1) 1. To impute is to reckon to, or to lay to one’s account. So far as the meaning of the word is concerned, it makes no difference whether the thing imputed be sin or righteousness; whether it is our own personally, or the sin or righteousness of another.
2. To impute sin, in Scriptural and theological language, is to impute the guilt of sin. And by guilt is meant not criminality or moral ill-desert, or demerit, much less moral pollution, but the judicial obligation to satisfy justice. Hence the evil consequent on the imputation is not an arbitrary infliction; not merely a misfortune or calamity; not a chastisement in the proper sense of that word, but a punishment, i.e., an evil inflicted in execution of the penalty of law and for the satisfaction of justice.
3. A third remark in elucidation of what is meant by the imputation of Adam’s sin is, that by all theologians, Reformed and Lutheran, it is admitted, that in the imputation of Adam’s sin to us, of our sins to Christ, and of Christ’s righteousness to believers, the nature of imputation is the same, so that the one case illustrates the others. When it is said that our sins were imputed to Christ, or that He bore our sins, it is not meant that he actually committed our sins, or that He was morally criminal on account of them, or that the demerit of them rested upon Him. All that is meant is that He assumed, in the language of the older theologians, "our law-place." He undertook to answer the demands of justice for the sins of men, or, as it is expressed by the Apostle, to be made a curse for them. In like manner, when it is said that the righteousness of Christ is imputed to believers, it does not mean that they wrought out that righteousness, that they were the agents of the acts of Christ in obeying the law; nor that the merit of his righteousness is their personal merit; nor that it constitutes their moral character; it simply means that his righteousness, having been wrought out by Christ for the benefit of his people, in their name, by Him as their representative, it is laid to their account, so that God can be just in justifying the ungodly. Much of the difficulty on this subject arises from the ambiguity of language. The words righteous and unrighteous have two distinct meanings. Sometimes they express moral character. A righteous man is an upright or good man. At other times, these words do not express moral character, but simply relation to justice. In this sense a righteous man is one with regard to whom the demands of justice are satisfied. He may be personally unrighteous (or ungodly) and legally righteous. If this were not so, no sinner could be saved. There is not a believer on earth who does not feel and acknowledge himself to be personally unrighteous, ill-deserving, meriting the wrath and curse of God. Nevertheless he rejoices in the assurance that the infinitely meritorious righteousness of Christ, his full atonement for all sin, constitutes Him legally, not morally, righteous in the sight of divine justice. When, therefore, God pronounces the unrighteous to be righteous, He does not declare them to be what they are not. He simply declares that their debt to justice has been paid by another. And when it is said that the sin of Adam is imputed to his posterity, it is not meant that they committed his sin, or were the agents of his act, nor is it meant that they are morally criminal for his transgression; that it is for them the ground of remorse and self-reproach; but simply that in virtue of the union between him and his descendants, his sin is the judicial ground of the condemnation of his race, precisely as the righteousness of Christ is the judicial ground of the justification of his people. So much for the statement of the question. Charles Hodge, Systematic Theology (Wm. B. Eerdmans: Michigan: 1981), 2:194-195.
2) The idea of the transfer of guilt or of vicarious punishment lies at the foundation of all the expiatory offerings under the Old Testament, and of the great atonement under the new dispensation. To bear sin, is in Scriptural language to bear the penalty of sin. The victim bore the sin of the offerer. Hands were imposed upon the head of the animal about to be slaughtered, to express the transfer of guilt. That animal must be free from all defect or blemish to make it the more apparent that its blood was shed not for its own deficiencies but for the sin of another. All this was symbolical and typical. There could be no real transfer of guilt made to an irrational animal, and no real atonement made by its blood. But these services were significant. They were intended to teach these great truths: (1.) That the penalty of sin was death. (2.) That sin could not be pardoned without an atonement. (3.) That atonement consists in vicarious punishment. The innocent takes the place of the guilty and bears the penalty in his stead. This is the idea attached to expiatory offerings in all ages and among all nations. This is the idea inculcated in every part of the Bible. And this is what the Scriptures teach concerning the atonement of Christ. He bore our sins; He was made a curse for us; He suffered the penalty of the law in our stead. All this proceeds on the ground that the sins of one man can be justly, on some adequate ground, imputed to another. In justification the same radical idea is included. Justification is not a subjective change in the moral state of the sinner; it is not mere pardon; it is not simply pardon and restoration to favour, as when a rebel is forgiven and restored to the enjoyment of his civil rights. It is a declaration that the demands of justice have been satisfied. It proceeds on the assumption that the righteousness which the law requires belongs either personally and inherently, or by imputation, to the person who is justified, or declared to be just. There is a logical connection, therefore, between the denial of the imputation of Adam’s sin, and the denial of the Scriptural doctrines of atonement and justification. The objections urged against the former bear equally against the latter doctrines. And it is a matter of history that hose who reject the one, reject also the others. Charles Hodge, Systematic Theology (Wm. B. Eerdmans: Michigan: 1981), 2:201.
3) To bear sin is to bear the guilt and punishment of sin. Charles Hodge, Systematic Theology (Wm. B. Eerdmans: Michigan: 1981), 2:504.
4) It has already been shown that to "bear sin" never means to sanctify, to effect a moral change by removing the power and pollution of sin, but uniformly, in the sacrificial language of the Bible, to bear the guilt or penalty for sin. Charles Hodge, Systematic Theology (Wm. B. Eerdmans: Michigan: 1981), 2:508.
[Note: The word “transfer” can be misleading or confusing. It is important to note that the guilt of sin is not literally “transferred” (to take from one place and moved to another) from the sinner to Christ. Christ is treated as though he were guilty, thereby bearing our guilt, but all the while we remain actually sinners and actually guilty, bearing our guilt in our own person until the point and time of justification and pardon. For example, by way of analogy, Adam remained guilty, even after his “original” sin is imputed to his descendants.]