II. The Difference between a penal and a pecuniary satisfaction. These differ precisely as do crime and debt, things and persons, and therefore the distinction is both obvious and important. Many, who either are incapable of understanding the question, are ignorant of its history, or who are unscrupulous as to the manner in which they conduct controversy, are continually charging our doctrine with the folly of representing the sacrifice of Christ as a purely commercial transaction, in which so much was given for so much, and in which God was in such a sense recompensed for his favours to us that however much gratitude we may owe to Christ, we owe on this behalf none to God. Long ago the doctrine of the Reformed Churches was unanswerably vindicated from such puerile charges by all its most authoritative expounders. “Here the twofold solution, concerning which jurists treat, should be accurately distinguished. The one, which ipso facto liberates the debtor or criminal because that very thing which was owed is paid, whether it was done by the debtor or by another in his name. The other, which ipso facto does not liberate, since not at all the very thing which was owed, but an equivalent, is paid, which, although it does not thoroughly and ipso facto discharge the obligation, yet having been accepted—since it might be refused—is regarded as a satisfaction. This distinction holds between a pecuniary and a penal indebtedness. For in a pecuniary debt the payment of the thing owed ipso facto liberates the debtor from all obligations whatsoever, because here the point is not who pays, but what is paid. Hence the creditor, the payment being accepted, is never said to extend toward the debtor any indulgence or remission, because he has received all that was owed him. But the case is different with respect to a penal debt, because in this case the obligation respects the person as well as the thing; the demand is upon the person who pays as well as the thing paid; i. e., that the penalty should be suffered by the person sinning; for as the law demands personal and proper obedience, so it exacts personal enduring of the penalty. Therefore, in order that a criminal should be absolved—a vicarious satisfaction being rendered by another hand—it is necessary that there should intervene a sovereign act of the supreme law-giver, which, with respect to the law, is called relaxation, and with respect to the debtor is called remission, because the personal endurance of the penalty is remitted, and a vicarious endurance of it is accepted in its stead. Hence it clearly appears that in this work (of Redemption) remission and satisfaction are perfectly consistent with each other, because there is satisfaction in the endurance of the punishment which Christ bore, and there is remission in the acceptance of a vicarious victim. The satisfaction respects Christ, from whom God demanded the very same punishment, as to kind of punishment, though not as to the degree nor as to the nature of the sufferings which the law denounced upon us. The remission respects believers, to whom God remits the personal, while he admits the vicarious, punishment. And thus appears the admirable reconciliation of justice and mercy—justice which executes itself upon the sin, and mercy which is exercised towards the sinner. Satisfaction is rendered to the justice of God by the Sponsor, and remission is granted to us by God” (Turretin, [Institutio Theologiae Elencticae,] Locus XIV. Quaestio 10, §[8; see below]).Archibald Alexander Hodge, The Atonement (Philadelphia, PA: Presbyterian Board of Publication, 1867), 34–37.
Hence pecuniary satisfaction differs from penal thus: (a.) In debt, the demand terminates upon the thing due. In crime, the legal demand for punishment is upon the person of the criminal. (b.) In debt, the demand is for the precise thing due—the exact quid pro quo, and nothing else. In crime, the demand is for that kind, degree and duration of suffering which the law—i. e., absolute and omniscient justice—demands in each specific case, the person suffering and the sin to be expiated both being considered. (c.) In debt, the payment of the thing due, by whomsoever it may be made, ipso facto liberates the debtor, and instantly extinguishes all the claims of the creditor, and his release of the debtor is no matter of grace. In crime, a vicarious suffering of the penalty is admissible only at the absolute discretion of the sovereign; remission is a matter of grace; the rights acquired by the vicarious endurance of penalty all accrue to the sponsor; and the claims of law upon the sinner are not ipso facto dissolved by such a satisfaction, but remission accrues to the designed beneficiaries only at such times and on such conditions as have been determined by the will of the sovereign, or agreed upon between the sovereign and the sponsor.
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Here is the section from Francis Turretin (1623–1687) that Hodge referenced above:
VIII. However, a twofold payment (noticed by jurists) must be accurately distinguished here. One “by the very act of payment sets at liberty” the guilty and the debtor, when the very thing is paid which is in the obligation, whether the payment is made by the debtor himself or by a surety in his name. Another in which “the mere act of payment is not sufficient to liberate the debtor.” For the payment is not the same thing precisely which is demanded in the obligation, but an equivalent, which although it does not by the very deed take away the obligation, yet being admitted (when it might be refused) is regarded as a satisfaction. In a pecuniary and a penal debt, this is evident. In a pecuniary debt, the payment of the debt by the very act frees the debtor (by whomsover the payment is made) because the person who pays is not attended to here, but only what is paid. Hence the creditor (payment being received) is not said to have treated the debtor with indulgence and to have forgiven the debt because he has received just as much as was due to him. But in a penal debt the case is different because the obligation regards not only things but persons (i.e., not only what is paid, but also him who pays, so that the punishment may be borne by the transgressor). For as the law demands individual personal obedience, so it also exacts a like punishment. Therefore in order that the guilty person may be freed by another’s or a vicarious satisfaction, the act of the judge and ruler ought to come in. That act is called “relaxation” (in relation to the law). In relaxation to the debtor or guilty person, it is called pardon because his personal punishment is dispensed with a vicarious punishment admitted and accepted in its place. However, because the subject under discussion (sin) does not have only a relation to debt, but also to criminality, the satisfaction is not of that kind (which by the act itself frees the debtor) unless the forbearance (epieikeia) and remission of the Judge comes in. The very thing itself which is in the obligation is not paid (viz., a personal enduring of the punishment), which the law according to strict justice (akribodikaion) demands, but only a vicarious suffering. Hence it clearly appears how well remission and satisfaction here agree with each other whatever outcry our opponents may raise against it. For in the enduring of punishment suffered by Christ, there is satisfaction, but in the admission and acceptance of a substitute, remission. The former respects Christ, from whom God demands a punishment, not numerically but specifically the same with that which we owed. But the latter respects believers, whom God frees from punishment in their own persons, while he admits a substitute. Thus we see how admirably mercy is tempered with justice—justice since it is exercised against sin and mercy exercised towards the sinner. Satisfaction is made to the justice of God by a surety and remission given to us by God.Francis Turretin, Institutes of Elenctic Theology, 3 vols., ed. James T. Dennison Jr., trans. George Musgrave Giger (Phillipsburg, NJ: P&R Publishing, 1992–1997), 2:419; Institutio Theologiae Elencticae, 14.10.8.