Perhaps Vos will help (Reformed Dogmatics, 3:145-148, emphasis added):
64. To what do the opponents of particular satisfaction appeal?
Mainly to three things:
a) To the universal offer of the gospel, concerning which all agree.
b) To a series of Scriptural passages that speak of bearing the sins of the entire world and of dying for all.
c) To some passages that make mention of a death of those for whom Christ has already died.
65. How should the first of these (the universal offer of the gospel) be judged?
The objection is that the presentation of the gospel becomes a meaningless form for those who do not share in the satisfaction of Christ. If we look more closely, this general objection involves three specific objections that are usually not sharply distinguished from each other, yet are essentially different.
a) It is irreconcilable with the truthfulness of God that He would offer the gospel and the merits of Christ in it to those for whom He Himself did not intend them. God would thereby give the impression that He wills to do something that in fact He does not will.
b) On our position, ministers of the gospel, one thinks, lose the right to direct a general invitation to people.
c) The hearers of the gospel could not have confidence to rely on the suretyship and the satisfaction of Christ as long as they have not received infallible assurance that they personally belong to the elect. My confidence in believing can only rest on the fact that Christ has suffered for me. If He has not suffered for all, then I will first need to know whether I belong among those for whom He has surely suffered before I can have solid ground under me.
66. What may be said to counter the first form of this objection?
a) That the offer of the gospel is not and does not present itself to be a revelation of God’s secret will or of the will of His decree. If this were so, a contradiction would in fact exist that would detract from God’s love of truth. If the following had to be concluded: God has the firm intention to bring them personally to salvation and now it depends on A or B whether you will meet God’s purpose or disappoint Him—if this was the content of the gospel—then particular election and satisfaction would indeed be excluded. This, however, is not the content of our gospel or of the gospel of Scripture. This gospel does not express itself concerning the secret will of God but speaks of His revealed will. We understand this revealed will to include the command of God that comes to man and in each particular instance is determined by the specific relationship of man to God. Now, there is no doubt that it is the obligation of man to accept the possibility of redemption that is offered to him in the gospel, hopefully and gratefully. God can make that demand, and the gospel comes with that demand to all men.
b) That the content of the gospel, as it is presented to all without distinction, is a declaration of the will of God that A and B, etc., may personally be saved, but that still in this regard should always be considered a conditional will. It is not only that we are not dealing with God’s secret will; we are also dealing with His revealed will under a specific condition. In God there is no unsatisfied desire that has silence imposed on it by His secret will. The desire of God can be understood as follows: If you believed, then the good pleasure of God would rest upon this act of faith. This conditional character is thus always to be kept in view and kept in the foreground.
c) It is true that in the sense just described the gospel comes to many for whom Christ has not died. But at the same time it is true that these are precisely those who willfully despise the sacrifice of Christ. It may never be portrayed as if countless sinners who, eager for salvation, are seeking a ransom [and] now have to be dismissed with the explanation, “This ransom was not meant for you.” In doing that, one would be entertaining purely abstract possibilities that under the present circumstances could never become reality. The truth is that not a single instance of this kind can occur. God’s ordaining is such that all those for whom Christ in His purposing has not died are precisely the same as those who reject Christ by their unbelief. Even if satisfaction were universal, this can make no difference regarding their personal attitude toward it. In reality, they would no more share in it then than now.
d) As noted above, the gospel is intended to deprive man of every excuse and to place the magnitude of his corruption in the clearest light. That is why God does not let the gospel be proclaimed only to the elect but also brings it indiscriminately to all men (as far as it in fact reaches them and, in principle, as far as we can bring it to them). Now a sifting takes place. But now, too, sin in its inner essence comes to full flowering because it becomes unbelief in the face of grace. It belongs to God’s righteousness toward sin that it will also reveal its true character to sinners themselves. The preaching of the gospel contributes to this. This came out most clearly at the time of the appearance of the Mediator on earth in the flesh. Unbelief reacted against Him, the incarnation of grace, in the most decisive way. Naturally, aggravation of guilt is inseparable from this reaction of sin and its related development. However, no one can dispute God’s right to bring man into contact with the gospel, even if by that his judgment becomes more severe. Whoever disputes this right takes an Arminian standpoint and tacitly assumes that God owed satisfaction to man. It is the obligation of man to accept in faith everything that God presents to him. And once this obligation is present, God cannot act unjustly when He punishes the failure to meet this obligation, regardless of whether man is able to fulfill his duty.
e) Preaching has as its goal to call everyone it reaches: “If you will, take freely from the water of life” [Rev 22:17]; and “If you come, He will by no means cast you out” [John 6:37]. But it has neither the calling nor the right to make of this “willing” something other than Scripture means by it. It is not to be presented in a Methodistic manner as a sudden, uncaused act of will, a kind of experiment that can be independent of all antecedent conditions. The willing to which Scripture alludes is the willing of faith, of saving faith, the deepest act a person can do, in which his entire being shares and concurs—an act that becomes entirely impossible and incomprehensible without a prior attitude of repentance, to which it is linked and from which it in part results. Thus to will, along with putting aside all confidence in one’s self, is to have such a delight in the work of Christ and such an inner conviction of its sufficiency that we reach out for it with all the strength that is in us.
Now, the freest preaching of the gospel must make clear that such a willing is the only means by which we can become partakers of Christ. If one will not be untruthful, then the significance of faith may never disappear. And the preventive against this difficulty is a preaching of the law accompanying the preaching of the gospel. Whoever does not first bring the sinner to an awareness of his lost condition will also not elicit true faith in his heart by preaching. It is simply not true that everyone has a right to Christ who just chooses to believe at whim. The faith to which the recent methods of evangelism incite is something irrational. The faith of Scripture is a faith supernaturally wrought by the Spirit of God but still not an unnatural faith.
