We have the designation of "all men" so all of humanity, all of the world is included. Within this group of humanity there are two categories, the believers and the unbelievers. This whole chapter thus far is speaking of these two categories. A little further, and two more categories are in view, false doctrine, which is concerned with the ascetic (what to eat, whether to marry) contrasted with true doctrine. Verses 1-3 are about men who depart from the faith and teach doctrines of devils, contrasted by the faithful brethren in verse 6. These unbelievers are people in Timothy's midst, even some in the church. He is preaching to both categories of people, who are hearing now two different doctrines.
Now, let's look at the immediate context:
1Ti 4:7-11 But refuse profane and old wives' fables, and exercise thyself rather unto godliness. (8) For bodily exercise profiteth little: but godliness is profitable unto all things, having promise of the life that now is, and of that which is to come. (9) This is a faithful saying and worthy of all acceptation. (10) For therefore we both labour and suffer reproach, because we trust in the living God, who is the Saviour of all men, specially of those that believe. (11) These things command and teach.Here we also find two categories. The life that is now, and the life which is to come. Thus far in the argument, Paul as set several items against each other.
Pure Doctrine False Doctrine
Bodily Exercise Godliness
Life that is now Life that is to come
Category A is concerned with truth, believers, and godliness and eternal life. Category B, which is being fought against, is to do with the earthly. These differences in worldliness and living for today contrasted by truth and living for eternity. Now we get to verse 10 in which Paul does connects this verse with the context of the previous chapter by saying "For, therefore". This is a worthy saying and because it is a worthy saying and to this end, we suffer for the true gospel and fight for true doctrine for the believers as we exercise ourselves to godliness. That is why Paul labors and suffers. "Because we trust in the living God, who is the Saviour of all men, specially of those that believe."
Again we have two categories of people, those who believe (Group A) and those who don't (Group B). Now, even my Arminian friends must admit that Jesus cannot be the same kind of Saviour to both categories. Jesus did not eternally save the rich man in Luke 16 who lifted his eyes up in Hell and save Lazarus in Paradise. Then it says especially of those that believe. Paul says that Jesus is the σωτήρ (sōtēr) the deliverer, sustainer, preserver of all men. God gives life to both believers and unbelievers. Those false brethren who teach sensuality and the doctrines of devils (1 Timothy 4:1) do so with their Lord's air, God's food "which God created" (1 Timothy 4:3) in the bodies God gave them (1 Timothy 4:8) . But Jesus is the eternal Saviour, not only of the body, but of the soul to those that believe. Following the flow of the chapter, I think this is clear that Paul is tying up his final thoughts on these two groups of people by showing two different categories of "salvation" or deliverance. Those that are profaning the truth of the gospel and promoting a sensuality are doing so by taking God's creation (I Timothy 6:13; Acts 17:28).
Jesus is the Saviour of all men because there is no other name under Heaven whereby we must be saved. He is the sustainer and protector and keeper of the whole universe. Paul uses the same idea in Acts 13:23 "Of this man's seed hath God according to his promise raised unto Israel a Saviour, Jesus..." Did God raise unto Israel a Saviour? Yes He did, but why is Paul preaching to the Gentiles? Because God had blinded the eyes of the Jews (Acts 28:25-28; Romans 9-11).
When I present the gospel, I compel men to come to Christ, and if they do in faith, Jesus will save them. Jesus is the only hope for humanity. He is the only Saviour of men. But especially the Saviour of those who believe, because Christ saves them.
Remember what Paul is doing here. He is instructing Timothy to preach the truth even when people don't want to hear it. Preach the truth when there are heretics in his number who are trying to lead people away. Preach the truth when church members are trying to split the church by preaching about fables and old wives tales. Preach the gospel, Timothy. Labor in the gospel, suffer for the gospel and keep these faithful sayings. Why? Because the truth that Timothy declares is the true gospel, that Jesus is the Saviour. He is the Saviour in an experimental way for those that believe. Christ died for them and saves them. Keep preaching to believers and unbelievers alike. Preach the gospel to the lost; preach it to the saved.