Predestination is a belief held by Calvinists; according to Calvinists, God's decision is by definition just, though incomprehensible to man. In their view, the doctrine is a necessary consequence of the definition of God: a being of infallibility, infinite power, and unrestricted knowledge. God cannot be ignorant of any future action of any human being including the acts of repentence or denial, but God's choices cannot be restricted in any way by that knowledge. Most importantly, his decisions are intrinsically right--they define rightness. The Calvinist viewpoint is expressed in Jonathan Edwards's famous sermon "Sinners in the Hands of an Angry God." An earlier and more methodical presentation in English is the Westminster Confession of Faith (1646).
Calvinists divide on the issue of predestination into infralapsarians and supralapsarians. Infralapsarians believe that God chose his elect considering the situation after the Fall, while supralapsarians believe that the Fall was ordained by God's decree of election. In infralapsarianism, election is God's response to the Fall, while in supralapsarianism the Fall is part of God's plan for election.
Arminians, on the other hand, hold that God does not so much choose, as infalliably predict, who will believe and, persevering, be saved. Although God knows from the beginning of the world who will go where, the choice is still with the individual.
Lutherans also believe in predestination, but they differ from Calvinists. Lutherans believe in single predestination, in which God only chooses who to save, while those he does not choose are damned not by his intent but merely by default. Calvinists believe in what is called double predestination, that is that God chooses both who to save and who to damn. Calvinists believe that double predestination is the necessary deductive logical position from any form of single predestination that does not include universal salvation.