First of all, then, I urge that supplications, prayers, intercessions, and thanksgivings be made for all people, 2 for kings and all who are in high positions, that we may lead a peaceful and quiet life, godly and dignified in every way. 3 This is good, and it is pleasing in the sight of God our Savior, 4 who desires all people to be saved and to come to the knowledge of the truth. 5 For there is one God, and there is one mediator between God and men, the man Christ Jesus, 6 who gave himself as a ransom for all, which is the testimony given at the proper time. (1 Timothy 2:1-6, ESV)
(For a better and a more recent defense of 1Tim 2:4 see here.)
This is one of the “Arminian Big Three” which you will get almost in every conversation about Calvinism in real life or online. Usually verses 3-4 are just quoted to make the case that God wants to save every single individual. The question is, does “all” in context really mean “every single individual in the world”? Or is this talking about God’s desire not His sovereign decree?
Will of Desire interpretation
There are some people who understand this passage and other passages like 2 Pet 3:9 to refer to God’s will of desire. God’s will of desire being, God’s desire that people should not murder, lie, steal, commit adultery or have other gods before Him (Ex 20), but He doesn’t decree that it should be done so. It is also called His will of precept.
So God’s will of desire refers to the things that God has not decreed in His sovereign plan before the foundation of the world, yet desires. In this interpretation, God would desire that all be saved, but He has not decreed that all should be saved, because He wants to show the full measure of His glory (Rom 9:22-24). I don’t find this interpretation compelling and I believe the following interpretation is more compelling.
The “all kinds of people” interpretation
The major Reformed interpretation takes the position that the word “all” in this context means “all kinds of people,” not every single individual, why do we say that? Because there are times in Scripture when “all” is used in the sense of “every single individual in the world”, but there are times which it isn’t used like that, but limited according to the context. Let’s look at a few verses, shall we? The portion we’re going to look at is in Titus 2. Here we see that Paul is telling Timothy to teach “sound doctrine.” Then we see him list types/groups of people:
2. Older men are to be sober-minded…
3. Older women likewise…
4. so train the young women to love their husbands and children
6. …urge the younger men
11. For the grace of God has appeared bringing salvation for all people,
12. training us to renounce ungodliness…
13. waiting for our blessed hope, the appearing of the glory of our great God and Savior Jesus Christ,
14. who gave himself for us to redeem us from all lawlessness and to purify for himself a people for his own possession who are zealous for good works.
We see that Paul in verse 11 says that salvation has been brought for all people, but considering the context we can safely say that it means “all kinds of people,” since in the previous verses he was talking about kinds of people (men, women, slaves, etc..). We can reasonably say that what Paul is saying through “all people” is “all kinds of people,” (as we understand that in our individualistic society) just as those kinds whom he mentioned in the passing verses. Further, verse 14 makes it clear that God has redeemed “us” and that Jesus has purified for Himself a people, not all people, but a people.
What does this have to do with 1 Tim 2:4, anyway? Well, we see in verse 2 kinds of people (“kings and all who are in high positions”) being mentioned. What Paul was asking Timothy to do is pray for “all” people. How are we to understand the “all” here? Did Paul mean that Timothy should pray for every single person in the world? Surely we don’t think that’s the case, but we see that after Paul says that Timothy should pray for “all” people we see in verse 2 that Paul specifies, limits, clarifies, narrows his use of the word “all,” by saying that Timothy should pray “for kings and all who are in high position.” So what Paul is saying to Timothy is this: Timothy, do not only pray for your brethren, who are those that are despised in the world, who are persecuted, who are hated, but don’t forget Jesus’ commandment to love our enemies. So, Timothy also pray for your persecutors that they may come to the knowledge of God, who desires to save all kinds of people, so that we may lead a peaceful life. Then it follows logically that if we accept the contextual meaning of “all” to mean “all kinds of” then the “all” in verse 6 also means that Jesus was a ransom for all kinds of people. Revelation 5:9 says that Jesus with His blood has ransomed a people for God from every tribe, language, people and nation; thus, Jesus has ransomed every kind of people, kings and servants, free and slaves, male and female, Jew and Gentile. Please note in Revelation 5:9, it says that our Glorious Lord ransomed with his blood a people for God from every tribe, tongue, people and nation, a specific people, not the tribes, tongues, peoples and nations.
And let us not forget the beauty of verse 5 where we are told that Jesus is the only mediator between men and God. A mediator is “one that mediates, especially one that reconciles differences between disputants.” Through Christ we have been reconciled to God (Col 1:21-22) and He is standing before the Father, as the Son interceding for us (Rom 8:26, 34; Heb 7:25), He is interceding for a specific people, not every single individual in the world. This also brings the picture of Christ as High Priest, as seen in the book of Hebrews, He is the one pleading for His sheep to the Father.
Let’s see what the Word of God says of the Lord’s intercessory work. For whom does Christ intercede?
Heb 7:23-27 The former priests were many in number, because they were prevented by death from continuing in office, 24 but he holds his priesthood permanently, because he continues forever. 25 Consequently, he is able to save to the uttermost those who draw near to God through him, since he always lives to make intercession for them. 26 For it was indeed fitting that we should have such a high priest, holy, innocent, unstained, separated from sinners, and exalted above the heavens. 27 He has no need, like those high priests, to offer sacrifices daily, first for his own sins and then for those of the people, since he did this once for all when he offered up himself.
Heb 9:24-28 For Christ has entered, not into holy places made with hands, which are copies of the true things, but into heaven itself, now to appear in the presence of God on our behalf. 25 Nor was it to offer himself repeatedly, as the high priest enters the holy places every year with blood not his own, 26 for then he would have had to suffer repeatedly since the foundation of the world. But as it is, he has appeared once for all at the end of the ages to put away sin by the sacrifice of himself. 27 And just as it is appointed for man to die once, and after that comes judgment, 28 so Christ, having been offered once to bear the sins of many, will appear a second time, not to deal with sin but to save those who are eagerly waiting for him.
In the book of Hebrews we see Christ’s High Priestly work. We see also that Christ intercessory work is rooted in His cross-work. He saves to the uttermost those who draw near to God, but then the question arises: Who draws near to God? The answer from Jesus’ lips is recorded in John 6:44 – No one can come to me unless the Father who sent me draws him. And I will raise him up on the last day. And on their behalf does He make His intercessory work. Imagine the Risen Lord of Glory interceding for someone for whom He did not died and for a one whom the Father had no chosen, He would fail miserably, but it’s impossible for the Lord of Glory to be rejected by the Father or for God to fail.
All Kinds of People
The ESV Study Bible explains: 
1 Tim. 2:4 Evangelistic prayer for all people is rooted in the fact that God desires all people to be saved. It appears that Paul is countering an exclusivist tendency in the false teachers or at least their downplaying of the importance of evangelizing the Gentiles (along with their emphasis on the Jewish law). This statement figures prominently in theological disagreements over the extent of the atonement. It cannot be read as suggesting that everyone will be saved (universalism) because the rest of the letter makes it clear that some will not be saved (4:1; 5:24; 6:10; cf. Matt. 25:30, 41, 46; Rev. 14:9–11). Does that mean God desires something (all people being saved) that he cannot fulfill? Both Arminian and Calvinist theologians respond tha...