Moïse Amyraut (1596 – 1664) was a Huguenot, as my own ancestors were as well, and this name means French Calvinist. Moses Amyraut was of the school of Saumer, and this man is interesting because of his modified Calvinism, that allowed for Hypothetical Universalism and hence became the eponymous founder of Amyrauldism.
A favorite theologian of mine, B.B. Warfield, consider Amyrauldism an "a logically inconsistent form of Calvinism and therefore an unstable form of Calvinism." I found Warfield's harsh dismissal of Amyrauldism provocative, regardless of whether I agree or not with Warfield, what he wrote in his "Plan of Salvation" against Moses Amyraut is famous.
I've had renewed interested in Amyrauldism, after learning that Jürgen Moltmann had studied him for his doctorate, and I've had great interest in the universalistic forms of Calvinism due to the influence of Karl Barth.
However, it's important to know that Calvinistic forms of Universalism are completely different in their arguments than what is popularly known by the term, "Universalism", and this popular term is not what I'm describing here.
B.B. Warfield's assessment of Amyrauldism in "The Plan of Salvation"
Moses Amyraut, who first formulated in the Reformed Churches the Post- redemptionist scheme, of which Pajonism is a debased form. Thus the school of Saumur has the bad eminence of having originated, and furnished from the names of its professors the current designations of, the two most reduced forms of Calvinism, Amyraldianism or Hypothetical Universalism as it is otherwise called, and Pajonism, or Congruism as it is designated according to its nature.
We have thus had brought before us four forms of Calvinism; and these, as we believe, exhaust the list of possible general types: Supralapsarianism, Sub- (or Infra-)lapsarianism, Post-redemptionism (otherwise called Amyraldianism, or Hypothetical Universalism), and Pajonism (otherwise called Congruism). These are all forms of Calvinism, because they give validity to the principle of particularism as ruling the divine dealings with man in the matter of salvation; and, as we have seen, the mark of Calvinism is particularism. If now, particularism were not only the mark of Calvinism but also the substance of Calvinism, all four of these types of Calvinism, preserving as they all do the principle of particularism, might claim to be not only alike Calvinistic, but equally Calvinistic, and might even demand to be arranged in the order of excellence according to the place accorded by each in its construction to the principle of particularism and the emphasis placed on it. Particularism, however, though the distinguishing mark of Calvinism, by which it may be identified as over against the other conceptions of the plan of salvation, in comparison with which we have brought it, does not constitute its substance; and indeed, although strenuously affirmed by Calvinism, is not affirmed by it altogether and soley for its own sake. The most consistent embodiment of the principle of particularism is not therefore necessarily the best form of Calvinism; and the bare affirmation of the principle of particularism though it may constitute one so far a Calvinist, does not necessarily constitute one a good Calvinist. No one can be a Calvinist who does not give validity to the principle of particularism in God's operations looking to the salvation of man; but the principle of particularism must not be permitted, as Pharaoh's lean kine devoured all the fat cattle of Egypt, to swallow up all else that is rich and succulent and good in Calvinism, nor can the bare affirmation of particularism be accepted as an adequate Calvinism.
Post-redemptionism, therefore (although it is a recognizable form of Calvinism, because it gives real validity to the principle of particularism), is not therefore necessarily a good form of Calvinism, an acceptable form of Calvinism, or even a tenable form of Calvinism. For one thing, it is a logically inconsistent form of Calvinism and therefore an unstable form of Calvinism. For another and far more important thing, it turns away from the substitutive atonement, which is as precious to the Calvinist as is his particularism, and for the safeguarding of which, indeed, much of his zeal for particularism is due. I say, Post-redemptionism is logically inconsistent Calvinism. For, how is it possible to contend that God gave his Son to die for all men, alike and equally; and at the same time to declare that when he gave his Son to die, he already fully intended that his death should not avail for all men alike and equally, but only for some which he would select (which, that is, because he is God and there is no subsequence of time in his decrees, he had already selected) to be its beneficiaries? But as much as God is God, who knows all things which he intends from the beginning and all at once, and intends all things which he intends from the beginning and all at once, it is impossible to contend that God intends the gift of his Son for all men alike and equally and at the same time intends that it shall not actually save all but only a select body which he himself provides for it. The schematization of the order of decrees presented by the Amyraldians, in a word, necessarily implies a chronological relation of precedence and subsequence among the decrees, the assumption of which abolishes God, and this can be escaped only by altering the nature of the atonement. And therefore the nature of the atonement is altered by them, and Christianity is wounded at its very heart.
The Amyraldians "point with pride" to the purity of their confession of the doctrine of election, and wish to focus attention upon it as constituting them good Calvinists. But the real hinge of their system turns on their altered doctrine of the atonement, and here they strike at the very heart of Calvinism. A conditional substitution being an absurdity, because the condition is no condition to God, if you grant him even so much as the poor attribute of foreknowledge, they necessarily turn away from a substitutive atonement altogether. Christ did not die in the sinner's stead, it seems, to bear his penalties and purchase for him eternal life; he died rather to make the salvation of sinners possible, to open the way of salvation to sinners, to remove all the obstacles in the way of salvation of sinners. But what obstacle stands in the way of the salvation of sinners, except just their sin? And if this obstacle (their sin) is removed, are they not saved? Some other obstacles must be invented, therefore, which Christ may be said to have removed (since he cannot be said to have removed the obstacle of sin) that some function may be left to him and some kind of effect be attributed to his sacrificial death. He did not remove the obstacle of sin, for then all those for whom he died must be saved, and he cannot be allowed to have saved anyone. He removed, then, let us say, all that prevented God from saving men, except sin; and so he prepared the way for God to step in and with safety to his moral government to save men. The atonement lays no foundation for this saving of men: it merely opens the way for God safely to save them on other grounds.
We are now fairly on the basis of the Governmental Theory of the Atonement; and this is in very truth the highest form of doctrine of atonement to which we can on these premises attain. In other words, all the substance of the atonement is evaporated, that it may be given a universal reference. And, indeed, we may at once recognize it as an unavoidable effect of universalizing the atonement that it is by that very act eviscerated. If it does nothing for any man that it does not do for all men why, then, it is obvious that it saves no man; for clearly not all men are saved. The things that we have to choose between, are an atonement of high value, or an atonement of wide extension. The two cannot go together. And this is the real objection of Calvinism to this compromise scheme which presents itself as an improvement on its system: it universalizes the atonement at the cost of its intrinsic value, and Calvinism demands a really substitutive atonement which actually saves. And as a really substitutive atonement which actually saves cannot be universal because obviously all men are not saved, in the interests of the integrity of the atonement it insists that particularism has entered into the saving process prior, in the order of thought, to the atonement.
~ B.B. Warfield, "The Plan of Salvation", Chapter V. Calvinism