1. Cases of exception for Kdei Dimeihem [that one may pay any amount to redeem the captive]:[1]

• Redeeming oneself:[2] The actual person being held in captivity may agree to pay his captors any amount of ransom money for the sake of redeeming himself, as for the captive himself, no limitations were instituted by the sages. [Nonetheless, some Poskim[3] rule that he is not obligated to do so.]
• Husband redeeming wife: Most Poskim[4] rule that a husband may pay more than market value to redeem his wife, and so is the Ashkenazi practice.[5] Nonetheless, many Poskim[6] rule that he is not obligated to do so, as explained in Halacha H. This allowance to redeem one’s wife for more than her value applies even if he himself is also in captivity, and will need to remain in captivity if he redeems his wife for more than her value.[7]
• Relative or other individual redeeming captive with his own money: Some Poskim[8] rule [based on the second approach written above in D] that even a relative may not redeem a captive for more than his market value due to Tikkun Haolam.[9] Other Poskim[10], however, rule [based on the first approach written above in D] that any individual may choose to redeem a captive for more than his market value, and certainly a relative, such as a father, may redeem his daughter for any amount they demand him to pay.[11] Practically, one is not to protest one who chooses to redeem the captive for more than his value from his own money, and so is the custom.[12]
• Pikuach Nefesh:[13] It is disputed amongst the Poskim as to whether the restriction against redeeming a captive for more than his value applies even in the event that the captives life is in danger, and he may be killed if he is not redeemed. Some Poskim[14] rule that there are no restrictions in such a case, and one may redeem the captive for as much money as requested, as Pikuach Nefesh defers all the laws of the Torah, and certainly defers a restriction of the sages.[15] Other Poskim[16], however, argue that the restriction of the sages applies even in the case of Pikuach Nefesh, and hence even if the life of the captive is held in balance, it is forbidden for one to redeem him for more than his value.[17] [Practically, one may be lenient in this matter.[18]]
• Save from Apostasy: Some Poskim[19] rule that if the captors force the Jewish captives to transgress the Jewish religion and force them to work on Shabbos for no need, then one may redeem the captive for more than his value. Nonetheless, there is no extra leniency given to redeeming a woman who is held captive even if there is worry of Giluiy Arayos.[20]
• A Torah scholar or child prodigy:[21] If the person being held captive is a Torah scholar, or is a child or student prodigy that has the potential of becoming a great Torah scholar, then he may be redeemed for any amount of ransom money, and the sages never instituted their restriction in such a case. [Famously, the Maharam was kidnapped in the end of the 13th century and was held for a very high ransom.[22] Now, despite the fact that he was considered the Gadol Hador, nonetheless, he refused to permit paying the large ransom for his release, and chose to die while in prison. See below!]
• Community agrees to forego the decree: Some Poskim[23] rule that the community has the right to forfeit the institutions of the Sages of Duchka Detzibura, and pay more than the value of the captive, and so is indeed the custom of many communities. Other Poskim[24] rule that the community has the right to pay more than the market value to redeem a captive, so long as it is not more than average amount that is requested in other ransom cases of Gentile captives.

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[1] See Pesakim Uteshuvos 252:4

[2] Michaber Y.D. 252:4; Tosafus Gittin 45a; Tosafus Kesubos 52a; Rosh Gittin 4:44; Braisa in Kesubos 52a; Yeish Cholin in Meiri Beis Habechira Gittin 45a; See Shach 252:11 “and not himself” which can be understood to mean that one may not redeem himself for more than his value. However, in truth this is not the intent of the Shach ibid as doing so would contradict what he himself writes in 252:4 and contradict the ruling of all the above Rishonim and Poskim. Rather, one must say that its meaning is as explained below that one may redeem his wife for more than her value even if he himself remains in captivity.

Other opinions: Some Poskim rule that even the person himself may not redeem himself for more than his value [1^st approach in Meiri Beis Habechira Gittin 45a]

[3] Rashal in Yam Shel Shlomo Gittin 4:66; See Haflah Kesubos 52; Gilyonei Hashas Gittin ibid

[4] Implication of Michaber E.H. 78:2, as learns Chelkas Mechokeik 78:2, that he may do so; Rama E.H. 78:2 [see Rama Y.D. 252:4]; Shach Y.D. 252:4 and 11; Beis Shmuel E.H. 78:2; Chelkas Mechokeik E.H. 78:2; Bach 252; Tur E.H. 78; Tosafus Gittin 45a; Tosafus Kesubos 52a; Rosh Kesubos 4:22 in name of Rameh; Kesubos 52a “Up until 10 times her value”; Rashal in Yam Shel Shlomo Gittin 4:66; See Maharam Milublin 15

Other opinions: Some Poskim rule that a husband may not pay more than market value even to redeem his wife. [Michaber E.H. 78:2, as learns Beis Shmuel and Chelkas Mechokeik 78:2 in his opinion, that it is forbidden to do so; Raban Shimon Ben Gamliel Kesubos 52a-b; Pesakim Uteshuvos 252:4 that he may not do so]

