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Cunningham:

The most important question, however, connected with this department of the subject, is not whether what Christ suffered was a punishment, or properly penal, but whether it was the penalty which the law had denounced against sin, and to which sinners, therefore, are justly exposed. Now, upon this point, there are three different modes of statement which have been adopted and defended by different classes of divines, who all concur in maintaining the doctrine of the atonement against the Socinians. Some contend that the only accurate and exact way of expressing and embodying the doctrine of Scripture upon the subject, is to say, that Christ suffered the very penalty the same thing viewed legally and judicially which the law had denounced against sin, and which we had incurred by transgression. Others think that the full import of the Scripture doctrine is expressed, and that the general scope and spirit of its statements upon this subject are more accurately conveyed, by maintaining that Christ did not suffer the very penalty, the same penalty which sinners had incurred, but that he suffered what was a full equivalent, or an adequate compensation for it, that His suffering was virtually as much as men deserved, though not the same. While others, again, object to both these statements, and think that the whole of what Scripture teaches upon this point is embodied in the position, that what Christ suffered was a substitute for the penalty which we had incurred.

Dr Owen zealously contends for the first of these positions, and attaches much importance to the distinction between Christ having suffered or paid the same penalty as we had incurred, and His having suffered or paid only an equivalent, or as much as we had deserved; or, as he expresses it, between His suffering or paying the idem and the tantundem. He lays down the doctrine which he maintained upon this point against Grotius and Baxter in this way: “That the punishment which our Savior underwent was the same that the law required of us; God relaxing His law as to the persons suffering, but not as to the penalty suffered.”¹ There are, however, divines of the strictest orthodoxy, and of the highest eminence, who have not attached the same importance to the distinction between the idem and the tantundem, and who have thought that the true import of the Scripture doctrine upon the subject is most correctly brought out by saying, that what Christ suffered was a full equivalent, or an adequate compensation, for the penalty men had incurred. Mastricht, for instance, whose system of theology is eminently distinguished for its ability, clearness, and accuracy, formally argues against the death of Christ being solutio “proprie sic dicta, qua id praieise prsestatur, quod est in obligatione”² and contends that “reatus tollitur satisfactione, qua non idem precise, quod est in obligatione, creditori pnustatur; sed tantundem, seu equivalens.” And Turretine³ seems, upon the whole, to agree with him, or rather, to conjoin the two ideas together, as being both true, though in somewhat different respects, and as not essentially differing from each other. He has not, indeed, so far as I remember, formally discussed the precise question about the idem and the tantundem, on which Owen and Maastricht have taken opposite sides; but in discussing the Socinian argument, that Christ did not make a true and real satisfaction for our sins, because lie did not in fact pay what was due to God by us, and especially because lie suffered only temporal, while we had incurred eternal, death, he meets the major proposition by asserting that there might be a true and proper satisfaction, though the same thing was not paid which was due, provided it was a full equivalent in weight and value, “etsi non idem, modo tantundem habeatur, sufficit;” while lie meets also the minor proposition of the Socinian argument, by asserting that Christ did pay what was due by us; the same, not of course in its adjuncts and circumstances, but in its substance,–His suffering, though temporary in duration, being, because of the infinite dignity of His person, properly infinite in weight or value as a penal infliction, and thus substantially identical, in the eye of justice and law, with the eternal punishment which sinners had deserved.

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Clifford:

Consistent with his commercialism, [John] Owen insisted that God’s justice was only satisfied by Christ’s payment of the same quantitative penalty or debt owed by the elect to God on account of their sins–the solutio ejusdem.³¹ Baxter (following Grotius at the only point where he could do so with any real justification) argued that, in virtue of the differences (in detail and duration) between Christ’s sufferings and the actual sufferings of the lost, Christ only paid a qualitative equivalent–the solutio tantidem.³² Since the penalty of the law threatens eternal punishment to impenitent offenders, Christ clearly did not suffer the identical punishment, for his resurrection terminated his banishment.³³ God therefore relaxed the law with regard both to the persons who should suffer (which Owen obviously agreed with)³⁴34 and to the penalty suffered. Clearly, there was not the ‘sameness’ Owen pleads for.

