There are many strange ideas in the religious world regarding salvation. Some contend that all people will be saved (Universalism). That notion is contradicted by dozens of passages (see Matthew 7:13,14). 

Others, like the Calvinists, argue that before the world was created God chose some, the elect, to be saved, and others He predetermined to be lost. That notion is plainly refuted by 1 Timothy 2:4. God “would have all men to be saved.” Note also verse 6 which affirms that Jesus gave Himself a ransom for all (which conflicts with the Calvinistic theory of limited atonement, i.e., that Christ died only for the elect). Underline this phrase and note: contradicts Calvinistic doctrine of predestination. See also verse 6.

Additionally, there are yet others (an even larger number probably) who subscribe to the notion that God will save all sincere people, whether they ever know and obey the truth or not. Such a concept is not in harmony with the divine teaching here set forth.

G.B. Winer, in his Grammar of New Testament Greek, has an interesting discussion of this passage. He notes that Paul first states the “general ultimate end,” that God desires salvation for all men. Then, the apostle gives the “means toward attaining the former,” which is — coming to a knowledge of the truth (p. 692).

This is in perfect harmony with John 8:32 — you shall know the truth, and the truth shall set you free. One does not obtain redemption through a knowledge of error, but by means of knowing the truth. 

How does this relate, for example, to the idea (advocated by some) that one may go through the process of being immersed, and yet never even understand the truth regarding the purpose of the ordinance, and God will honor the “obedience” anyhow? Does that notion really harmonize with the principle of this passage? Underscore the phrase “knowledge of the truth,” and marginally note: Knowledge of truth essential to valid obedience.