First, Owen takes issue with the distinction between reatus poenae [guilt related to penalty] and reatus culpae [guilt related to fault] which was commonly made by medieval theologians. He writes:
Others say that our sins were imputed unto him "quoad reatum poena" ["as to the guilt of the penalty"] but not "quoad reatum culpae" ["as to the guilt of the fault"]. But I must acknowledge that unto me this distinction gives "inanem sine mente sonum" ["an empty unmeaning sound"]. The substance of it is much insisted on by Feuardentius, Dialog. v. p. 467; and he is followed by others. That which he would prove by it is, that the Lord Christ did not present himself before the throne of God with the burden of our sins upon him, so as to answer unto the justice of God for them. Whereas, therefore, "reatus," or "guilt," may signify either "dignitatem poenae" ["deserving penalty"]," or "obligationem ad poenam" ["obligated to penalty"] as Bellarmine distinguisheth, De Amiss. Grat, lib. vii . cap. 7, with respect unto Christ the latter only is to be admitted. And the main argument he and others insist upon is this, that if our sins be imputed unto Christ, as unto the guilt of the fault, as they speak, then he must be polluted with them, and thence be denominated a sinner in every kind. And this would be true, if our sins could be communicated unto Christ by transfusion, so as to be his inherently and subjectively; but their being so only by imputation gives no countenance unto any such pretence (pp. 196-97).
Guilt, in the Scripture, is the respect of sin unto the sanction of the law, whereby the sinner becomes obnoxious unto punishment; and to be guilty is to be ὑπόδικος τῷ Θεῷ, liable unto punishment for sin from God, as the supreme lawgiver and judge of all. And so guilt, or "reatus," is well defined to be "obligatio ad poenam, propter culpam, aut admissam in se, aut imputatum, juste aut injuste" ["obligation to penalty, close to being fault, or giving access into it, or reckoning, legitimately or illegitimately"] .... And the distinction of " dignitas poenae" ["desert of penalty"] and "obligatio ad poenam" ["obligation to penalty"] is but the same thing in diverse words; for both do but express the relation of sin unto the sanction of the law: or if they may be conceived to differ, yet are they inseparable; for there can be no "obligatio ad poenam" ["obligation to penalty"] where there is not "dignitas poenae" ["desert of penalty"].
Much less is there any thing of weight in the distinction of "reatus culpae" and "reatus poenae;" for this "reatus culpae" is nothing but "dignitas poenae propter culpam." Sin hath other considerations, namely, its formal nature, as it is a transgression of the law, and the stain of filth that it brings upon the soul; but the guilt of it is nothing but its respect unto punishment from the sanction of the law. And so, indeed, "reatus culpae" is "reatus poenae," the guilt of sin is its desert of punishment. And where there is not this "reatus culpae" there can be no "poena," no punishment properly so called; for "poena" is "vindicta noxae," the revenge due to sin. So, therefore, there can be no punishment, nor "reatus poenae," the guilt of it, but where there is "reatus culpae," or sin considered with its guilt; and the "reatus poenae" that may be supposed without the guilt of sin, is nothing but that obnoxiousness unto afflictive evil on the occasion of sin which the Socinians admit with respect unto the suffering of Christ, and yet execrate his satisfaction.
...There is, therefore, no imputation of sin where there is no imputation of its guilt; for the guilt of punishment, which is not its respect unto the desert of sin, is a plain fiction, there is no such thing "in rerum natura" ["in existence"]. There is no guilt of sin, but in its relation unto punishment [emphasis mine] (p. 199).
So far so good. I think Owen is correct to say that punishment makes no sense if there is no responsibility. In other words, the attempt to separate punishment and responsibility and make Christ obligated to the former but not the latter is non-sensical because the only reason for punishment is in response to a culpable act. To punish someone who is not culpable is as Owen says, "an obnoxious affliction of evil." However, as we will see, Owen does not think Jesus is culpable in real sense but in some type of formal sense.
