Hypothetical universalism
Hypothetical universalism is the belief that Christ died in some sense for every person, but his death effected salvation only for those who were predestined for salvation. In the history of Reformed theology, there have been several examples of hypothetical universalist systems, all of which are considered errant by traditional Calvinism. Amyraldism is one of these, but hypothetical universalism as a whole is sometimes erroneously equated with it. Hypothetical universalism is believed to be outside the bounds of the Reformed tradition. For example, Canon VI states: "Wherefore, we can not agree with the opinion of those who teach : l) that God, moved by philanthropy, or a kind of special love for the fallen of the human race, did, in a kind of conditioned willing, first moving of pity, as they call it, or inefficacious desire, determine the salvation of all, conditionally, i.e., if they would believe, 2) that he appointed Christ Mediator for all and each of the fallen; and 3) that, at length, certain ones whom he regarded, not simply as sinners in the first Adam, but as redeemed in the second Adam, he elected, that is, he determined graciously to bestow on these, in time, the  saving gift of faith; and in this sole act election properly so-called is complete. For these and all other similar teachings are in no way insignificant deviations from the proper teaching concerning divine election; because the Scriptures do not extend unto all and each God’s purpose of showing mercy to man, but restrict it to the elect alone, the reprobate being excluded even by name, as Esau, whom God hated with an eternal hatred (Rom 9:11). The same Holy Scriptures testify that the counsel and will of God do not change, but stand immovable, and God in the  heavens does whatsoever he will (Ps 115:3; Isa 47:10); for God is infinitely removed from all that human imperfection which characterizes inefficacious affections and desires, rashness repentance and change of purpose. The appointment, also, of Christ, as Mediator, equally with the salvation of those who were given to him for a possession and an inheritance that can not be taken away, proceeds from one and the same election, and does not form the basis of election. —J. H. Heidegger, Francis Turretin, Helvetic Consensus Formula (1675) History. English hypothetical universalism was advanced by John Preston, John Davenant, and James Ussher. This  scheme teaches that God ineffectually decrees that all men be saved by deeming an intent for the atonement for all men, but because God knows that some men will not have faith he makes an effectual decree to save those whom he predestines to salvation. The primary thought in hypothetical universalism is that Christ died for the world in a universal sense (Paul Helm, Hypothetical Universalism). Amyraldian hypothetical universalism, associated with John Cameron and Moïse Amyraut, differs by asserting that God decrees the election of some to salvation logically subsequent to the decree to provide salvation through Christ. This represents  a change to the traditional infralapsarian scheme of the logical order of God's decrees, where God's decree to save some was conceived of as logically preceding his decree to provide salvation. It is the same order as that advocated by Jacobus Arminius and his followers, though Amyraldians differed from Arminians by asserting that there are two phases to God's decree to save some. First, God decrees the salvation of all through Christ, but this decree is ineffectual because some people do not have faith. God then decrees that some will have faith and be saved. Hypothetical universalism