Now, one characteristic of the next age is that it will last forever, and so being eternal can sometimes be a reference to how long something lasts — but that is based on context. The word is always a reference to the next age.
The NT (following Judaism) uses “eon” or “age” to divide time into “this present eon” and “the eon that is about to be” or “the coming eon.” The contrast is not simply between time and timelessness, for the “eon that is about to be” is future and shares a specific and identifiable character. The biblical picture of the start of the “coming age” is dramatically painted with broad sequential brush strokes. The new age is not simply a restoration to the primitive and naïve innocence of the earliest stage, but a consummation according to the purposes of “him who is and who was and who is to come” (Rv 1:4). Thus it is designated as the new creation.
The NT clearly teaches that the “age that is to be” has now begun in the life and ministry of Christ, although there is a definite overlap in the two ages. The frequency of such terms as “the first fruits,” “the earnest of the Spirit,” and “the last days,” reflects this understanding (e.g., Heb 6:5: “and have tasted … the powers of the age to come”). The believer enjoys the blessings of the future age imported into the present through Christ’s redemptive work.
The concept of eternity, then, does not stand in opposition and contrast to time as timelessness. Eternity is the unlimited and incalculable space of time bounded at its beginning by the introduction of the kingdom of God in Christ and stretching out into the unlimited future. Both time (“the present evil age,” Gal 1:4) and eternity are governed by God as the Lord of all time, the one who gives content and meaning to both. For the believer the midpoint of time (even though the second coming of Christ and the consummation of the present eon have not yet occurred) is found in the first Easter. It is not the consummation that brings eternity; eternity is the accomplishment of God’s sovereign and eternal purpose in Christ for the whole universe.
Walter A. Elwell and Barry J. Beitzel, Baker Encyclopedia of the Bible, 1988, 726.
The NT makes a striking modification of the contemporary Jewish division of time into the present age and the age to come. There is still a point of transition in the future between ‘this time’ and ‘the world to come’ (Mk. 10:30; Eph. 1:21; Tit. 2:12–13), but there is an anticipation of the consummation, because in Jesus God’s purpose has been decisively fulfilled. The gift of the Spirit is the mark of this anticipation, this tasting of the powers of the world to come (Eph. 1:14; Heb. 6:4–6; cf. Rom. 8:18–23; Gal. 1:4). Hence John consistently stresses that we now have eternal life, zōē aiōnios (e.g. Jn. 3:36). It is not simply that aiōnios has qualitative overtones; rather John is urging the fact that Christians now have the life into which they will fully enter by resurrection (Jn. 11:23–25). This ‘overlapping’ of the two ages is possibly what Paul has in mind in 1 Cor. 10:11.
“TIME,” New Bible Dictionary, 1188.
The meaning is lost nearly entirely in the English “eternal” or “eternity,” but in the Greek, there’s always an allusion to the next age, and not necessarily to lasting forever.
In other words, “life eternal” is not just life that lasts forever, although it’s certainly that. The sense is more precisely life that begins anew at the general resurrection, when the next age in its fullness begins. It’s life to be lived in the next age — which will be forever, but also fully redeemed from the curse on creation — so it’s not just about how long we’ll live.
Hence, “eternal punishment” or “eternal death” are punishment and death in the next age. The death lasts forever, not the dying. That is, to die eternally is to die with no hope of the resurrection in the next age, so that the death is forever — in contrast to eternal life, in which we die in this age only to live anew in the next age. It’s “dead forever” in contrast to “alive forever.” But it’s also destroyed along with the rest of the unredeemed, rather than alive in a fully redeemed world.
And so —
(Heb 6:1-2 ESV) Therefore let us leave the elementary doctrine of Christ and go on to maturity, not laying again a foundation of repentance from dead works and of faith toward God, 2 and of instruction about washings, the laying on of hands, the resurrection of the dead, and eternal judgment.
— doesn’t refer to judgment that will take forever to be complete. “Eternal” judgment is judgment aionios, judgment in the next age.
In fact, much of the NT language of eternal punishment comes from Isa 65 (covered earlier) and —
(Isa 33:10-14 ESV) 10 “Now I will arise,” says the LORD, “now I will lift myself up; now I will be exalted. 11 You conceive chaff; you give birth to stubble; your breath is a fire that will consume you. 12 And the peoples will be as if burned to lime, like thorns cut down, that are burned in the fire.” 13 Hear, you who are far off, what I have done; and you who are near, acknowledge my might. 14 The sinners in Zion are afraid; trembling has seized the godless: “Who among us can dwell with the consuming fire? Who among us can dwell with everlasting burnings?”
Sounds like John the Baptist, doesn’t it? and the reference to “everlasting burnings” sounds like Jesus.
Is Isaiah referring to perpetual conscious torment of the damned? Well, he also says that this fire will “consume you” and will be like “thorns cut down, that are burned in the fire.” Indeed, the point of v. 14 is not that they expect to suffer forever, but that they cannot survive at all against a being like God. Hence, God’s eternal destruction will utterly destroy his enemies.