The ESV Study Bible (2008) discusses I Timothy 2:4:
Evangelistic prayer for all people is noted 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 that God “desires” something more than universal salvation. Arminians hold that God’s greater desire is to preserve genuine human freedom (which is necessary for genuine love) and therefore he must allow that some may choose to reject his offer of salvation. Calvinists hold that God’s greater desire is to display the full range of his glory (Rom. 9:22-23), which results in election depending upon the freedom of his mercy and not upon human choice (Rom. 9:15-18). However one understands the extent of the atonement, this passage clearly teaches the free and universal offer of the gospel to every single human being; “desires” shows that this offer is a bona fide expression of God’s good will. Come to the knowledge of the truth highlights the cognitive aspect of conversion, i.e., individuals must come to understand key truths in order to be converted. “The truth” occurs often in the Pastorals as a synonym for the gospel (cf. I Tim. 3:15; 4:3; 2 Tim. 2:15, 18, 25; 3:7, 8; 4:4; Titus 1:1, 14).