“These will go away into eternal punishment, but the righteous into eternal life,” (Matthew 25:46).

In the context of conditionalism, “eternal punishment” means eternal nonexistence.¹See article Conditionalism and conflating eternal punishment with non-existence for an explanation of why eternal punishment is not eternal nonexistence
They contrast eternal punishment with eternal life and say that since eternal life means to have a living relationship with God in a physical body forever, then “eternal punishment” must mean the punishment that leads to nonexistence otherwise, they too would have eternal life.

The phrase “eternal life” is never defined in Scripture. It is however associated with many good things and contrasted with bad things. For example, it is associated with abiding with God (1 John 2:25), generic blessing (Matt. 19:16; Luke 10:25; John 3:15, etc.), grace and righteousness (Rom. 5:21), justification (Titus 3:7), never perishing (John 10:28), resurrection (John 6:40, 54), and sanctification (Rom. 6:22).  It is contrasted with death (Rom. 6:23), eternal punishment (Matt. 25:46), God’s wrath (John 3:36), and perishing (John 3:16; 6:27).  So, we naturally conclude that eternal life is good and eternal punishment is bad.  (See Word Study on eternal life)

One occurrence of eternal punishment

However, there is nothing in the context of Matthew 25:46 that defines what eternal punishment is. In fact, the only occurrence of the phrase “eternal punishment” is in this verse we are now studying. The closest parallel using the words “eternal” and “punishment” is Jude 7 which says, “just as Sodom and Gomorrah and the cities around them since they in the same way as these indulged in gross immorality and went after strange flesh, are exhibited as an example in undergoing the punishment of eternal fire.”  That verse clearly says that people are alive now in conscious punishment.  For more on this see the article Jude 6-7, angels undergoing the punishment of eternal fire.

Eternal death

However, notice that in Matt. 25:46 eternal punishment is contrasted with eternal life. It does not say “eternal death” is contrasted with eternal life which might possibly imply, to the conditionalist, that death is nonexistence and life is continued existence. Instead, we see the contrast of eternal punishment with eternal life. What is interesting is that the phrase “eternal death” does not occur anywhere in the entire Bible. Yet, the phrase is sometimes used by conditionalists to designate the opposite of eternal life.

• “Eternal life is the opposite of eternal death; the two stand in stark contrast to each other.”²Fudge, Edward William. The Fire That Consumes: A Biblical and Historical Study of the Doctrine of Final Punishment, Third Edition (p. 210). Cascade Books, an imprint of Wipf and Stock Publishers. Kindle Edition.
• “Paul never gives reason to suppose that eternal death is anything other than the absence of life—not merely the blessings of the age to come that are wrapped up in the phrase “eternal life,” but sentient, personal, embodied existence itself.”³ibid., Fudge, p. 211
• “the apostle never speaks of eternal death, but— death. He never joins the term aiōnios, eternal, with it, as he does with life, neither does our Lord, nor do any of the sacred writers, for this death is of itself a finality. It is not a never-ending reality, a progressive form of being as life is, but an end, a cessation of life.”⁴A Consuming Passion: Essays on Hell and Immortality in Honor of Edward Fudge (Kindle Locations 1799-1801). Pickwick Publications, an Imprint of Wipf and Stock Publishers. Kindle Edition.

What the annihilationists do is contrast eternal punishment with eternal life and say that since eternal life means the person is alive, the opposite, eternal punishment, must mean that they are not alive. But this is reading into the text what is not there. Punishment is something that is experienced and, according to annihilationism, eternal punishment means eternal nonexistence. But, in stating this they conflate eternal punishment with nonexistence. (See article Conditionalism and conflating eternal punishment with non-existence)

Matthew 25:41

“Then He will also say to those on His left, ‘Depart from Me, accursed ones, into the eternal fire which has been prepared for the devil and his angels,” (Matthew 25:41).

Worth mentioning is the earlier verse of Matthew 25:41. In it, Jesus says that the wicked will depart into the eternal fire which has been prepared for the devil and his angels. Only five verses later Jesus speaks of the eternal punishment that is contrasted with eternal life (Matt. 25:46). Jesus equates eternal fire with eternal punishment (v. 41 and 46) and since Jesus said that angels do not die (Luke 20:36) and that the eternal fire was prepared for the devil and his angels (Matt. 25:41). Furthermore, Revelation 20:10 says that the devil is thrown into the lake of fire with the beast and the false prophet where they will be tormented day and night forever and ever. We can conclude that the eternal fire of Matthew 25:41 along with the eternal punishment of Matthew 25:46 are conscious and without end since it is a torment that is “day and night forever and ever,” (Rev. 20:10).

Conclusion

Nothing in the context of Matthew 25:46 tells us what eternal punishment is. In fact, the phrase that it is contrasted with “eternal life” is also never defined in Scripture. However, we know that eternal life is associated with many good things and contrasted with many bad things. But, the annihilationist contrasts eternal punishment with eternal life and reinterprets eternal punishment to mean eternal death; that is, nonexistence in their minds. However, the phrase “eternal death” does not occur in the Bible. So, the conditionalists are reading into the text a meaning that is not there. In addition, Matthew 25:41 which is just five verses earlier says that the wicked will depart and be cast into the eternal fire which has been prepared for the devil and his angels (v. 41). But in Luke 20:36 Jesus says angels do not die. Therefore, the fire that consumes them (the wicked angles) must be eternal and their existence that will never end. Furthermore, since Revelation 20:10 says that the devil is thrown into the lake of fire along with the beast and the false prophet and that they will be tormented day and night forever and ever, we can conclude that all of this means that Matthew 25:46 not only cannot be used to support the annihilationist assumption. If anything, it supports the idea that eternal punishment is conscious and experienced by the wicked.