64. To what do the opponents of particular satisfaction appeal?
Mainly to three things:
a) To the universal offer of the gospel, concerning which all agree.
b) To a series of Scriptural passages that speak of bearing the sins of the entire world and of dying for all.
c) To some passages that make mention of a death of those for whom Christ has already died.
65. How should the first of these (the universal offer of the gospel) be judged?
The objection is that the presentation of the gospel becomes a meaningless form for those who do not share in the satisfaction of Christ. If we look more closely, this general objection involves three specific objections that are usually not sharply distinguished from each other, yet are essentially different.
a) It is irreconcilable with the truthfulness of God that He would offer the gospel and the merits of Christ in it to those for whom He Himself did not intend them. God would thereby give the impression that He wills to do something that in fact He does not will.
b) On our position, ministers of the gospel, one thinks, lose the right to direct a general invitation to people.
c) The hearers of the gospel could not have confidence to rely on the suretyship and the satisfaction of Christ as long as they have not received infallible assurance that they personally belong to the elect. My confidence in believing can only rest on the fact that Christ has suffered for me. If He has not suffered for all, then I will first need to know whether I belong among those for whom He has surely suffered before I can have solid ground under me.
66. What may be said to counter the first form of this objection?
a) That the offer of the gospel is not and does not present itself to be a revelation of God’s secret will or of the will of His decree. If this were so, a contradiction would in fact exist that would detract from God’s love of truth. If the following had to be concluded: God has the firm intention to bring them personally to salvation and now it depends on A or B whether you will meet God’s purpose or disappoint Him—if this was the content of the gospel—then particular election and satisfaction would indeed be excluded. This, however, is not the content of our gospel or of the gospel of Scripture. This gospel does not express itself concerning the secret will of God but speaks of His revealed will. We understand this revealed will to include the command of God that comes to man and in each particular instance is determined by the specific relationship of man to God. Now, there is no doubt that it is the obligation of man to accept the possibility of redemption that is offered to him in the gospel, hopefully and gratefully. God can make that demand, and the gospel comes with that demand to all men.
b) That the content of the gospel, as it is presented to all without distinction, is a declaration of the will of God that A and B, etc., may personally be saved, but that still in this regard should always be considered a conditional will. It is not only that we are not dealing with God’s secret will; we are also dealing with His revealed will under a specific condition. In God there is no unsatisfied desire that has silence imposed on it by His secret will. The desire of God can be understood as follows: If you believed, then the good pleasure of God would rest upon this act of faith. This conditional character is thus always to be kept in view and kept in the foreground.
c) It is true that in the sense just described the gospel comes to many for whom Christ has not died. But at the same time it is true that these are precisely those who willfully despise the sacrifice of Christ. It may never be portrayed as if countless sinners who, eager for salvation, are seeking a ransom [and] now have to be dismissed with the explanation, “This ransom was not meant for you.” In doing that, one would be entertaining purely abstract possibilities that under the present circumstances could never become reality. The truth is that not a single instance of this kind can occur. God’s ordaining is such that all those for whom Christ in His purposing has not died are precisely the same as those who reject Christ by their unbelief. Even if satisfaction were universal, this can make no difference regarding their personal attitude toward it. In reality, they would no more share in it then than now.
d) As noted above, the gospel is intended to deprive man of every excuse and to place the magnitude of his corruption in the clearest light. That is why God does not let the gospel be proclaimed only to the elect but also brings it indiscriminately to all men (as far as it in fact reaches them and, in principle, as far as we can bring it to them). Now a sifting takes place. But now, too, sin in its inner essence comes to full flowering because it becomes unbelief in the face of grace. It belongs to God’s righteousness toward sin that it will also reveal its true character to sinners themselves. The preaching of the gospel contributes to this. This came out most clearly at the time of the appearance of the Mediator on earth in the flesh. Unbelief reacted against Him, the incarnation of grace, in the most decisive way. Naturally, aggravation of guilt is inseparable from this reaction of sin and its related development. However, no one can dispute God’s right to bring man into contact with the gospel, even if by that his judgment becomes more severe. Whoever disputes this right takes an Arminian standpoint and tacitly assumes that God owed satisfaction to man. It is the obligation of man to accept in faith everything that God presents to him. And once this obligation is present, God cannot act unjustly when He punishes the failure to meet this obligation, regardless of whether man is able to fulfill his duty.
e) Preaching has as its goal to call everyone it reaches: “If you will, take freely from the water of life” [Rev 22:17]; and “If you come, He will by no means cast you out” [John 6:37]. But it has neither the calling nor the right to make of this “willing” something other than Scripture means by it. It is not to be presented in a Methodistic manner as a sudden, uncaused act of will, a kind of experiment that can be independent of all antecedent conditions. The willing to which Scripture alludes is the willing of faith, of saving faith, the deepest act a person can do, in which his entire being shares and concurs—an act that becomes entirely impossible and incomprehensible without a prior attitude of repentance, to which it is linked and from which it in part results. Thus to will, along with putting aside all confidence in one’s self, is to have such a delight in the work of Christ and such an inner conviction of its sufficiency that we reach out for it with all the strength that is in us.
Now, the freest preaching of the gospel must make clear that such a willing is the only means by which we can become partakers of Christ. If one will not be untruthful, then the significance of faith may never disappear. And the preventive against this difficulty is a preaching of the law accompanying the preaching of the gospel. Whoever does not first bring the sinner to an awareness of his lost condition will also not elicit true faith in his heart by preaching. It is simply not true that everyone has a right to Christ who just chooses to believe at whim. The faith to which the recent methods of evangelism incite is something irrational. The faith of Scripture is a faith supernaturally wrought by the Spirit of God but still not an unnatural faith.