It seems to me that it is the word “life” in the phrase “aionion life” that gives it quality, not the word “aionion”. Remove the word “aionion” from the phrase & the quality remains. Remove the word “life” from the phrase & the quality is removed, while nothing but quantity of duration (i.e. aionion) remains. Jesus said “I am the Life” (Jn.14:6). He never said “this is aionion, to know God”, which would have been total nonsense. But He does say that He is Life. Therefore to know Him is to know Life & vica versa.
Jn.17:2 according as Thou givest Him authority over all flesh, that everything which Thou hast given to Him, He should be giving it to them, even life eonian." 3 Now it is eonian life that they may know Thee, the only true God, and Him Whom Thou dost commission, Jesus Christ. (CLV)
"The knowledge of God is not given as the definition of eonian life, but eonian life is imparted that they may be knowing Him. " (Concordant Commentary p.167 re John 17:3) concordant.org/expositions/conco … s-account/
Eonian life is obtained after the resurrection from the dead:
Dan.12:2 From those sleeping in the soil of the ground many shall awake, these to eonian life and these to reproach for eonian repulsion."
Which (Dan.12:2) was the only OT verse the Jews had to understand the meaning of aionion life.
The relation between life, eonian life & the resurrection is also confirmed by John’s gospel in the chapters leading up to chapter 17:
Jn.5:29 and will come forth; those who did the good deeds to a resurrection of life, those who committed the evil deeds to a resurrection of judgment.
Jn.6:39 And this is the will of Him who sent Me, that I shall lose none of those He has given Me, but raise them up at the last day. 40 For it is My Father’s will that everyone who looks to the Son and believes in Him shall have aionion life, and I will raise him up at the last day.
44“No one can come to Me unless the Father who sent Me draws him, and I will raise him up at the last day.
Jn.11:25 Jesus said to her, “I am the Resurrection and the Life. He who is believing in Me, even if he should be dying, shall be living.”
Jn.12:50 And I know that his command is the life of the coming age. What I speak, then, is what the father has told me to speak.’ (NTE)
NT Wright’s version/s (The Kingdom New Testament or NTE) says life aionion is “the life of God’s coming age”:
John 17:2 Do this in the same way as you did when you gave him authority over all flesh, so that he could give the life of God’s coming age to everyone you gave him. 3 And by “the life of God’s coming age” I mean this: that they should know you, the only true God, and Jesus the Messiah, the one you sent. (NTE) biblegateway.com/verse/en/John%2017:3
Much the same is the version by EO scholar David Bentley Hart & others:
John 17:2b that he might give them life in the Age.
3 And this is life in the Age: that they might know you, the sole true God, and him whom you sent, Jesus the Anointed. (DBH)
Jn.17:3 and this is the life age-during, that they may know Thee, the only true God, and him whom Thou didst send – Jesus Christ; (YLT)
Jn.17:3 And in this consists the Life of the Ages–in knowing Thee the only true God and Jesus Christ whom Thou hast sent. (WEY)
Jn.17:3 And, this, is the age-abiding life, That they get to know thee, the only real God, and him whom thou didst send, Jesus Christ. (RO)
Jn.17:3 This and is the age-lasting life, that they might know thee the only true God, and whom thou hast sent Jesus Anointed. (DG)
After a believer’s mortal body dies, he has an eonian glory & body in the heavens:
2 Cor.4:17 For the momentary lightness of our affliction is producing for us a transcendently transcendent eonian burden of glory,
18 at our not noting what is being observed, but what is not being observed, for what is being observed is temporary, yet what is not being observed is eonian." 2 Cor.5:1 For we are aware that, if our terrestrial tabernacle house should be demolished, we have a building of God, a house not made by hands, eonian, in the heavens." 2 For in this also we are groaning, longing to be dressed in our habitation which is out of heaven
So eonian life isn’t limited to this mortal life only, but is also for those who have died “in Christ”, e.g. the martyrs Stephen & James in the book of Acts. Believers will obtain “life eonian” in the “coming eon”:
29 Now He said to them, "Verily, I am saying to you that there is no one who leaves house, or wife, or brothers, or parents, or children on account of the kingdom of God, 30 who may not by all means be getting back manyfold in this era, and in the coming eon, life eonian. (Lk.18:29-30)
29 Jesus averred to him, "Verily, I am saying to you that there is no one who leaves a house, or brothers, or sisters, or father, or mother, or wife, or children, or fields, on My account and on account of the evangel, 30 who should not be getting back a hundredfold now, in this era, houses and brothers and sisters and mother and father and children and fields, with persecutions, and in the coming eon, life eonian. (Mk.10:29-30)
Which eon occurs after Christ’s return when life eonian will be obtained:
46 And these shall be coming away into chastening eonian, yet the just into life eonian. (Mt.25:46)
41 Then shall He be declaring to those also at His left, 'Go from Me, you cursed, into the fire eonian, made ready for the Adversary and his messengers. (Mt.25:41)
Eonian life is also a hope and a promise:
1 Jn.2:25 this is the promise which He promises us: life eonian
Titus 1:2 In hope of eonian life
Titus 3:7 3: heirs according to the hope of eonian life.
Jude 1:20 Now you, beloved, building yourselves up in your most holy faith, praying in holy spirit,
21 keep yourselves in the love of God, anticipating the mercy of our Lord Jesus Christ for life eonian.
The willfully disobedient do not have such a promise or hope & will forfeit life eonian:
Jn.3:36 He who is believing in the Son has life eonian, yet he who is stubborn as to the Son shall not be seeing life, but the indignation of God is remaining on him."
2 Thess1:4 so that we ourselves glory in you in the ecclesias of God, for your endurance and faith in all your persecutions and the afflictions with which you are bearing -" 5 a display of the just judging of God, to deem you worthy of the kingdom of God, for which you are suffering also, 6 if so be that it is just of God to repay affliction to those afflicting you, 7 and to you who are being afflicted, ease, with us, at the unveiling of the Lord Jesus from heaven with His powerful messengers, 8 in flaming fire, dealing out vengeance to those who are not acquainted with God and those who are not obeying the evangel of our Lord Jesus Christ" 9 who shall incur the justice of eonian destruction from the face of the Lord, and from the glory of His strength" 10 whenever He may be coming to be glorified in His saints and to be marveled at in all who believe (seeing that our testimony to you was believed) in that day.
Rom.2:4 Or are you despising the riches of His kindness and forbearance and patience, being ignorant that the kindness of God is leading you to repentance? 5 Yet, in accord with your hardness and unrepentant heart you are hoarding for yourself indignation in the day of indignation and revelation of the just judgment of God, 6 Who will be paying each one in accord with his acts: 7 to those, indeed, who by endurance in good acts are seeking glory and honor and incorruption, life eonian
16 in the day when God will be judging the hidden things of humanity, according to my evangel, through Jesus Christ