When Scripture talks about the eventual fate of the unrepentant, those who never turn to Christ in faith, it is a bleak picture of God’s wrath and punishment. It’s not a fun thing to talk about, but it is a reality that makes Christians so thankful for Christ and his saving work and the eternal life he gives. It also is one of many reasons why we share the gospel with those who don’t believe. One aspect of this topic is the fact that the punishment is eternal. Here’s how Geerhardus Vos explained it:
The judgment assigns to each individual his eternal destiny, which is absolute in its character either of blessedness or of punishment…. Only two groups are recognized, those of the condemned and of the saved (Matthew 25:33, 14; John 5:29); no intermediate group with as yet undetermined destiny anywhere appears. The degree of guilt is fixed according to the knowledge of the Divine will possessed in life (Matthew 10:15; 11:20–24; Luke 10:12–15; 12:47, 48; John 15:22, 24; Romans 2:12; 2 Peter 2:20–22). The uniform representation is that the judgment has reference to what has been done in the embodied state of this life; nowhere is there any reflection upon the conduct or product of the intermediate state as contributing to the decision (2 Corinthians 5:10).
The state assigned is of endless duration, hence described as aionios, “eternal.” While this adjective etymologically need mean no more than “what extends through a certain aeon or period of time,” yet its eschatological usage correlates it everywhere with the “coming age,” and, this age being endless in duration, every state or destiny connected with it partakes of the same character. It is therefore exegetically impossible to give a relative sense to such phrases as pur aionion, “eternal fire” (Matthew 18:8; 25:41; Jude 1:7), kolasis aionios, “eternal punishment” (Matthew 25:46), olethros aionios, “eternal destruction” (2 Thessalonians 1:9), krisis aionios or krima aionion, “eternal judgment” (Mark 3:29; Hebrews 6:2). This is also shown by the figurative representations which unfold the import of the adjective: The “unquenchable fire” (Matthew 3:12), “the never-dying worm” (Mark 9:43–48), “The smoke of their torment goeth up for ever and ever” (Revelation 14:11), “tormented day and night forever and ever” (Revelation 20:10). The endless duration of the state of punishment is also required by the absolute eternity of its counterpart, zoe aionios, “eternal life” (Matthew 25:46).
In support of the doctrine of conditional immortality it has been urged that other terms descriptive of the fate of the condemned, such as apoleia, “perdition,” phthora, “corruption,” olethros, “destruction,” thanatos, “death,” point rather to a cessation of being. This, however, rests on an unscriptural interpretation of these terms, which everywhere in the Old Testament and the New Testament designate a state of existence with an undesirable content, never the pure negation of existence, just as “life” in Scripture describes a positive mode of being, never mere existence as such. Perdition, corruption, destruction, death, are predicated in all such cases of the welfare or the ethical spiritual character of man, without implying the annihilation of his physical existence.
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