Hodge:

This is what is meant when it is said, or implied in Scripture, that Christ gave Himself as a propitiation, not for our sins only, but for the sins of the whole world. He was a propitiation effectually for the sins of his people, and sufficiently for the sins of the whole world. Augustinians have no need to wrest the Scriptures. They are under no necessity of departing from their fundamental principle that it is the duty of the theologian to subordinate his theories to the Bible, and teach not what seems to him to be true or reasonable, but simply what the Bible teaches.

Charles Hodge, Systematic Theology, 2:558-9.

1) “The human conscience is the mirror and index of the divine attribute of justice.  The two are correlated.  What therefore God’s justice demands, man’s conscience demands.  ‘Nothing,’ says Matthew Henry, ‘can pacify an offended conscience but that which satisfied an offended God.’  The peace which the believer in Christ’s atonement enjoys, and which is promised by the Redeemer to the believer, is the subjective experience in man that corresponds to the objective reconciliation in God.  The pacification of the human conscience is the consequence of the satisfaction of divine justice.  God’s justice is completely satisfied for the sin of man by the death of Christ.  This is an accomplished fact: ‘Jesus Christ the righteous is the propitiation for the sins of the whole world.’ (1 John 2:2). The instant any individual man of this world of mankind believes that divine justice is thus satisfied, his conscience is at rest.  The belief is not needed in order to establish the fact.  Whether a sinner believes Christ died for sin or not will make no difference with the fact, though it will make a vast difference with him: ‘If we believe not, yet he abides faithful: he cannot deny himself’ (2 Tim. 2:13).  Unbelief cannot destroy a fact.  Should not a soul henceforth believe on the Son of God, it would nevertheless be a fact that he died an atoning death on Calvary and that this death is an ample oblation for the sin of the world.  But it must be remembered that the kind of belief by which a man obtains a personal benefit from the fact of Christ’s death is experimental, not historical or hearsay. And a sinful man may have no skeptical doubt that the death of Christ on Mount Calvary has completely expiated human guilt and may even construct a strong argument in proof of the fact and still have all the miserable experience of an unforgiving sinner, may still have remorse and the fear of death and the damnation of hell. Whenever there is an experimental belief of the actual and accomplished fact of Christ’s atonement, there is a subjective pacification of the conscience corresponding to the objective reconciliation of divine justice.  But this subjective effect of Christ’s death is neither the primary nor the whole effect of it.  It presupposes the objective satisfaction or propitiation. In this instance, as in all others, the object is prior to the subject and determines its consciousness.” Shedd, Dogmatic Theology, 2:409-11.

2) In the third place, an atonement, either personal or vicarious, when made, naturally and necessarily cancels legal claims. This means that there is such a natural and necessary correlation between vicarious atonement and justice, that the former supplies all that is required by the latter. It does not mean that Christ’s vicarious atonement naturally and necessarily saves every man; because the relation of Christ’s atonement to divine justice is one thing, but the relation of a particular person to Christ’s atonement is a very different thing. Christ’s death as related to the claims of the law upon all mankind, cancels those claims wholly. It is an infinite “propitiation for the sins of the whole world,” 1 John 2:2. But the relation of an impenitent person to this atonement, is that of unbelief and rejection of it. Consequently, what the atonement has effected objectively in reference to the attribute of divine justice, is not effected subjectively in the conscience of the individual. There is an infinite satisfaction that naturally and necessarily cancels legal claims, but unbelief derives no benefit from the fact…

This reasoning applies to vicarious atonement equally with personal. Justice does not require a second sacrifice from Christ, in addition to the first. “Christ was once offered to bear the sins of many,” Hebrews 10:28 [sic]. This one offering expiated “the sins of the whole world,” and justice is completely satisfied in reference to them. The death of the God-man naturally and necessarily cancelled all legal claims. When a particular person trusts in this infinite atonement, and it is imputed to him by God, it then becomes his atonement for judicial purposes as really as if he had made it himself, and then it naturally and necessarily cancels his personal guilt, and he has the testimony that it does in his peace of conscience. Shedd, Dogmatic Theology, 2:437, 438.

3) The Christian gospel–the universal offer of pardon through the self-sacrifice of one of the divine persons–should silence every objection to the doctrine of endless punishment.  For as the case now stands, there is no necessity, so far as the action of God is concerned, that a single human being should ever be the subject of future punishment…

“For the Scriptures everywhere describe God as naturally and spontaneously merciful and declare that all the legal obstacles to the exercise of this great attribute have been removed by the death of the Son of God ‘for the sins of the whole world‘ (1 John 2:2).  In the very centre of the holy revelations of Sinai, Jehovah proclaimed it to be his inherent and intrinsic disposition to be ‘merciful and gracious, long-suffering, forgiving iniquity and transgression’ (Exod. 34:6-7). Shedd, Dogmatic Theology 2:749