Now Owen presents his position:
That, therefore, which we affirm herein is, that our sins were so transferred on Christ, as that thereby he became אָשֵׁם, ὑπόδικος τῷ Θεῷ, "reus," responsible unto God, and obnoxious unto punishment in the justice of God for them. He was "alienae culpae reus," perfectly innocent in himself; but took our guilt on him, or our obnoxiousness unto punishment for sin (p. 200).
He deals with the objection that such a transfer as he proposes would result in Christ becoming an actual sinner himself.
But it is fiercely objected against what we have asserted, that if the guilt of our sins was imputed unto Christ, then was he constituted a sinner thereby; for it is the guilt of sin that makes any one to be truly a sinner. This is urged by Bellarmine, lib. ii., De Justificat, not for its own sake, but to disprove the imputation of his righteousness unto us; as it is continued by others with the same design. For saith he, "If we be made righteous, and the children of God, through the imputation of the righteousness of Christ, then was he made a sinner, 'et quod horret animus cogitare, filius diaboli;' by the imputation of the guilt of our sins or our unrighteousness unto him." ...
Nothing is more absolutely true, nothing is more sacredly or assuredly believed by us, than that nothing which Christ did or suffered, nothing that he undertook or underwent, did or could constitute him subjectively, inherently, and thereon personally, a sinner, or guilty of any sin of his own. To bear the guilt or blame of other men's faults, to be "alienae culpae reus," makes no man a sinner, unless he did unwisely or irregularly undertake it. But that Christ should admit of any thing of sin in himself, as it is absolutely inconsistent with the hypostatical union, so it would render him unmeet for all other duties of his office, Heb. vii. 25, 26 (p. 201).
So, according to Owen, even though the responsiblity for man's sin is transferred to Christ thus allowing him to be punished justly; nevertheless, Christ does not become personally and subjectively a sinner. If he did become subjectively a sinner, then of course that would overthrow the doctrine of the atonement (as well as the Trinity and the whole Christian faith). Thus, Owen is going to argue that in some way, Christ became objectively a sinner and personally culpable without becoming subjectively a sinner.
None ever dreamed of a transfusion or propagation of sin from us unto Christ, such as there was from Adam unto us. For Adam was a common person unto us, we are not so to Christ: yea, he is so to us; and the imputation of our sins unto him is a singular act of divine dispensation, which no evil consequence can ensue upon.
To imagine such an imputation of our sins unto Christ as that thereon they should cease to be our sins, and become his absolutely, is to overthrow that which is affirmed; for, on that supposition, Christ could not suffer for our sins, for they ceased to be ours antecedently unto his suffering. But the guilt of them was so transferred unto him, that through his suffering for it, it might be pardoned unto us (p. 201).
Owen seems to be saying that our sins were not removed from us and placed upon Christ because that would mean they are no longer our sins. Instead, somehow Christ joins himself to us in such a way that he shares the responsibility and penal consequences that our sins deserve (This is quite a game of mental gymnastics that Owen is playing).