[5] The reason: As Ishto Kigufo, a man’s wife is like his own body, and hence the husband may redeem her for more than her value just as he may redeem himself for more than his value. [Tosafus ibid and ibid]

[6] Michaber E.H. 78:2; Shach Y.D. 252:11; Simple understanding of Rama 78:2; Rambam Ishus 14:19; Raban Shimon Ben Gamliel in Kesubos 52a; Rif Kesubos 19a

Other opinions: Some Poskim rule that by the first time she is held captive, the husband is obligated to pay up to 10 times her value [Beis Shmuel E.H. 78:2 in opinion of Rama ibid; Rashal in Yam Shel Shlomo Gittin 4:66; Tana Kama in Kesubos 52a “He must pay up until 10 times her value”; See Maharam Milublin 15; Chelkas Mechokeik 78:2 in opinion of Rama]

[7] See Shach 252:11 “and not himself”; Beis Shmuel E.H. 78:2

[8] Implication of Michaber 252:4 that the only exception to the Takana is to redeem oneself for more than his market value; Shach 252:4 in opinion of Michaber ibid; Implication of Michaber E.H. 78:2, as learns Beis Shmuel and Chelkas Mechokeik 78:2 in his opinion, that it is forbidden to do so even by one’s wife; Possible implication of Rama E.H. 78:2 that only one’s wife may be redeemed for more than her value and that other relatives [however, see Beis Shemuel and Chelkas Mechokeik ibid who entertain that perhaps the intention of the Rama ibid is that the husband is obligated to do so]; Raban Shimon Ben Gamliel Kesubos 52a-b; Meiri Beis Habechira Gittin 45a; Kneses Yechezkal Y.D. 38 in his main approach; See Ran Gittin 22b; All Poskim ibid who rule that Ligrivu Tfei is main reason;

[9] The reason: According to the second approach, it is forbidden to redeem a captive for more than the value of the captive, as irrelevant of who pays the ransom money, paying more money than the market value motivates future kidnappings, and is a danger to the community. [Rashi Gittin ibid]

[10] Shach 252:4 in name of Bach 252; Rashal in Yam Shel Shlomo Gittin 4:66 that so is the custom today; Kneses Yechezkal Y.D. 38 in his Limud Zechus approach that the Rif and Rosh did not give a conclusion in this matter, and that so agrees the Maharam Milublin ibid; All Poskim ibid who rule that Duchka Detzibura is main reason; Bigdei Yom Tov 37; Shema Avraham 12; Meiyn Ganim 18

[11] The reason: According to the first approach it is permitted to redeem a captive even if the value is much more than the value of the captive, being that it does not entail a financial burden onto the community. [Shach ibid; Rashi ibid]

[12] Shach ibid; Bach ibid; Derech Emunah Matanos Aniyim 8:78 that so is custom; See Rashal and Radbaz ibid that today we are anyways lenient to redeem

[13] See Pischeiy Teshuvah 252:4

The story of Rebbe Yehoshua Ben Chanania and a debate of its understanding: The Gemara in Gittin 58a states: Rebbe Yehoshua Ben Chanania visited a large metropolitan in Rome and was told that there is a certain very beautiful Jewish child incarcerated in the local prison. He went to the person and had a conversation with the child and realized that the child is a prodigy of Torah scholarship and stated that he is assured that he will become a great Torah leader amongst Israel and hence he will not move from his place until he redeems him for all the money that is requested. They say, that he did not move from there until he redeemed him for a large sum of money and it was not very long until he became a great leader among Israel and his name was Rebbe Yishmael Ben Elisha. [See Shaar Hagilgulim Hakdama 38 that he was a Gilgul of Yosef Hatzadik, and hence had beautiful hair, and was held in prison] The Rishonim all question the basis for this redemption for more than the value of the captive which contradicts the institution of the sages, and several answers are given, including: 1) it was a case of danger of life, and by danger of life the sages did not institute the regulation. [1^st answer in Tosafus Gittin 58a; 2^nd answer brought and negated in Ramban Gittin 45a; 2^nd answer in Meiri Beis Habechira Gittin 45a] 2) the institution does not apply to a Torah prodigy. [1^st answer in Tosafus Gittin 45a; 2^nd answer in Tosafus Gittin 58a; Ramban Gittin 45a; 3^rd approach in Meiri Beis Habechira Gittin 45a] 3) During times of the Churban the Takana of Ligrivu Tfei is not relevant. [2^nd answer in Tosafus Gittin 45a; 1^st answer in Ramban Gittin 45a; 1^st answer in Meiri Beis Habechira Gittin 45a] See Kneses Yechezkal Y.D. 38 for why Tosafus in the two areas did not bring both reasons

