That argument is extremely confusing. Who can understand what the author is trying to say? First he speaks of "aionas aionion" as meaning a "finite period" & then, in the same sentence, he refers to it being "forever and forever". Which is it, forever or finite?
If someone said to me "I have had no rest day or night", this could mean for a period of 24 hours. Not forever and ever.
The phrase 'forever and ever' in Rev.14:11 literally translates as into/to "ages of ages". So having no rest day or night to/into "ages" can mean for a short or long time of finite duration.
Here is the literal translation from a Greek-English Interlinear:
Revelation 14:11 Interlinear: and the smoke of their torment doth go up to ages of ages; and they have no rest day and night, who are bowing before the beast and his image, also if any doth receive the mark of his name.
And another more literal translation than yours:
Young's Literal Translation
and the smoke of their torment doth go up to ages of ages; and they have no rest day and night, who are bowing before the beast and his image, also if any doth receive the mark of his name.
Scripture also speaks of night being "no more". So can "day and night" be forever?
For 12 arguments re "ages of ages" ending, see posts 130 & 131 @
What is the 2nd Death? (Annihilationsim vs. Eternal Torment)
This includes everyone in the universe, including the dead and demons:
Rev.5:13 And every creature which is in heaven, and on the earth, and under the earth, and such as are on the sea, and all that are in them, heard I saying, Blessing, and honour, and glory, and power, be unto him that sitteth upon the throne, and unto the Lamb into the ages of the ages.
John speaks of "every creature" & to emphasize this again he repeats "and all that are in them":
Rev.5:13 And every creature which is in heaven, and on the earth, and under the earth, and such as are on the sea, and all that are in them, heard I saying, Blessing, and honour, and glory, and power, be unto him that sitteth upon the throne, and unto the Lamb into the ages of the ages.
This worship (v.13) uses the same worshipful words as the redeemed of vs 9-10 use in v.12:
12 Saying with a loud voice, Worthy is the Lamb that was slain to receive power, and riches, and wisdom, and strength, and honour, and glory, and blessing.
All this being in the context of salvation - "the Lamb that was slain" (v.12 & 13).
Lk.12:47 And that servant, which knew his lord's will, and prepared not himself, neither did according to his will, shall be beaten with many stripes. 48 But he that knew not, and did commit things worthy of stripes, shall be beaten with few stripes. For unto whomsoever much is given, of him shall be much required: and to whom men have committed much, of him they will ask the more.
This sounds like just payback, not endless annihilation or tortures:
Rev.18:6 Reward her even as she rewarded you, and double unto her double according to her works: in the cup which she hath filled fill to her double.
10:28 A man that hath set at nought Moses' law dieth without compassion on the word of two or three witnesses: 29 of how much sorer punishment, think ye, shall he be judged worthy, who hath trodden under foot the Son of God, and hath counted the blood of the covenant, wherewith he was sanctified, an unholy thing, and hath done despite unto the Spirit of grace?
Generally capital punishment under Moses' law was by stoning. Stoning to death is not a very sore or long lasting punishment. People suffered far worse deaths via the torture methods of the eternal hell believing Medieval Inquisitionists and the German Nazis under Hitler.
Therefore, if the writer of Hebrews believed that wicked, rebellious, Christ rejectors would be punished with something so monstrous as being endlessly annihilated or tormented, he would not have chosen to compare their punishment to something so lame as being stoned to death. Clearly he did not believe Love Omnipotent is an unfeeling terminator machine or sadist who abandons forever the beings He created in His own image & likeness so easily.
Mt.18:23 Therefore is the kingdom of heaven likened unto a certain king, which would take account of his servants. 24 And when he had begun to reckon...
34 And his lord was wroth, and delivered him to the tormentors, till he should pay all that was due unto him. 35 So likewise shall my heavenly Father do also unto you, if ye from your hearts forgive not every one his brother their trespasses.
Furthermore, the context of Matthew 5:25-26, both before & after those 2 verses, is making references to Gehenna. Verses 21-26 have to do with anger & being reconciled & v.22 warns of Gehenna. In verses 27-30 the subject is adultery & v.30 warns regarding Gehenna.
Matt 5:25-26 Come to terms quickly with your adversary before it is too late and you are dragged into court, handed over to an officer, and thrown in jail. I assure you that you won't be free again until you have paid the last penny.
"They must pay (as GMac says) the uttermost farthing -- which is to say, they must tender the forgiveness of their brethren that is owed, the repentance and sorrow for sin that is owed, etc. Otherwise they do stay in prison with the tormenters. (their guilt? their hate? their own filthiness?) At last resort, if they still refuse to let go that nasty pet they've been stroking, they must even suffer the outer darkness. God will remove Himself from them to the extent that He can do so without causing their existence to cease. As Tom Talbot points out so well, no sane person of free will (and the child must be sane and informed to have freedom) could possibly choose ultimate horror over ultimate delight throughout the unending ages."
Why affirm belief in Hell?
Rom 5:18 Consequently, then, as it was through one offense for ALL MANKIND for condemnation, thus also it is through one just act for ALL MANKIND for life's justifying."
Rom 5:19 For even as, through the disobedience of the one man, THE MANY were constituted sinners, thus also, through the obedience of the One, THE MANY shall be constituted just."
Paul makes a parallel between "the many" who were condemned & sinners and those who will be justified & constituted just.
“In Romans 5, the justification is co-extensive with the condemnation. Since all share in one, all share in the other. If only a certain portion of the human race had partaken of the sin of Adam, only a certain portion would partake of the justification of Christ. But St. Paul affirms all to have been involved in one, and all to be included in the other.”
Therefore there is salvation after death. And corrective punishment.
https://www.tentmaker.org/books/hope_beyond_hell.pdf
Jesus shall see of the travail of His soul & be satisfied. Not satisfied a little bit, but the vast majority fried alive forever.
"He shall see of the travail of his soul, and shall be satisfied: by his knowledge shall my righteous servant justify many; for he shall bear their iniquities." (Isa.53:11).
For how "many" (not few) did He "bear their iniquities"? All.
https://www.tentmaker.org/books/hope_beyond_hell.pdf
