The Spirit's work in Regeneration to Glorify God

"Inspiration was an act of the Spirit on a special group of people, enabling them to perform a task no others were permitted to do. There is another act of the Spirit which applies to a large group irrespective of their individual personalities. In fact, there are two. As such they can be discussed before itemizing more particular examples. The first of these is regeneration. At the beginning of Kuyper's gigantic volume, he takes pains to say that the chief purpose of the Spirit is not to regenerate sinners, but to glorify God. 'The chief thing is not that the elect be fully saved, but that God be justified in all His works . . .' (p. 9). Undoubtedly this is so; but anyone whether the Spirit or a human being, or even an animal, can glorify God in several ways. For that matter the inanimate planets and the sands of the sea glorify God. Hence what attracts our attention now is not so much the Spirit's ultimate purpose as it is one chosen activity for accomplishing it." - Gordon H. Clark, The Holy Spirit, Pg. 31

Abraham Kuyper's belief

"God Himself makes man religious by means of the sensus divinitatis, i.e., the sense of the Divine, which He causes to strike the chords on the harp of his soul. A sound of need interrupts the pure harmony of this divine melody, but only in consequence of sin. In its original form, in its natural condition, religion is exclusively a sentiment of admiration and adoration which elevates and unites, not a feeling of dependence which severs and depresses. Just as the anthem of the Seraphim around the throne is one uninterrupted cry of 'Holy, - Holy, - Holy!,' so also the religion of man upon this earth should consist in one echoing of God's glory, as our Creator and Inspirer. The starting-point of departure and the point of arrival, the fountain, from which the waters flow, and at the same time, the ocean into which they finally return. To be irreligious is to forsake the highest aim of our existence, and on the other hand to covet no other existence than for the sake of God, to long for nothing but for the will of God, and to be wholly absorbed in the glory of the name of the Lord, such is the pith and kernel of all true religion. 'Hallowed be thy Name. Thy kingdom come. Thy Will be done,' is the threefold petition, which gives utterance to all true religion. Our watchword must be, - 'seek first the kingdom of God,' and after that, think of your own need. First stands the confession of the absolute sovereignty of the Triune God; for of Him through Him, and unto Him are all things. And therefore our prayer remains the deepest expression of all religious life. This is the fundamental conception of religion as maintained by Calvinism, and hitherto, no one has ever found a higher conception." - Abraham Kuyper in Lectures on Calvinism

Calvin vs. Luther starting point?

"Now I wish to be second to none in my praise of Luther's heroic initiative. In his heart, rather than in the heart of Calvin, was the bitter conflict fought which led to the world-historic breach. Luther can be interpreted without Calvin, but not Calvin without Luther. To a great extent Calvin entered upon the harvest of what the hero of Wittenberg had sown in the clearest insight into the reformatory principle, worked it out most fully, and applied it most broadly, history... points to the Thinker of Geneva and not to the Hero of Wittenberg. Luther as well as Calvin contended for a direct fellowship with God, but Luther took it up from its subjective, anthropological side, and not from its objective, cosmological side as Calvin did. Luther's starting-point was the special-soteriological principle of a justifying faith; while Calvin's extending far wider, lay in the general cosmological principle of the sovereignty of God. As a natural result of this, Luther also continued to consider the Church as the representative and authoritative 'teacher,' standing between God and the believer, while Calvin was the first to seek the Church in the believers themselves.” Abraham Kuyper – Lectures On Calvinism

Before the foundations of the world God chose some men for salvation and some men for eternal destruction

