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There is a distinction between the explicit text of the prayer and its usage, although I think the text broadly speaking would apply to souls in the Jewish equivalent of purgatory. Regarding its usage, the Jewish Encyclopedia has some discussion about the Kaddish and the state of the dead.In the Kaddish there is no mention of death or the departed. The prayer is basically a glorification of G-d and it is meant to bring a measure of peace to the family of the deceased. By custom, it is recited for eleven months for a parent and one month for a spouse, sibling, or child. However, it is both permissible and desirable to pray the Kaddish for those whose soul has passed on because it means that the soul of the departed must be worthy of G-d’s blessings to have inspired such faith and devotion in their family even in the midst of great loss.
In the course of time the power of redeeming the dead from the sufferings of Gehenna came to be ascribed, by some, to the recitation of the Ḳaddish.
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In “Otiyyot de-R. 'Aḳiba,” a work of the geonic time, it is said, under the letter “zayin,” that “at the time of the Messiah God shall sit in paradise and deliver a discourse on the new Torah before the assembly of the pious and the angelic hosts, and that at the close of the discourse Zerubbabel shall rise and recite the Ḳaddish with a voice reaching from one end of the world to the other; to which all mankind will respond ‘Amen.’ All souls of Jews and Gentiles in Gehenna will respond with ‘Amen,’ so that God’s mercy will be awakened and He will give the keys of Gehenna to Michael and Gabriel, the archangels, saying: ‘Open the gates, that a righteous nation which observeth the faith may enter’ [Isa. xxvi. 2, “shomer emumim” being explained as “one that sayeth ‘Amen’”]. Then the 40,000 gates of Gehenna shall open, and all the redeemed of Gehenna, the wicked ones of Israel, and the righteous of the Gentiles shall be ushered into paradise.” The following legend is later: Akiba met a spirit in the guise of a man carrying wood; the latter told Akiba that the wood was for the fire in Gehenna, in which he was burned daily in punishment for having maltreated the poor while tax-collector, and that he would be released from his awful torture if he had a son to recite the Bareku and the Ḳaddish before a worshiping assembly that would respond with the praise of God’s name. On learning that the manhad utterly neglected his son, Akiba cared for and educated the youth, so that one day he stood in the assembly and recited the Bareku and the Ḳaddish and released his father from Gehenna (Masseket Kallah, ed. Coronel, pp. 4b, 19b; Isaac of Vienna, “Or Zarua’,” ed. Jitomir, ii. 11; Tanna debe Eliyahu Zuṭa xvii., where “R. Johanan b. Zakkai” occurs instead of “R. Akiba”; “Menorat ha-Ma’or,” i. 1, 1, 1; Manasseh ben Israel, “Nishmat Ḥayyim,” ii. 27; Baḥya ben Asher, commentary on Shofeṭim, at end; comp. Testament of Abraham, A. xiv.).
The idea that a son or grandson’s piety may exert a redeeming influence in behalf of a departed father or grandfather is expressed also in Sanh. 104a; Gen. R. lxiii.; Tanna debe Eliyahu R. xvii.; Tanna debe Eliyahu Zuṭa xii.; see also “Sefer Ḥasidim,” ed. Wiztinetzki, No. 32. In order to redeem the soul of the parents from the torture of Gehenna which is supposed to last twelve months ('Eduy. ii. 10; R. H. 17a), the Ḳaddish was formerly recited by the son during the whole year (Kol Bo cxiv.). Later, this period was reduced to eleven months, as it was considered unworthy of the son to entertain such views of the demerit of his parents (Shulḥan ‘Aruk, Yoreh De’ah, 376, 4, Isserles’ gloss; see Jahrzeit). The Ḳaddish is recited also on the Jahrzeit. The custom of the mourners reciting the Ḳaddish in unison is approved by Jacob Emden, in his “Siddur,” and that they should recite it together with the reader is recommended by Ẓebi Hirsch Ḥayot, in “Minḥat Ḳena’ot,” vii. 1. That the daughter, where there is no son, may recite the Ḳaddish was decided by a contemporary of Jair Ḥayyim Bacharach, though it was not approved by the latter (Responsa, No. 123; “Leḥem ha-Panim,” p. 376). A stranger, also, may recite the Ḳaddish for the benefit of the dead (Joseph Caro, in “Bet Yosef” to Yoreh De’ah, l.c.).
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