Hodge:

1) The word satisfaction is the one which for ages has been generally used to designate the special work of Christ in the salvation of men. With the Latin theologians the word is “satisfactio,” with the German writers, “Genugthun,” its exact etymological equivalent, “the doing enough.” By the satisfaction of Christ is meant all He has done to satisfy the demands of the law and justice of God, in the place and in behalf of sinners. This word has the advantage of being precise, comprehensive, and generally accepted, and should therefore be adhered to. There are, however, two kinds of satisfaction, which as they differ essentially in their nature and effects, should not be confounded. The one is pecuniary or commercial; the other penal or forensic. When a debtor pays the demand of his creditor in full, he satisfies his claims, and is entirely free from any further demands. In this case the thing paid is the precise sum due, neither more nor less. It is a simple matter of commutative justice; a quid pro quo; so much for so much. There can be no condescension, mercy, or grace on the part of a creditor receiving the payment of a debt. It matters not to him by whom the debt is paid, whether by the debtor himself, or by someone in his stead; because the claim of the creditor is simply upon the amount due and not upon the person of the debtor. In the case of crimes the matter is different. The demand is then upon the offender. He himself is amenable to justice. Substitution in human courts is out of the question. The essential point in matters of crime, is not the nature of the penalty, but who shall suffer. The soul that sins, it shall die. And the penalty need not be, and very rarely is, of the nature of the injury inflicted. All that is required is that it should be a just equivalent. For an assault, it may be a fine; for theft, imprisonment; for treason, banishment, or death. In case a substitute is provided to bear the penalty in the place of the criminal, it would be to the offender a matter of pure grace, enhanced in proportion to the dignity of the substitute, and the greatness of the evil from which the criminal is delivered. Another important difference between pecuniary and penal satisfaction, is that the one ipso facto liberates. The moment the debt is paid the debtor is free, and that completely. No delay can be admitted, and no conditions can be attached to his deliverance. But in the case of a criminal, as he has no claim to have a substitute take his place, if one be provided, the terms on which the benefits of his substitution shall accrue to the principal, are matters of agreement, or covenant between the substitute and the magistrate who represents justice. The deliverance of the offender may be immediate, unconditional, and complete; or, it may be deferred, suspended on certain conditions, and its benefits gradually bestowed.

As the satisfaction of Christ was not pecuniary, but penal or forensic; a satisfaction for sinners, and not for those who owed a certain amount of money, it follows, —1. That it does not consist in an exact quid pro quo, so much for so much. This, as just remarked, is not the case even among men. The penalty for theft is not the restitution of the thing stolen, or its exact pecuniary value. It is generally something of an entirely different nature. It may be stripes or imprisonment. The punishment for an assault is not the infliction of the same degree of injury on the person of the offender. So of slander, breach of trust, treason, and all other criminal offences. The punishment, for the offence is something different from the evil which the offender himself inflicted. All that justice demands in penal satisfaction is that it should be a real satisfaction, and not merely something graciously accepted as such. It must bear an adequate proportion to the crime committed. It may be different in kind, but it must have inherent value. To fine a man a few pence for wanton homicide would be a mockery; but death or imprisonment for life would be a real satisfaction to justice. All, therefore, that the Church teaches when it says that Christ satisfied divine justice for the sins of men, is that what He did and suffered was a real adequate compensation for the penalty remitted and the benefits conferred. His sufferings and death were adequate to accomplish all the ends designed by the punishment of the sins of men. He satisfied justice. He rendered it consistent with the justice of God that the sinner should be justified. But He did not suffer either in kind or degree what sinners would have suffered. In value, his sufferings infinitely transcended theirs. The death of an eminently good man would outweigh the annihilation of a universe of insects. So the humiliation, sufferings, and death of the eternal Son of God immeasurably transcended in worth and power the penalty which a world of sinners would have endured. Charles Hodge, Systematic Theology, 2: 470-471.

2) While Protestants and the Church generally have held the doctrine that the satisfaction of Christ, because of the dignity of his person and the nature and degree of his sufferings was and is infinitely meritorious, absolutely perfect from its intrinsic worth, and completely efficacious in its application to all the sins of the believer, the Scotists in the Middle Ages, and after them Grotius and the Remonstrants, denied that the work of Christ had inherent value to satisfy divine justice, but said that it was taken as a satisfaction, acceptatione gratuita…

It is obvious that the objections presented in the above extracts arise from confounding pecuniary with judicial or legal satisfaction. There is an analogy between them, and, therefore, on the ground of that analogy it is right to say that Christ assumed and paid our debts. The analogy consists, first, in the effect produced, namely, the certain deliverance of those for whom the satisfaction is made; secondly, that a real equivalent is paid; and, thirdly, that in both cases justice requires that the liberation of the obligee should take place. But, as we have already seen, the two kinds of satisfaction differ, first, in that in penal satisfaction the demand is not for any specific degree or kind of suffering; Charles Hodge, Systematic Theology, 2: 485, 487.