[14] Rashal in Yam Shel Shlomo Gittin 4:66; 2^nd answer in Tosafus Gittin 58a based on story of Rebbe Yehoshua Ben Chanania; 2^nd answer in Meiri Beis Habechira Gittin 45a; Kneses Yechezkal Y.D. 38 according to reason of Duchka Detzibura and that one may choose to follow this reason; Nachalas Leyehoshua 5, brought in Ashel Avraham Otzer Mefarshim 3, brought in Pischeiy Tehsuvah ibid; Sdei Chemed 74; Erech Lechem of Maharikash 252; Beis Hillel 252:2; Beis Dovid Y.D. 120

[15] The reason: Now, although every captive is considered to be in a state of Pikuach Nefesh as explicitly recorded in the Talmud Bava Basra 8b based on the verse in Yirmiyah, nonetheless, a general captive which is held for purposes of ransom is not found in a state of immediate danger, as opposed to one whose life is being immediately threatened. [Meiri Beis Habechira Gittin 45a; Sdei Chemed Divrei Chachamim 77; Pesakim Uteshuvos 252:1 footnote 5]

[16] Ramban Gittin 45a; Maharam Milublin 15 “Not one Posek has ever written that if the captives life is under threat, then one may redeem him for more than his value” [see, however, Beis Hillel 252:2, brought in Pischeiy Tehsuvah ibid who states that he forgot the Toasafus ibid who writes so; See however, Kneses Yechezkal ibid]; Yad Eliyahu 43, brought in Pischeiy Tehsuvah ibid; See Kneses Yechezkal Y.D. 38 that according to the reason of “Lo Ligrivu Tfei” the institution applies even in a case of danger of life for the captive;

[17] The reason: As every captive is considered to be in a state of Pikuach Nefesh as explicitly recorded in the Talmud Bava Basra 8b based on the verse in Yirmiyah, and nonetheless the sages instituted a restriction in redeeming them for more than their value, and hence the institution applies even in the case of immediate Pikuach Nefesh. [Ramban Gittin 45a]

[18] Kneses Yechezkal ibid; Sdei Chemed 74 that so rule most Rabbanim; Minchas Yitzchak Likkutei Teshuvos 110; Shevet Halevi 5:137-4; Yabia Omer C.M. 10:6; Shiurei Torah Lerofim in name of Rav Elyashiv that whenever it is a case of doubt regarding an institution, one may be lenient [See Maggid Mishneh Gezeila 4:7; Ketzos Hachosehn 362:3]; Derech Emunah Matanos Aniyim 8:78 that one is obligated to do so today; See Rashal and Radbaz ibid that today we are anyways lenient to redeem; Pesakim Uteshuvos ibid

[19] Rashal in Yam Shel Shlomo Gittin 4:66; Radbaz 1:40; Pesakim Uteshuvos 252:1 footnote 8; See Maharam Milublin 15 who concludes that perhaps one may redeem a captive who may be converted to another religion if the captive once converted may become a source of anti-Semitism; See regarding redeeming the children after the father who caused himself to be captured passes away: Michaber Y.D. 252:6; Shach 252:6; Rambam Matanos Aniyim 8:13; Mishneh Gittin 46b and Gemara 47a; Sheilas Yaavetz 1:68, brought in Pischeiy Teshuvah 252:7

See regarding Desecrating Shabbos in order to help save a Jew from leaving Judaism:  Admur 396:29; Michaber 30614; Tosafus Shabbos 4a; Eiruvin 32:b; Gittin 41b; See also Admur 329:10; Rama 329:8

[20] See Ramban Gittin 45a; Shach 252:9-10; Beir Sheva p. 22

[21] Michaber Y.D. 252:4 “However, if the captive is a Torah scholar, or is a Torah student with seen potential for becoming a great scholar then they may be redeemed even for a large sum of money.”; 1^st answer in Tosafus Gittin 45a; 2^nd answer in Tosafus Gittin 58a; Rosh Gittin 4:44; Rashba Gittin 45a; Ran Gittin 23a; Ramban Gittin 45a; Ritva Kesubos 52b; Implication of Gittin 58a as was done by Rebbe Yehoshua Ben Chananya, as explained in 1^st approach in Tosafus Gittin 45a and 2^nd approach in Gittin 58a [however, according to the 2^nd approach in Tosafus Gittin 45a and 1^st approach in Gittin 58a the reason is not because he was a Gadol Hador.]; 3^rd approach in Meiri Beis Habechira Gittin 45a; Rashal in Yam Shel Shlomo Gittin 4:66 regarding Maharam of Rothernberg; Radbaz 1:40 and 498; Sefer Chassidim 925

[22] See Rashal in Yam Shel Shlomo Gittin 4:66

[23] Rashal in Yam Shel Shlomo Gittin 4:66; Nachlas Yehoshua 5; Bibayis El Cheder 58

[24] Radbaz 1:40