The Gemara in Sanhedrin 74a cites Ravin in the name of Rebbi Yochanan that if a Nochri forces a Jew to do even a slight transgression in public, the Jew is obligated to give up his life rather than transgressing. The Gemara on 74b asks on this that Esther ha'Malkah committed a public transgression when she married Achashverosh, so why did she not give up her life to avoid it? Abaye answers that Esther was "Karka Olam" - the woman is only passive, so she is not required to give up her life. Rava answers that Achashverosh did this for personal enjoyment - not specifically to force Esther to go against her religion.

(a) Tosfos Sanhedrin 74b DH v'Ha asks, "Why did the Gemara challenge R. Yochanan's assertion merely from the fact that Esther transgressed in the public eye? There is a stronger question that could have been asked on Esther. Even if her transgression would not have been public knowledge she should still have given up her life, because her transgression concerned "Arayos" - a forbidden relationship. Everyone (even Rebbi Yishmael above 74a who maintains that one is not obligated to give up one's life in order to avoid worshipping idols) agrees that one has to give one's life to avoid transgressing Arayos. This is evident from the Gemara earlier on 74a in which everyone agrees that Na'arah ha'Me'urasah is "Yehareg v'Al Ya'avor".

1. Tosfos in Sanhedrin answers this question in the name of Rabeinu Tam that when a Jewess has "Bi'ah" with a Nochri man this does not carry the capital penalty because the Bi'ah of a Nochri is not considered Bi'ah. Therefore, had it not been public knowledge, Esther would not have been obligated to give up her life.

2. Rebbi Yitzchak ben Rebbi Mordechai (the Rivam) disagrees with R. Tam and maintains that the Bi'ah of a Nochri is considered Bi'ah (I am not going to examine the proofs for this at the present moment.) Therefore, Rivam suggests a different answer to Tosfos' question. The reason that the Gemara did not ask that Esther was transgressing Arayos is because the Gemara knew, even before Abaye gave his answer, that Karka Olam is a sufficient reason that this is not considered Arayos.

This is because the fact that one has to give up one's life not to transgress Arayos is derived (Sanhedrin 74a) from the laws of murder. Tosfos asserts that one is not obligated to sacrifice one's life to avoid committing murder in a passive way; for instance, a person is not obligated to give up his life to avoid being thrown on a baby and crushing him. Tosfos reasons that the Gemara says that one must give up one's life not to commit murder because, "How do we know that the blood of the murderer is redder, maybe the blood of the victim is redder?" However in a case where the murderer is passive and performs no action, we can employ the opposite argument - "How do we know the blood of the victim is redder, maybe the blood of the murderer is redder?" Since a person does not have to give up his life to avoid committing passive murder, it follows that a woman also is not obliged to sacrifice her life in order not to commit passive Arayos.

The above applies to passive Arayos in private. In contrast, the Gemara thought in its question, that transgressing b'Fahresya is worse, and even though it is passive one might have to die instead. (Incidentally I think this might fit with the Gemara in Sanhedrin 107a, where we find that King Dovid said that it is better to worship Avodah Zarah rather than allowing the name of Hash-m to be desecrated in public.) However Abaye answered that being passive is sufficient reason to allow oneself not to give up one's life even if the passive sin is done publicly.

(b) Now, if we look at Tosfos Yoma 82a DH Mah we will see that the first part of Tosfos there follows the opinion of Rivam. It is only about halfway down page 82b that Tosfos cites the opinion Rabeinu Tam, asking on him the questions that Rivam asks on Rabeinu Tam in Sanhedrin.

Thus Tosfos in Sanhedrin and in Yoma are quite similar in the way that they cite the arguments for Rabeinu Tam's and Rivam's opinions, except that Tosfos in Sanhedrin first cites Rabeinu Tam and afterwards Rivam while Tosfos in Yoma does it the other way around.

Obviously there are very many details in Tosfos that I have not discussed at all, but I have outlined the two major opinions in Tosfos.

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