1 Timothy 2:1
1I exhort therefore, first of all, that petitions, prayers, intercessions, and givings of thanks be made for all men,
“First of all” makes intercession the church’s opening work, not an afterthought. Four kinds of prayer—need, desire, advocacy, thanks—are urged for all people, not for a favored circle. Wesley hears thanksgiving “for all men, in the full sense of the word,” because God “willeth all men to be saved” and Christ is “the Mediator of all.”
Arminian readers take the command at face value: if God sincerely wills the salvation of every person, the church must actually pray for every person. Intercession is partnership with that gracious will. Narrowing “all” into a private list would shrink both the prayer meeting and the heart of God our Savior.
Paul speaks of public prayers offered not only for believers but for all mankind. Calvin notes the perverse thought, “We have nothing to do with strangers,” and hears Paul meet it: include all, and do not limit petitions to the body of the church already gathered.
Reformed readers still pray for all, because God commands it and because the gospel is to be preached without fencing off ranks or nations. The wideness of intercession matches promiscuous proclamation. It does not, on this reading, require that every individual be elect; it requires that no class of neighbor be treated as beyond prayer.
Key contrast Both take the command to pray for “all people” as wide. Arminians detect a sincere universal saving will behind that wideness; Reformed readers hear prayer matching a gospel preached to all kinds of people, without concluding that every individual is elect.