First, There is in sin a transgression of the preceptive part of the law; and there is an obnoxiousness unto the punishment from the sanction of it. It is the first that gives sin its formal nature; and where that is not subjectively, no person can be constituted formally a sinner. However any one may be so denominated, as unto some certain end or purpose, yet, without this, formally a sinner none can be, whatever be imputed unto them. And where that is, no non-imputation of sin, as unto punishment, can free the person in whom it is from being formally a sinner. When Bathsheba told David that she and her son Solomon should be חַטָּאִים (sinners)[1 Kings 1:21], by having crimes laid unto their charge; and when Judah told Jacob that he would be a sinner before him always on the account of any evil that befell Benjamin (it should be imputed unto him)[Gen. 43:9]; yet neither of them could thereby be constituted a sinner formally. And, on the other hand, when Shimei desired David not to impute sin unto him, whereby he escaped present punishment, yet did not that non-imputation free him formally from being a sinner [2 Sam. 19:19-20]. Wherefore sin, under this consideration, as a transgression of the preceptive part of the law, cannot be communicated from one unto another, unless it be by the propagation of a vitiated principle or habit. But yet neither so will the personal sin of one, as inherent in him, ever come to be the personal sin of another. Adam hath upon his personal sin communicated a vicious, depraved, and corrupted nature unto all his posterity; and, besides, the guilt of his actual sin is imputed unto them, as if it had been committed by every one of them: but yet his particular personal sin neither ever did, nor ever could, become the personal sin of any one of them any otherwise than by the imputation of its guilt unto them. Wherefore our sins neither are, nor can be, so imputed unto Christ, as that they should become subjectively his, as they are a transgression of the preceptive part of the law. A physical translation or transfusion of sin is, in this case, naturally and spiritually impossible; and yet, on a supposition thereof alone do the horrid consequences mentioned depend. But the guilt of sin is an external respect of it, with regard unto the sanction of the law only. This is separable from sin; and if it were not so, no one sinner could either be pardoned or saved. It may, therefore, be made another's by imputation, and yet that other not rendered formally a sinner thereby. This was that which was imputed unto Christ, whereby he was rendered obnoxious unto the curse of the law; for it was impossible that the law should pronounce any accursed but the guilty, nor would do so, Deut xxvii. 26 (p. 202).
Owen is saying that a person can agree to be held responsible for someone else's sin and justly punished for it, without having that person's sin beome subjectively his. He uses the biblical illustrations of Bathsheba and Solomon being treated as sinners by Adonijah (1 Kings 1:21) and Judah agreeing to be held responsible if anything happens to Benjamin (Gen. 43:9).
First, in the case of Bathsheba and Solomon, if Adonijah treats them as sinners, he does so unjustly. His reason for treating them as sinners (criminals) would be because he sees them as a threat to his kingship. Second, in the case of Judah and Benjamin, Judah agrees that if anything happens to Benjamin, he will bear the blame. That makes sense. He is merely agreeing that he will protect Benjamin and that it will be his fault (subjectively) if harm comes to the boy. How these illustrations are supposed to reflect the imputation of man's sins to Jesus is beyond me. In the first case, the imputation to Bathsheba and Solomon would be unjust and in the second case, the imputation would be deserved because Judah has agreed to protect Benjamin and if he doesn't then it is subjectively his fault.
Owen then maintains that the guilt of sin is separate from the sin itself (external to it) and can be legitimately transferred to another party. He says that if this is not so, then "no one sinner could either be pardoned or saved." I fail to see how the guilt can be separated from that which caused the guilt. If the cause is removed, then so is the effect. When a person is pardoned, the guilt and the crime are not being separated. Merely the judge is agreeing to forego punishment. It is true that here a logical division between the punishment and the crime is being made but I fail to see how such a logical division can be used to claim that the punishment could be transferred to someone else.
Now Owen turns to the question of how God the Father could be angry at God the Son, which presents a host of theological problems. He writes:
But it will be said that if our sins, as to the guilt of them, were imputed unto Christ, then God must hate Christ; for he hateth the guilty.... [But]God in this matter is considered as a rector, ruler, and judge. Now, it is not required of the severest judge, that, as a judge, he should hate the guilty person, no, although he be guilty originally by inhesion, and not by imputation. As such, he hath no more to do but consider the guilt, and pronounce the sentence of punishment (p. 203).
It is true that a judge would not necessarily be angry with the criminal or hate him personally. However, in the case of God we are not talking about a party who is disconnected from the crime. Sin, according to the Bible, is an offense against God himself. It is an offense against his person. The Bible says that God is angry and full of wrath as a result of the sin. He is not presented as an objective and unaffected third party (which a judge would be).
So, while Owen has made a valiant effort to defend the PST, it seems to me that his attempt also fails. There does not seem to be anyway to justify the punishment of a person unless that person is himself responsible in some way for the crime for which the punishment is demanded. One can go through all manner of mental gymnastics to try to justify it, but at the end of the day, in my opinion, it cannot be justified.