Some people have issues with the idea of a penal substitution and satisfaction, with regard to Christ's death on behalf of his people. There are actually many challenges that are posed against this teaching, but one particular argument goes something like this: If Christ fully met the demands of justice in his death, then salvation is not a matter of free forgiveness from God, but rather it is God acting under legal obligation to save, since nothing is really forgiven, since full punishment was meted out, and all the debt of sin fully paid for. I was reading some of John Owen again, and this was one of the objections raised against him, as a result of his "The Death of Death in the Death of Christ". This is because Owen uses language like
idem (= "same") regarding Christ's satisfaction, meaning that Christ suffered the very same as that deserved by those in whose place he died. Some (eg Richard Baxter) objected that this leaves no room for forgiveness and free pardon, since pardon implies a relaxation of justice. Basically Owen says that there are two aspects to the penal requirements of justice, firstly, the particular penalty demanded by the law, and secondly, the particular person to be punished under the law. In the case of God's forgiveness in Christ, justice is not relaxed with regard to the penalty, but it is relaxed with regard to the person being punished, and therefore there is still free pardon involved.
Here is Owen's own summary, from a response to Baxter:
The freedom, then, of pardon hath not its foundation in any defect of the merit or satisfaction of Christ, but in three other things:-
(1.) The will of God freely appointing the satisfaction of Christ, John iii. 16; Rom. v. 8; 1 John iv. 9.
(2.) In a gracious acceptation of that decreed satisfaction in our steads; so many, no more.
(3.) In a free application of the death of Christ unto us. Remission, then, excludes not a full satisfaction by the solution of the very thing in the obligation, but only the solution or satisfaction of him to whom pardon and remission is granted.
[from Of the Death of Christ, p446 in Works, Vol. 10]