4) But, secondly, there are degrees of mercy. Because God does not show the degree of it to a particular sinner, it does not follow that he does not show him any at all. He may grant him the mercy of common grace, and which this is resisted and nullified by his hostile self-will arid obstinate love of sin, he may decide not to bestow the mercy of special grace, and yet not be chargeable with destitution of love and compassion towards him.¹ Any degree of love is love; and any degree of compassion is compassion. To contend that the Divine love must be of exactly the same degree towards all creatures alike or else it is not love, is untenable. It is certain that God can feel love and pity towards the souls of all men, as his creatures and as sinners lost by their own fault, and manifest it in that measure of grace which “leads to repentance” (Rom. 2:4), and would result in it if it were not resisted, and yet not actually save them all from the consequences of their own action. This Scriptures plainly teach that God so loved the whole world that he gave his only-begotten Son to make expiation for “the sins of the whole world;” and they just as plainly teach that a part of this world of mankind are sentenced, by God, to eternal death for their sins. The Arminian and the Calvinist both alike deny the doctrine of universal salvation, yet believe that this is compatible with the doctrine of God’s universal benevolence. Both deny the inference that if God does not save every human being, he does not love the soul of every human being; that if lie does not do as much for one person as he does for another, he is merciful towards him. It is a fallacy to maintain, that, unless God does all that is possibly can to save a sinner, he does not do anything towards his salvation; as it would be fallacious to maintain, that unless God bestows upon a person all the temporal blessings that are within his power, he does not show him any benevolence at all. This fallacy lies under the argument against preterition. It is asserted that if God “passes by” a sinner in the bestowment of regenerating grace, he has no love for his soul, no desire for its salvation, and does nothing towards its welfare.

Footnote 1: Man is compelled to speak of God’s decision or decree in this way, though strictly there is no before or after for him. All his decrees are eternal and simultaneous. Yet there is an order of nature. Special grace supposes the failure of common grace.

William G.T. Shedd, Calvinism Pure and Mixed (New York: Charles Scribner’s Sons, 1893), 45-46.

Dabney

But there are others of these passages, to which I think, the candid mind will admit, this sort of explanation is inapplicable. In John 3:16, make “the world” which Christ loved, to mean “the elect world,” and we reach the absurdity that some of the elect may not believe, and perish. In 2 Cor. 5:15, if we make the all for whom Christ died, mean only the all who live unto Him—i. e., the elect it would seem to be implied that of those elect for whom Christ died, only a part will live to Christ. In 1 John 2:2, it is at least doubtful whether the express phrase, “whole world,” can be restrained to the world of elect as including other than Jews. For it is indisputable, that the Apostle extends the propitiation of Christ beyond those whom he speaks of as “we,” in verse first. The interpretation described obviously proceeds on the assumption that these are only Jewish believers. Can this be substantiated? Is this catholic epistle addressed only to Jews? This is more than doubtful. It would seem then, that the Apostle’s scope is to console and encourage sinning believers with the thought that since Christ made expiation for every man, there is no danger that He will not be found a propitiation for them who, having already believed, now sincerely turn to him from recent sins.

Dabney, Lectures, p., 525.

Hodge:

There is still another ground on which it is urged that Augustinians cannot consistently preach the gospel to every creature. Augustinians teach, it is urged, that the work of Christ is a satisfaction to divine justice. From this it follows that justice cannot condemn those for whose sins it has been satisfied. It cannot demand that satisfaction twice, first from the substitute and then from the sinner himself. This would be manifestly unjust, far worse than demanding no punishment at all. From this it is inferred that the satisfaction or righteousness of Christ, if the ground on which a sinner may be forgiven, is the ground on which he must be forgiven. It is not the ground on which he may be forgiven, unless it is the ground on which he must be forgiven. If the atonement be limited in design it must be limited in its nature, and if limited in its nature it must be limited in its offer.

This objection again arises from confounding a pecuniary and a judicial satisfaction between which Augustinians are so careful to discriminate. This distinction has already been presented on a previous page. There is no grace in accepting a pecuniary satisfaction. It cannot be refused. It ipso facto liberates. The moment the debt is paid the debtor is free; and that without any condition. Nothing of this is true in the case of judicial satisfaction. If a substitute be provided and accepted it is a matter of grace. His satisfaction does not ipso facto liberate. It may accrue to the benefit of those for whom it is made at once or at a remote period; completely or gradually; on conditions or unconditionally; or it may never benefit them at all unless the condition on which its application is suspended be performed. These facts are universally admitted by those who hold that the work of Christ was a true and perfect satisfaction to divine justice. The application of its benefits is determined by the covenant between the Father and the Son. Those for whom it was specially rendered are not justified from eternity; they are not born in a justified state; they are by nature, or birth, the children of wrath even as others. To be the children of wrath is to be justly exposed to divine wrath. They remain in this state of exposure until they believe, and should they die (unless in infancy) before they believe they would inevitably perish notwithstanding the satisfaction made for their sins. It is the stipulations of the covenant which forbid such a result. Such being the nature of the judicial satisfaction rendered by Christ to the law, under which all men are placed, it may be sincerely offered to all men with the assurance that if they believe it shall accrue to their salvation. His work being specially designed for the salvation of his own people, renders, through the conditions of the covenant, that event certain; but this is perfectly consistent with its being made the ground of the general offer of the gospel. Lutherans and Reformed agree entirely, as before stated, in their views of the nature of the satisfaction of Christ, and consequently, so far as that point is concerned, there is the same foundation for the general offer of the gospel according to either scheme. What the Reformed or Augustinians hold about election does not affect the nature of the atonement. That remains the same whether designed for the elect or for all mankind. It does not derive its nature from the secret purpose of God as to its application.

C. Hodge, Systematic Theology, 2:557-8.