"In the same way Calvinism has derived from its fundamental relation to God a peculiar interpretation of man's relation to man, and it is this only true relation which since the 16th century has ennobled social life. If Calvinism places our entire human life immediately before God, then it follows that all men or women, rich or poor, weak or strong, dull or talented, as creatures of God, and as lost sinners, have no claim whatsoever to lord over one another, and that we stand... as equals before God, and consequently equal as man to man. Hence we cannot recognize any distinction among men, save such as has been imposed by God Himself, in that He gave one authority over the other, or enriched one with more talents than the other, in order that the man of more talents should serve the man with less, and in him serve his God. Hence Calvinism condemns not merely all open slavery and systems of caste, but also all covert slavery of woman and of the poor; it is opposed to all hierarchy among men; it tolerates no aristocracy save such as it able, either in person or in family, by the grace of GOd, to exhibit superiority of character or talent, and to show that it does not claim this superiority for self-aggrandizement or ambitious price, but for the sake of spending it in the service of God. So Calvinism was bound to find its utterance in the democratic interpretation of life; to proclaim the liberty of nations; and not to rest until both politically and socially every man, simply because he is man, should be recognized, respected and dealt with as a creature created after the Divine likeness." - Abraham Kuyper, Lectures on Calvinism

The question is what is the Intentions of God

"Just because the crier - if we may use this figure for comparison - travels up and down the streets and alleys of the village to invite all to the auction sale, does this cancel out the condition that he really is inviting only: (1) those who desire to buy something; (2) those who have money to buy; and (3) those who have opportunity to go t the auction? By this illustration we can clearly see that by sating all these exceptions, one distorts the nature of the dispute, does not at all advance a solution, and unnecessarily prevents a meeting of the minds.
The only way by which you achieve clarity is to inquire about the intention of God and proceed directly to what thoughts filled the heart of Christ when he, the Son of God, died." - Abraham Kuyper, Particular Grace

Either one is a universalist or a particularist

"The two ways of conceiving the issue stand in sharp contrast before us now. On the one hand, there are the universalists, or advocates of general grace, who maintain this position: When Jesus died on the cross, it was God's will and Christ's purpose to bring about the kind of atonement that, if need be, was sufficient for all men. In addition, they contend that this atonement, offered in Jesus' name to all men, would be a blessing to as many as, according to Jesus' intention, desired to accept this salvation, while the atonement would remain unused only by as many as did not believe, even though it was so appointed for them and even though Jesus had intended and expected that they would believe.
On the other hand, there are the particularists, or advocates  of special grace, who teach this: The church must preach to all creatures that there is atonement obtained through Christ's death for everyone who believes, has believed, or will believe; that is, because all believers are elect, atonement is only for the elect, not according to the [foreseen] result, but according to Christ's purpose and God's counsel. Particularists also teach concerning the application of this salvation that it is not concerned with possibly but as yet unconverted persons; on the contrary, it has to do with a persons whom the Lord loves with an eternal love, even before they were born, and whom he calls by name." - Abraham Kuyper, Particular Grace

God's intention is always the question

"In God's holy garden, we must not want to plant trees upside down - with their roots facing the sky and their branches in the soil! To turn things upside down from the very beginning is a perversion of the whole way. Let the cause, the fountainhead, the root, remain in God, and let nothing else ever be seen in us than the resultant effect, the stream that flows from its source, and the branch with its bud and blossom. There is no election, therefore, on the basis of a foreseen faith, but there is faith as the result of an antecedent election.
And if it is now established that Christ was God, and hence as God knew whom he had chosen and who would come to saving faith as a the result of that election, then it is self-evident that our Mediator, who never desired to bring any other atonement than for those who would believe, intended the provision of the atonement solely and exclusively for his own.
That is why, when discussing whether Christ has died for all individuals or for all the elect, we can never employ the distinction between God's will and God's decree, as the Hessian and Bremen delegates advocated it at Dordt, since this distinction exclusively applies when considering our intention, but never may be given validity when there is a discussion of God's intention.
When Joseph was about to be sold by his brothers, it was God's revealed will to Judah and Reuben, 'Do not sell your brother!' Yet it was God's hidden decree that 'Joseph will be sold by his brothers.'
Accordingly, when we are talking about our activity, about what we are doing or what we intend, oh then most definitely, not only may we, but we must continually reckon with this golden maxim of evangelical wisdom: 'Blind as regards the outcome, but fully obedient to the commandment!'
On the contrary, when, as here, we are discussing not what we but what Christ intended, and not what we but what God willed, then everyone senses that it is the height of absurdity to dare to distinguish in God himself between what he wills and, nevertheless, does not will!" - Abraham Kuyper, Particular Grace

