The Lord is good to all: and his tender mercies are over all his worksAll your works shall give thanks to you, O LORD, and all your saints shall bless you. (Psalm 145: 9-10.)

having made known to us the secret of His will, according to His good pleasure, that He purposed in Himself, in regard to the dispensation of the fullness of the times, to bring into one the whole in the Christ, both the things in the heavens, and the things on the earth—in Him. (Eph. 1:9-10.)

Whoever does not love, does not know God. For God is love. (1 John 4:8.)

And when I am lifted up from the earth, I will draw all to myself. (John 12:32, New Catholic Bible.)

I exhort therefore, first of all, that there be offered supplications, prayers, intercessions, thanksgivings for the whole race of mankind: for kings, and all that are in a state of eminence, that we may lead a quiet and peaceable life in all godliness and seriousness. For this is becoming, and acceptable before God our Savior; who wills all men to be saved, and come to the acknowledgment of truthFor there is one God, and one mediator between God and men, the man Christ Jesus; who gave himself a ransom for all, the testimony to be born in his appointed timesof which I am ordained a preacher and apostle, (I speak the truth in Christ, I lie not,) a teacher of the Gentiles in faith and truth. (1 Timothy 2:1-7.)

For you are not come to a mountain that might be touched, and a burning fire, and a whirlwind, and darkness, and storm, And the sound of a trumpet, and the voice of words, which they that heard excused themselves, that the word might not be spoken to them: For they did not endure that which was said: And if so much as a beast shall touch the mount, it shall be stoned. And so terrible was that which was seen, Moses said: I am frighted, and tremble. But you are come to mount Sion, and to the city of the living God, the heavenly Jerusalem, and to the company of many thousands of angels, And to the church of the firstborn ("firstborn" in Greek is plural), who are written in the heavens, and to God the judge of all, and to the spirits of the just made perfect, And to Jesus the mediator of the new testament, and to the sprinkling of blood which speaketh better than that of Abel. (Hebrews 12:18-24, Catholic Public Domain Version.)

Every excellent gift and every perfect gift is from above, descending from the Father of lights, with whom there is no change, nor any shadow of alteration. For by his own will he produced us through the Word of truth, so that we might be a kind of beginning among his creatures. (James 1:17-18, Catholic Public Domain Version.)

And he is the propitiation for our sins. And not only for our sins, but also for those of the whole world. (1 John 2:2, Catholic Public Domain Version.)

...as through one offense to all men [it is] to condemnation, so also through one declaration of “Righteous” [it is] to all men to justification of life; for as through the disobedience of the one man, the many were constituted sinners: so also through the obedience of the One, will the many be constituted righteous. And law came in, that the offense might abound, and where sin abounded, grace hyper-abounded, that even as sin reigned in death, so also grace may reign, through righteousness, to continuous life, through Jesus Christ our Lord. (Romans 5:18-21, Literal Translation.)

But now Christ is risen from the dead, the firstfruits of them that sleep: For by a man came death, and by a man the resurrection of the dead.And as in Adam all die, so also in Christ all shall be made alive.But every one in his own order: the firstfruits Christ, then they that are of Christ, who have believed in his coming. Afterwards the end, when he shall have delivered up the kingdom to God and the Father, when he shall have brought to nought all principality, and power, and virtue. For he must reign, until he hath put all his enemies under his feet. And the enemy death shall be destroyed last: For he hath put all things under his feet. And whereas he saith,All things are put under him; undoubtedly, he is excepted, who put all things under him. And when all things shall be subdued unto him, then the Son also himself shall be subject unto him that put all things under him, that God may be all in all. (1Corinthians 15:20-28, Douay Rheims Translation.)

For I would not have you ignorant, brethren, of this mystery, (lest you should be wise in your own conceits), that blindness in part has happened in Israel, until the fulness of the Gentiles should come in. And so all Israel should be saved, as it is written: There shall come out of Sion, he that shall deliver, and shall turn away ungodliness from Jacob. And this is to them my covenant: when I shall take away their sins. As concerning the gospel, indeed, they are enemies for your sake: but as touching the election, they are most dear for the sake of the fathers. For the gifts and the calling of God are without repentance. For as you also in times past did not believe God, but now have obtained mercy, through their unbelief; So these also now have not believed, for your mercy, that they also may obtain mercy. For God hath concluded all in unbelief, that he may have mercy on all. O the depth of the riches of the wisdom and of the knowledge of God! How incomprehensible are his judgments, and how unsearchable his ways! For who hath known the mind of the Lord? Or who hath been his counsellor? Or who hath first given to him, and recompense shall be made him? For of him, and by him, and in him, are all things: to him be glory for ever. Amen. (Romans 11:25-36, Douay Rheims.)