Ransom as metaphor:

1) Dr Beman’s second objection is, that the system he opposes destroys “all mercy in God the Father, in the salvation of sinners, because it represents God as. totally disinclined to the exercise of compassion, till every jot and tittle of the legal curse was inflicted. On the same principle, grace or pardon in the release of the sinner from future punishment, would be out o the question; for what grace, or pardon, or favour, can there be in the discharge of debtor, whose demand (debt?) has been cancelled to the uttermost farthing?” p. 122. This objection is the staple of his book. On p. 100, he represents us as teaching that “the Son of God endured the exact amount of suffering due on legal principle, to sinners.” On p. 107, he says, “The amount of Christ’s sufferings must consequently be the same as the aggregate sufferings included in the eternal condemnation of all those who are saved by his merit… The agonies which he suffered mere equal to the endless misery of all those who rill be saved by his interposition in their behalf.” On p. 146, he says, “If one soul were to be saved by the atonement, Christ must sustain an amount of suffering equal to that involved in the eternal condemnation of that one soul; and if. a thousand were to be saved a thousand times that mount, and in the same proportion for any greater number who are to be rescued from perdition and exalted to glory. To this scheme there are insurmountable objections.” True enough, but who hold that scheme? Dr Beman attributes it to all who believe in the atonement, and do not adopt his scheme; for he says there are but two. This doctrine, that the sufferings of Christ amounted to the aggregate sufferings of those who are to be saved, that he endured just so much for so many, is not found in any confession of the Protestant churches. nor in the writings of any standard theologian, nor in the recognised authorities of any church of which we have any knowledge. The whole objection is a gross and inexcusable misrepresentation. In a more moderate form it was brought forward by the Socinians, and repelled by the writers of that and subsequent ages. De Moor is generally recognised as the theologian of most authority among the churches of Holland, and Turrettin is admitted to be one of the strictest of the Geneva, school, and they both answer this calumny, by denying that, according to their doctrine, there is any necessity for the assumption that Christ’s sufferings were equal to the sufferings of all his people. Thus Turrettin, after quoting at length the objection from Socinus, answers it, first, by showing that the Scriptures teach that the one death of Christ mas a satisfaction or all; that as by the one sin of Adam, many mere made sinners, so by the, righteousness of Christ, many are made righteous. 2. By insisting on the distinction between pecuniary and penal satisfaction. A piece of money in the hand of a king is of no more value than in the hands of a peasant, but the life of a king is of more value than that of a peasant, and one commander is often exchanged for many soldiers. 3. He says the adversaries forget that Christ is God, and therefore, though his sufferings could not be infinite as they were endured by his finite nature, they were of infinite value in virtue of the infinite dignity of his person. Sin, he says, is an infinite evil, because committed against an infinite God, through the act of a finite nature. So the sufferings of Christ. though endured in his human nature, are of infinite value from the dignity of his person.

Dr Beman, under this head, frequently objects that we degrade the atonement into a mere commercial transaction, a payment of a debt, which, from the nature of the case, excludes the idea of free remission. Our first remark on this objection is, that the Scriptures use this same figure, and therefore it is right it should be used. When it is said, Christ purchased the church with his own blood, that we are redeemed not with corruptible things as silver and gold, but with the precious blood of Christ, such language means something. In every metaphor there is a point of comparison; the essential idea involved in the figure, must be found in subject to be illustrated. To purchase is to acquire, and to acquire, by giving or doing something which secures a title to the thing acquired. When it is said that Christ purchased the church, it is certainly meant that he acquired it, that it is his, and that by his death he has secured a title to it, founded in the justice and promise of God. This does not make redemption a commercial transaction, nor imply that there are not essential points of diversity between acquiring by money and acquiring by blood. Hence our second remark is, that if Dr Beman will take up any elementary work on theology, he will find the distinction between pecuniary and penal satisfaction clearly pointed out, and the satisfaction of Christ shown to be of the latter, and not of the former kind. I. In the one, the demand is upon the thing due; in the other case, it is upon the person of the Hence, 2. The creditor is bound to accept the payment of the debt, no matter when or by whom offered; whereas in the case of a crime or sin, the sovereign is bound neither to provide a substitute, nor to accept of one when offered. If he does either, it is s matter of grace. 3. Hence penal satisfaction does not ipso facto liberate; the acceptance is a matter of arrangement or covenant, and the terms of that covenant must depend on the mill of the parties. Dr Beman lapsed into an important truth when he said, “Christ suffered by covenant,” p. 98. What that covenant is, we learn from Scripture, and from the manner in which it is executed. The Bible teaches that, agreeably to that covenant, the merits of Christ do not avail to the benefit of his people immediately; his children remain under condemnation as well as others until they believe; and when they do believe, they receive but the first fruits of their inheritance, they are but imperfectly sanctified, and are still subject to many evils; but being in a justified state, their sufferings are chastisements and not punishments, that is, they are designed for their own improvement, and not to satisfy justice.

The satisfaction of Christ, therefore, being for sin and by suffering, is expressly and formally declared not to be of the nature of pecuniary satisfaction. Charles Hodge, “Beman on the Atonement,” in Essays and Reviews, in (New York, Robert Carter & Brothers, 1857), 163-6.

[Notes: C.f., Hodge’s other relevant comments here.]