God's uncoerced choice

As God decreed before the foundations of the world in eternity past to glorify Himself - not because there was a need of God but because the glory of God is instrinsic to who He is and His nature so that what He does and how He reveals Himself cannot be seperated from His divine being. That God chose within Himself to Glorify Himself (Father, Son, and Holy Spirit and to make known His divine attributes) can only be but apart from any considerations of the creature or any other created thing. What God does is completely free and sovereign and is by His own free uncoercive choice and pleasure. What does this mean other than what happens in this world is already predetermined by the sovereign will of the triune God. That Christ was chosen to be the mediator of a particular persons and that His work was intended to bring about the sole redemption of those persons is based upon the choice of the whole person of who the mediator would be. That the relationship between the Head (Christ) and the Body (the Church was so natural that nothing was added to it or had to be touched upon later. That the Holy Spirit would honor the head by applying the redeming work of Christ to the Body of Christ.
Now If I might further say that God had also reprobated certians ones for the very purpose of bringout His divine pleasure in the making known who are the elect, and who is the Christ and His work.

Read: Abraham Kuyper, Herman Hoeksema, and Geerhardus Vos for more information and clarification

Not all without exception but all without disctinction

The idea is that Christ death was a death that went out towards different kinds of people not just towards certain kinds. As was the case for the old dispensation where God chose a people for Himself to further out His redemptive purposes. Jesus was born of the Jewish religion not of the Greek system where the belief was pagan. Jesus was a Jew. Salvation was from the jews scripture says. To the Jew first then to the Greek. The Jews were God's chosen people in that the Messiah came from them (Romans 9:1-5). Of course this does not mean that under the old testament dispensation that there were no pagans who were brought from Darkness to Light. However, they had to become Jewish. An offshoot of this is that the Christians in Acts were wondering whether to make Gentile Christians to first become Jews so that they could become Christians. But the conclusion made was no for salvation is by Grace Alone which is the point of the letter to the Galatians.
Of course the wall of seclusion was not knocked down until after Jesus accomplished his mission. The seclusion was that only the Jews were God's people and anyone outside of Jewish community were considered filthy.
The statement made in John 3:16 was astounding for the purpose - John writes was to show that God qualitative love was not just toward the Jewish audience but extended out toward the rest of the world of the gentile. So when scripture makes reference that Christ died for all people it should really be read as all kinds of people. The atonement was in fact particular in intent in that God purposed that Christ should die for the salvation of His elect those whom He had Chose since before the foundation of the world who were spread abroad throughout the world.
The good news is that now the gospel is for all kinds of people. it is not just for the wealthy or the poor people but all people are to repent of sin and trust in Christ for righteousness sake. 1 Timothy 2 speaks of this truth. So today where one might be born in a Christian home the temptation might be that because He is of the Christian family he is saved. This is not true at all. Scripture says for all have sin and fall short of the glory of God. Therefore all must find there refuge in Adam number two. The idea is that as we preach the gospel to all people only those whom the Father has chosen to come to faith in His Son Jesus Christ will come by the regenerating work of the Holy Spirit who works so graciously and free (Ephesian 3:14-19).
Now this by no means says that Christ died for all men without exception that all men everywhere universally have been bought with a price by the blood of Christ for certianly He died for only His elect people whom God chose most freely in eternity past. Only God's elect will come to faith at the hearing of the gospel at the particular point that God decreed. The reprobate will be hardened by God's good providence.

A good book to read on this subject is Abraham Kuyper's Particular Grace