For therefore we labor and are reviled, because we hope in the living God, who is the Saviour of all men, especially of the faithful. (1 Timothy 4:10, Douay Rheims.)

For in him were all created in heaven and on earth, visible and invisible, whether thrones, or dominations, or principalities, or powers: all were created by him and in him. And he is before all, and by him all consists. And he is the head of the body, the church, who is the beginning, the firstborn from the dead; that in all things he may hold the primacy: Because in him, it hath well pleased the Father, that all fullness should dwell; And through him to reconcile all unto himself, making peace through the blood of his cross, both as to that on earth, and that in heaven. (Colossians 1:16-20, Literal Translation.)

Note: Augustine's reasoning concerning the meaning of aionian in Matthew 25:46 (though followed by most theologians since) is clearly fallacious, because it is simply not true that unless aionian signifies endless duration there (in the context of life and chastening) we're left with no scriptural promise of unending life for the saints. Augustine (and those who follow him) ignore the fact that whatever aionian life and aionian punishment mean in Matthew 25:46, we still have a clear promise of unending life in passages like Luke 20:34-36. Where Christ said "...The children of this world (Greek: age, eion) marry, and are given in marriage: But they that shall be accounted worthy of that world (Greek age, eion), and of the resurrection from the dead, shall neither be married, nor take wives. Neither can they die any more: for they are equal to the angels, and are the children of God, being the children of the resurrection." And we're still told that God is immortal in passages like Romans 1:26. So Augustine's fears of what would be lost if we don’t understand aionian to mean unending were unfounded. And his view is even more fallacious when it's realized that unending duration was not what the Greek speaking world understood aionian, aionios, and aionas to mean in the Pratristic era. The following quote from a non-Christian (neo-Platonist) writing in the 6th century shows this.

Do not suppose that the soul is punished for endless eons (apeirou aionas) in Tartarus. Very properly, the soul is not punished to gratify the revenge of the divinity, but for the sake of healing. But we say that the soul is punished for an aionion period (aionios) calling its life and its allotted period of punishment, its aeon.

Source: Olnmpiodorus the Younger (AD 550)

And this quote from an 8th century commentary on Holy Scripture, shows that centuries later, even the Latin words used to translate aionios, aionian, and aionas in the Latin Vulgate were not necessarily understood to mean endless durion.

Ambrosius Autpertus (An 8th century Bennedictine monk, abbot, and Theologian who wrote commentaries on Holy Scripture.)

 Rev 20:10 “And the devil that deceived them was cast into the lake of fire and brimstone, where the beast and the false prophet are: and they shall be tormented day and night for ever and ever (Latin saecula saeculorum)." But when it says, "they shall be tormented day and night for ever and ever (Latin: saecula saeculorum)," it is not to be taken in such a way that no sentence of God’s mercy is left at all: but because very long times (Latin: saecula saeculorum) are appointed for punishments, which human frailty cannot measure. It can happen that even the evil spirits themselves, who are now obstinate in their wickedness, after very long times are freed by God’s mercy, when they put off the nature which they corrupted, and are reformed to that for which they were created. But if this is so, it does not detract from divine justice, because they will have paid for a very long time what they deserved.

Source: Ambrosius Autpertus--Commentary on the Apocalypse (c. 784 AD), Book 10, ch. 36. Patrologia Latina 89:1391.

So Augustine and those who follow his reasoning are clearly wrong when they say that the Greek and Latin words often translated eternal punishment in Matthew 25:46 must have that meaning or we're left with no promise of eternal life. Matthew 25:46 can be translated "And these will go to the chastening of that Age, but the just to the life of that Agewithout robbing us of the promise of eternal life. And the Greek word translated "punishment" in Matthew 25:46 (kolasis) is a word that was originally used for pruning trees. Which in itself suggests that the purpose of punishment is remedial (and that therefore the duration of the punishment cannot be endless.)