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Who will have all men to be saved, and to come unto the knowledge of the truth.
Arminian view: You can't get much clearer than this. God wills for all men to be saved. But clearly not all are, so there must be an element of freedom involved.
Calvinist view: This obviously can't be universal, for in 2:1 Paul tells Timothy to give prayers and supplications for "all men." Did he go down a list of men one at a time and pray for them? That he specifies kings and such next (v.2) shows he does not mean absolutely all men. "All men" means all kinds of men.
The Calvinist attempt to use this verse nestles around the hyperbolic implication that to pray for "all men" one must pray for them one at a time. This is a non-objection. In this day and age men belonged to classes or groups by nation or by other criteria; the idea of praying for people one at a time (under a rubric of "all men") would never have occurred to a collectivist-minded writer. Beyond this do we not even today pray, for example, for every man on a ship in the Navy, as a collective, to be safe in their journey? Rather, prayer for "all men" implies the human race as a collective. What for? That depends on needs common to all men, but it's not hard to pray for such broad things as God's will being done for all men, or for the general peace, prosperity, and well-being (in terms of agape love) of all men, and so on. This would not require knowing every individual and their needs.
A secondary Calvinist objection states that if this means all men individually, then Christ, who is the mediator between God and men (2:5), then this implies that Christ "fails" as mediator when they choose not to follow Christ. This view fails on the same point as the idea that God's grace "fails" if someone does not accept it. A mediator does not "fail" if someone refuses to come to the negotiation table, and no honor would be detracted from, nor failure attributed to, a mediator in such a situation.