What differentiates Neo-Calvinism in Kuyper's line from historic Calvinism? The presumptivist system stands out most prominently, but it is simply the visible appearance of a life-and-world view that often parades itself as the Christian life-and-world view, but which may with propriety be named Hyper-Covenantism, a synonym for Kuyper-Calvinism or Neo-Calvinism. As the name suggests, Hyper-Covenantism is an exaggeration of the historic Calvinist doctrine of God's covenant with man, a classical formulation of which is to be found in the Westminster Confession, chapter VII, with detailed expositions to be found in the writings of John Ball, Samuel Rutherford, Thomas Boston and Herman Witsius, among many others.(16) The aberrations of Cocceius may be regarded as a precursor of Hyper-Covenantism. What is Hyper-Covenantism? Just as Augustine has recently been charged with responsibility for inventing Pelagianism, which was only latent in Pelagius' own teaching,(17) the risk may be run of inventing a new aberration from orthodoxy in formulating explicitly a set of theses, sometimes openly avowed by Neo-Calvinists and sometimes presupposed more or less unconsciously, but pervading Neo-Calvinist doctrine and practice. Kuyper himself is most certainly not to be charged with propounding or approving every one of the following Hyper-Covenantist theses, although the fundamental and central theses were contributed by him and the others have been developed, whether validly or invalidly, from Kuyper's outlook. Seven theses may be formulated and expounded.

For the most part Kuyper followed the Reformed fathers in matters of doctrine, commonly opting for high Calvinism where the fathers were not unanimous, as on the questions of supralapsarianism and the ordo salutis.(14) Only on the question of the authority of the magistrate with respect to the first table of the law did Kuyper avowedly reject the historic Reformed view, charging the fathers and the Confession with unfaithfulness to the genuine Reformed conception.(15) Yet in propounding the thesis that the children of the covenant are to be presumed to be regenerated and dealt with as such, Kuyper adapted a view possessing the tenuous support of a highly controversial disputation by Voetius, a tempting view in connection with the controversy over paedobaptism, but one alien to the line of Calvinism known to the English-speaking world and, in Dutch Calvinism, foreign to Comrie no less than to à Brakel. Whatever varying opinions had been expressed by Reformed divines as to the condition of infants of Christian parents, a system of doctrine and practice based on presumptivism is the invention of Kuyper-Calvinists, who alone have made bold to incorporate it, as well as disputable theses on common grace, among the binding doctrinal articles of the church.

As to the historic position of Princeton Presbyterianism, the following statement by Archibald Alexander is decisive: "The education of children should proceed on the principle that they are in an unregenerate state, until evidences of piety clearly appear, in which case they should be sedulously cherished and nurtured. . . . Although the grace of God may be communicated to a human soul, at any period of its existence, in this world, yet the fact manifestly is, that very few are renewed before the exercise of reason commences; and not many in early childhood."(30) The view of Voetius and Kuyper involves the anomaly of a time gap between regeneration and effectual calling, particularly appalling in the case of the apostle Paul, of whom, on the basis of Gal. 1:15, the younger Kuyper is reported to have preached as an example of a regenerated blasphemer.(31)