vekhomer one can apply a kal vekhomer to learn a halakha.
Starting with
a kal vekhomer and then applying a binyan av to learn a halakha is undecided.
No matter
what methodology one uses after a banyan av to learn a halakha is always undecided.
.
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