Mt 12:32 And whoever says a word against the Son of man will be forgiven; but whoever speaks against the Holy Spirit will not be forgiven, either in this age or in the age to comeThe phrase “in the age to come” generally refers to the afterlife (cf., Mk 10:30; Lk 18:30; 20:34-35; Eph 1:21). But, there is no forgiveness in hell and forgiveness is not necessary in heaven. Thus, this must refer to purgatory.
Lk 12:46-48 the master of that servant will come on a day when he does not expect him and at an hour he does not know, and will punish him, and put him with the unfaithful. 47 And that servant who knew his master's will, but did not make ready or act according to his will, shall receive a severe beating. 48 But he who did not know, and did what deserved a beating, shall receive a light beating. Every one to whom much is given, of him will much be required; and of him to whom men commit much they will demand the more.The coming of the master is certainly an allusion to Judgment, either once we die or at the end of time. At this time, those who knew His will and did not do it will be put with the unfaithful and punished severely. This is the condemnation of hell. But, those who sinned unknowingly will receive, at their Judgment, a light beating. But, hell is a severe punishment for those who knowingly sin, and there is no beatings (or punishment) for those in heaven. Thus, this light beating refers to Purgatory, where all our lesser sins are purged away.
Phil 2:10 that at the name of Jesus every knee should bow, in heaven and on earth and under the earthJesus is not worshipped in hell, and heaven is already mentioned in this verse, so the place (for lack of a better word) under the earth where knees bow at the name of Christ is Purgatory.
2 Tim 1:16-18 May the Lord grant mercy to the household of Onesiph'orus, for he often refreshed me; he was not ashamed of my chains, 17 but when he arrived in Rome he searched for me eagerly and found me-- 18 may the Lord grant him to find mercy from the Lord on that Day--and you well know all the service he rendered at Ephesus.Onesiphorus is already dead, yet Paul still prays that he will find mercy from the Lord "on that day", or at the Judgment (cf. Rom 2:5,16; 1 Cor 1:8; 3:13; 5:5; 2 Cor 1:14; Phil 1:6,10; 2:16; 1 Thes 5:2,4,5,8; 2 Thes 2:2,3; 2 Tim 4:8). But, there is no mercy, and nor can we pray for, those in hell, and those in heaven do not need mercy. Thus, Paul is praying for the dead because he knows there's the possibility Onesiphorus is undergoing a purging.
1 Cor 3:12-17 Now if any one builds on the foundation with gold, silver, precious stones, wood, hay, straw, 13 each man's work will become manifest; for the Day will disclose it, because it will be revealed with fire, and the fire will test what sort of work each one has done. 14 If the work which any man has built on the foundation survives, he will receive a reward. 15 If any man's work is burned up, he will suffer loss, though he himself will be saved, but only as through fire. 16 Do you not know that you are God's temple and that God's Spirit dwells in you? 17 If any one destroys God's temple, God will destroy him. For God's temple is holy, and that temple you are.Pay close attention to what is going on here. It is not in every day life that the fire is refining. It is on "the Day" which, as well have already seen, is Judgment Day. It is when we stand before Christ that the perishable works of a man's life will be consumed. "He will suffer loss, though he himself will be saved." This can only describe that last act of sanctification called Purgatory. "For our God is a consuming fire" (Heb 12:29). The flashes of his love "are flashes of fire, a most vehement flame" (So 8:6), and through it are "the spirits of just men made perfect" (Heb 12:23).
Now, I understand that there are responses to all the verses of Scripture that I have used, and I also know that it may seem hard for some to believe that the NT writers had something like Purgatory in mind. But, it is not that far-fetched. The Jews believed in a purging after death. Even if you don't consider Maccabees a canonical book of the Bible, it is still a reliable historical record of Jewish belief and practice. In Maccabees, we read of their prayers and atonement for the dead:
2 Macc 12:43-45 He also took up a collection, man by man, to the amount of two thousand drachmas of silver, and sent it to Jerusalem to provide for a sin offering. In doing this he acted very well and honorably, taking account of the resurrection. 44 For if he were not expecting that those who had fallen would rise again, it would have been superfluous and foolish to pray for the dead. 45 But if he was looking to the splendid reward that is laid up for those who fall asleep in godliness, it was a holy and pious thought. Therefore he made atonement for the dead, that they might be delivered from their sin.
There is also a very interesting practice that takes place in the First Book of Samuel:
1 Sam 31:11-13 But when the inhabitants of Ja'besh-gil'ead heard what the Philistines had done to Saul, 12 all the valiant men arose, and went all night, and took the body of Saul and the bodies of his sons from the wall of Beth-shan; and they came to Jabesh and burnt them there. 13 And they took their bones and buried them under the tamarisk tree in Jabesh, and fasted seven days.Now, I'm open to correction on this point, but the Jews here seem to be fasting for the dead, which would further affirm their belief in a purging in the afterlife.
Of course, when they celebrate the Kaddish, they are witnessing to this belief. From the entry on the "Kaddish" in the Jewish Encyclopedia:
The kaddish for the dead was originally recited at the close of the seven days' mourning, with the religious discourses and benedictions associated with it, but, according to Masseket Soferim xix. 12, only at the death of a scholar; afterward, in order not to put others to shame, it was recited after every burial (Naṭmanides, "Torat ha-Adam," p. 50; see Mourning).The NT writers were Jews. It's not hard to imagine that they held this belief. This is even more obvious when you consider that the early Church retained this belief as well (see this article).
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 kaddish.
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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).
I hope that helps. For more information on Purgatory, see my "Resources on Purgatory" blog post.