- First machlokes between the Rabbonon and Rebbe Shimon: סקילה vs. שריפה
In the Mishnah on the previous Daf, the Rabbonon list the four מיתות בית דין in descending order of severity: סקילה שריפה הרג חנק. Rebbe Shimon’s order is: שריפה סקילה חנק והרג. The Gemara proceeds to demonstrate all the relative severities of the four מיתות, according to each opinion. The Rabbonon consider סקילה more severe than שריפה, because סקילה is given to a מגדף – blasphemer and one who serves avodah zarah, which are especially severe aveiros, שכן פושט ידו בעיקר – because he thereby challenges the most fundamental principle of faith. The Gemara asks that perhaps שריפה is more severe, since it is a בת כהן’s punishment for adultery, whose severity is שכן מחללת את אביה – that she disgraces her father!? According to Rashi, the Rabbonon respond that פושט יד בעיקר is more severe. Therefore, they must limit שריפה to a בת כהן who is a נשואה (where a בת ישראל receives חנק), but an בת כהן arusah would receive סקילה, like a בת ישראל, since they consider it more חמור than שריפה.
Rebbe Shimon holds that שריפה applies to all cases of בת כהן, including an ארוסה. Since she receives שריפה instead of סקילה, this proves that שריפה is more חמור than סקילה.
- Second machlokes: סייף vs. חנק
The Rabbonon taught in the Mishnah that "הרג" (i.e., סייף) is more חמור than חנק. The Gemara explains that סייף is given to the residents of an עיר הנדחת, whose severity is seen from the fact that ממונם אבד – their property is destroyed. The Gemara asks that perhaps חנק is more חמור, since it is given to one who strikes his father or mother, whose severity is שכן הוקש כבודן לכבוד המקום – because their honor is compared to Hashem’s honor!? It answers that nonetheless, פושט ידו בעיקר עדיף – challenging the most fundamental principle of faith is more severe. Rebbe Shimon holds חנק is more חמור than סייף, and the Gemara explains: וכי איזה כח מרובה – which sin’s seriousness is greater, כח המדיח או כח הנידח – the seriousness of the one who leads others astray (to worship עבודה זרה) or the seriousness of the one who was led astray? Certainly, leading others astray is the more severe sin! Although the Rabbonon say a מדיח receives סקילה, Rebbe Shimon holds a מדיח’s punishment is חנק, proving that חנק is more חמור than סייף (the נידחים’s punishment).
- Deriving that שריפת בת כהן is for adultery
A Baraisa states that if the passuk had only said, "ובת איש כהן כי תחל" – if a Kohen’s daughter profanes, one would think אפילו חללה את השבת – even if she desecrated Shabbos, she would be killed with שריפה. Therefore, the passuk says "לזנות" – through adultery, teaching: בחילולין שבזנות הכתוב מדבר – the passuk is only discussing profaning through adultery. The next Daf will explain that only according to Rebbe Shimon, who holds שריפה is more חמור than סקילה, would one think that a בת כהן receives שריפה for חילול שבת (instead of סקילה), since Kohanim were given more mitzvos (still, it would only apply to a female כהנת, because Shabbos is permitted to male Kohanim for avodah).
The Baraisa continues that one might think this punishment applies even to the relations of a פנויה – an unmarried woman (which the Gemara will explain is according to Rebbe Elazar, who holds that relations with a פנויה render her a זונה), so we derive from a gezeirah shavah (אביה אביה) that it refers to a married woman. The Baraisa then considers that שריפה is only for relations with her father, but the phrase "היא מחללת" – she profanes (meaning, she profanes her father’s status, but he did not profane hers) proves it is discussing relations with others.