Although a strict particularist like William Cunningham denied the importance of this issue,³⁵ Owen saw clearly that his doctrine of limited atonement hung upon the ‘sameness’ between Christ’s sufferings and those deserved by the elect. However, he could only argue his case with the aid of Aristotle’s metaphysics. His very language betrays him: ‘When I say the same, I mean essentially the same in weight and pressure, though not in all the accidents of duration and the like; for it was impossible that he should be detained by death.’³⁶ He therefore resorts to Aristotle’s dubious essence-accidents theory³⁷ to prove his point. In Baxter’s view even this statement ‘yieldeth the cause,’³⁸ but after learning of Baxter’s criticism Owen granted that ‘There is a sameness in Christ’s sufferings with that in the obligation in respect of essence, and equivalency in respect of attendencies.’³⁹

But Owen’s use of this philosophical distinction simply obscures the fact that there is a real difference between Christ’s temporary sufferings and the eternal sufferings deserved by the elect. He cannot establish his concept of ‘sameness’ without philosophical double-talk. If he is prepared to grant an equivalence in either respect, he is forced to concede that there is only a similarity, and not a sameness at all. Clearly, Aristotle’s metaphysical formula⁴⁰ only serves to permit unreal and meaningless distinctions. Had Baxter been as nimble as David Hume⁴¹ at this point, he would have exploded Owen’s case; however, Aristotle had a few more years to reign in scholastic circles. In view of later criticism of ‘the philosopher’ it is possible to see how Owen’s questionable commercialism falls to the ground, and with it the classical doctrine of limited atonement. In other words, he cannot demonstrate that the sufferings of Christ were commensurate with the deserved sufferings of the elect without the doubtful support of Aristotle. He fails, therefore, to prove that the atonement is necessarily limited by its nature. Indeed, his thesis requires that the sinner be eternally saved at the ‘expense’ of the Saviour’s eternal loss.

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Woods:

6. Was the death of Christ a full equivalent for the punishment of sinners? and was it a legal substitute?

The exact meaning of equivalent is, equal in value or worth, of equal avail, or of equal influence. The question then is, whether the death of Christ is in a moral view of equal avail, or equal in value, with the punishment of sinners. To this we have already attended. Christ’s death answered the ends of punishment, so that the honor of the Lawgiver, the authority of the law and the welfare of the moral world are as well secured, as they could have been by the merited punishment of transgressors. And this is the same as to say, the death of Christ is, in a moral view, of equal value with their punishment, or is an equivalent for it. And it is a full equivalent, because it fully answers the ends of punishment, answers them as perfectly as they could have been answered by the infliction of punishment according to the threat of the law. It might be shown, that the death of Christ is more than an equivalent for the punishment of sinners, as it doubtless answers the ends of a just punishment in a higher degree than could have been answered by the punishment itself, besides accomplishing other objects of everlasting importance, which the punishment of sinners could never have accomplished; so that, in the final result, the vicarious death of Christ will be the cause of vast gain to the universe.

But is the death of Christ a legal substitute, and a legal equivalent? The answer to this must vary according to the sense we affix to the word legal. If by a legal substitute or equivalent, be meant that which is provided by law, or that which is exactly conformed to the letter of the law; then the death of Christ is not legal. For the law itself provides for nothing in case of transgression, but the punishment of transgressors. Its precepts and its sanctions, taken literally, relate only to those who are the proper subjects of law. But if by a legal substitute is meant a substitute which supports the principles and answers the ends of law; then the death of Christ is a legal substitute, and a legal equivalent. In its efficacy to accomplish the great purposes of a moral government, it is fully equal, not to say superior, to the direct execution of the penalty of the law.

Leonard Woods, “Lectures,” in The Works of Leonard Woods, (Boston: John P. Jewett & Company, 1851), 478-479.  [Italics original and underlining mine.]

Shedd:

1) Accepted by the law and lawgiver. The primal source of law has no power to abolish penalty any more than to abolish law, but it has full power to substitute penalty. In case of a substitution, however, it must be a strict equivalent, and not a fictitious or nominal one. It would contravene the attribute of justice, instead of satisfying it, should God, for instance, by an arbitrary act of will, substitute the sacrifice of bulls and goats for the penalty due to man; or if he should offset any finite oblation against the infinite demerit of moral evil. The inquiry whether the satisfaction of justice by Christ’s atonement was a strict and literal one, has a practical and not merely theoretical importance. A guilt-smitten conscience is exceedingly timorous, and hence, if there be room for doubting the strict adequacy of the judicial provision that has been made for satisfying the claims of law, a perfect peace, the “peace of God,” is impossible. Hence the doctrine of a plenary satisfaction by an infinite substitute is the only one that ministers to evangelical repose. The dispute upon this point has sometimes, at least, resulted from a confusion of ideas and terms. Strict equivalency has been confounded with identity. The assertion that Christ’s death is a literal equivalent for the punishment due to mankind, has been supposed to be the same as the assertion, that it is identical with it; and a punishment identical with that due to man would involve remorse, and endless duration. But identity of punishment is ruled out by the principle of substitution or vicariousness, a principle that is conceded by all who hold the doctrine of atonement. The penalty endured by Christ, therefore, must be a substituted, and not an identical one. And the only question that remains is, whether that which is to be substituted shall be of a strictly equal value with that, the place of which it takes, or whether it may be of an inferior value, and it must be one or the other. When a loan of one hundred dollars in silver is repaid by one hundred dollars in gold, there is a substitution of one metal for another. It is not an identical payment; for this would require the return of the very identical hundred pieces of silver, the ipsissima pecunia, that had been loaned. But it is a strictly and literally equivalent payment. All claims arc cancelled by it. In like manner, when the suffering and death of God incarnate is substituted for that of the creature, the satisfaction rendered to law is strictly plenary, though not identical with that which is exacted from the transgressor. It contains the clement of infinitude, which is the clement of value in the case, with even greater precision than the satisfaction of the creature does; because it is the suffering of a strictly infinite Person in a finite time, while the latter is only the suffering of a finite person in an endless but not strictly infinite time. A strictly infinite duration would be without beginning, as well as without end. William G.T. Shedd, Discourses and Essays, (Andover: Warren F. Draper, 1862), 307-308.  [Underlining mine.]

2) In saying that the suffering substituted for that of the actual criminal must be of equal value, it is not said that it must be identical suffering. A substituted penalty cannot be an identical penalty, because identical means the same in every respect. Identity is inconsistent with any exchange whatever. To speak of substituting an identical penalty is a contradiction in terms. The identical punishment required by the moral law is personal punishment, involving personal remorse; and remorse can be experienced only by the actual criminal. If, in commercial law, a substituted payment could be prevented, a pecuniary debtor would be compelled to make an identical payment. In this case, he must pay in person and wholly from his own resources. Furthermore, he could not pay silver for gold, but gold for gold; and not only this, but he must pay back exactly the same pieces of gold, the ipsissima pecunia, which he had received. Identical penalty implies sameness without a difference in any particular. Not only is the quantity the same, but the quality is the same. But substituted penalty implies sameness with a difference in some particular. And in the case before us, that of Christ’s satisfaction, the difference is in the quality: the quantity being unchanged. The vicarious suffering of Christ is of equal value with that of all mankind, but is not the same in kind.

Equivalency, not identity, is the characteristic, therefore, of vicarious penalty. The exchange, implied in the term substitution, is of quality not of quantity. One kind of judicial suffering; that is, suffering endured for the purpose of satisfying justice; is substituted for another kind. Christ’s sufferings were of a different nature or quality from those of a lost man. But there was no difference in quantity, or value. A less degree of suffering was not exchanged for a greater degree. The sufferings of the mediator were equal in amount and worth to those whose place they took. Vicarious penalty then is the substitution of an equal quantity, but a different quality of suffering. The mediator suffers differently from the lost world of sinners, but he suffers equally.

Equivalency satisfies justice as completely as identity. One hundred dollars in gold extinguishes a debt of one hundred dollars as completely as does one hundred dollars in silver. If the sufferings of the mediator between God and man are of equal value with those of the world of mankind, they are as complete a satisfaction of justice as the eternal death of mankind would be, although they do not, in their nature or quality, involve any of that sense of personal wickedness and remorse of conscience which enters into the punishment of a lost man. They get their value from the nature of the God-man, and it is the value of what is substituted which justice looks at.

The following extract from Samuel Hopkins (System of Doctrine, Works, I. 321) enforces this truth. “The mediator did not suffer precisely the same kind of pain, in all respects, which the sinner suffers when the curse is executed on him. He did not suffer that particular kind of pain which is the necessary attendant or natural consequence of being a sinner, and which none but the sinner can suffer. But this is only a circumstance of the punishment of sin, and not of the essence of it. The whole penalty of the law may be suffered, and the evil may be as much and as great, without suffering that particular sort of pain. Therefore, Christ, though without sin, might suffer the whole penalty; that is, as much and as great evil as the law denounces against transgression.” William G.T. Shedd, Dogmatic Theology, (Grand Rapids, Michigan: Zondervan, 1971),, 2:454-456. [Underlining mine.]