Chullin Daf 115 צולין דַף 115

On the previous Daf, Rav Ashi had darshened that כל שתעבתי לך הרי הוא בבל תאכל – anything I have made abominable for you by forbidding it is included in the prohibition, “you shall not eat.” The Gemara raises numerous challenges to this principle, including: שילוח הקן ליתסר – a mother bird which was sent away to fulfill the mitzvah of sending away [a mother from its] nest should be prohibited, since it was initially forbidden to be taken from the nest first, and so should be a "תועבה" and remain forbidden in consumption!? The Gemara answers: לא אמרה תורה שלח לתקלה – the Torah did not say to send away the mother bird to be a stumbling block for those who may inadvertently eat it without realizing it is prohibited.

The Gemara continues to present various sources for the prohibitions of eating or deriving benefit from בשר בחלב. Rebbe Eliezer’s yeshivah quoted a passuk which first prohibits eating נבלה, then permits selling it to a gentile, and concludes with the prohibition to cook a kid in its mother’s milk. This juxtaposition teaches: כשתמכרנה לא תבשלנה ותמכרנה – when you sell [neveilah] to the gentile, do not cook it in milk and sell it, because בשר בחלב is forbidden in benefit. Rebbe Yishmael’s yeshivah darshened: לא תבשל גדי בחלב אמו ג' פעמים – the Torah states the passuk “you shall not cook a kid in the milk of its mother” three times. These three prohibitions teach: אחד לאיסור אכילה – one for the prohibition to eat meat cooked in milk, ואחד לאיסור הנאה – one for the prohibition to benefit from it, ואחד לאיסור בשול – and one for the prohibition to cook meat with milk.

Rav Mordechai quoted several principles about how a מה הצד (i.e., צד השוה) may be refuted:

כל מה הצד מגופו פרכינן – any common characteristic derivation can be refuted from within, מעלמא לא פרכינן – but cannot be refuted from elsewhere. Meaning, if the two מלמדים share a characteristic that the למד – derived [case] lacks, the צד השוה is refuted. However, an outside case which shares their common characteristic but not their common halachah being derived does not refute the צד השוה.

The next principle Rav Mordechai quotes is challenged, and emended as follows: חדא מחדא – when the halachah of one place is being derived from one source, קולא וחומרא פרכינן – then we can refute the derivation based on a unique leniency or stringency found in the מלמד (depending on whether a leniency or stringency is being derived), but כל דהו לא פרכינן – we cannot refute it based on a mere difference between the מלמד and למד (which would not logically cause the halachah). חדא מתרתי – When the halachah of one place is being derived  from two sources (through a צד השוה), אפילו כל דהו פרכינן – we can refute it based on a mere difference between the מלמדים and the למד. If a halachah is derived from three sources, then if the derivation reverts to a צד השוה, it can be refuted with a פירכא כל דהוא, but if not, it can only be refuted with a קולא or חומרא.