In blue are quotes from A.A. Hodge’s, The Atonement. My comments are in black.
"The entire Lutheran Church agrees with the Reformed as to the nature of the Atonement. They hold that Christ by his active and passive obedience fully satisfied all the demands of the law upon those in whose place he acted, and that he purchased for them the operations of the Holy Spirit, and all the fruits thereof; * and yet they hold that Christ died in this sense indiscriminately in behalf of all men. There is no doubt that the great mass of learned and able Lutheran theologians have explicitly held both of these views. This is certainly a practical proof that both sides of their doctrine may be intelligently held as true in the same mind at the same time. And yet it is no less plain that the several positions they adopt as to sin, human ability, divine grace, foreknowledge, predestination, redemption, &c., are obviously incapable of being reduced even to the appearance of logical consistency. They teach that Christ purchased faith and repentance for all for whom he died. If any man repents and believes, they deny his co-operation with grace previous or in order to his regeneration, and they attribute the result solely to the grace of God given for Christ's sake. If any man does not repent and believe, they deny that Christ has done any less for him, and attribute the result solely to his own sin. But the question must be answered, Who makes the difference? If both have from Adam the same absolute inability, and if both have as the purchase of Christ the same grace, what is the differentiating factor in the case? What determines the infidelity of the one and the faith of the other?
The Arminian grants to all men sufficient ability to co-operate with grace, and hence consistently makes the free self-determination of the sinner's own will the seat of difference between the believer and non-believer. The Calvinist, denying the ability to co-operate with grace alike to all men, consistently makes a sovereign discriminating grace the seat of the difference between them. The Lutheran holds that all men are alike impotent; that all men have alike the same grace; that the cause of faith, wherever it exists, is wholly to be attributed to grace, and the cause of unbelief to sin; yet, while there is such difference between faith and unbelief, there is no difference among men either as to sin or grace. But we answer, If it be grace alone that makes one believe, then the other has not the same grace or he also would believe. And if Christ purchased spiritual graces for all those for whom he died, he could not have died for those who fail to receive the grace" (A.A. Hodge, The Atonement, pp. 367-368; italics Hodge's).
* Formula Concordiae, Part I., chap. ii., and Part II., chap. ii.
When A.A. Hodge says "if Christ purchased spiritual graces for all those for whom he died, he could not have died for those who fail to receive the grace," he is not denying that Christ died for the non-elect in a different sense that does not purchase this grace. For Hodge believes that Christ secured other so-called non-saving "graces" that come short of salvation. Note Hodge's self-righteous blasphemy:
"Remember what we have over and over again affirmed, (a) Christ did
literally and absolutely die for all men, in the sense of securing for
all a lengthened respite and many temporal benefits, moral as well as
physical; (b) his Atonement was sufficient for
all; (c) exactly adapted to the needs of each; (d) it is offered
indiscriminately to all; hence, as far as God's preceptive will is concerned, the Atonement
is universal. It is to be preached to all, and to be accepted by all.
It is for all as far as determining the duty of all and laying
obligations upon all. And practically it makes salvation objectively
available to all upon the condition of faith. God's decretive will or design in making the Atonement is a very different matter" (A.A. Hodge, The Atonement, p. 427; italics Hodge's).
A.A. Hodge believed that Jesus Christ "did literally and absolutely die for"
the non-elect in order to secure non-saving "benefits." At least one implication of Hodge's scheme is that securing of a lengthened respite for
the non-elect to
establish their own righteousness is a "moral
benefit." Does God the Holy Spirit through the Apostle Paul indicate
that
establishing one's own righteousness is in "some sense" a moral
benefit
(Romans 10:1-4)?