1 Timothy 4:10
"For it is for this we labor and strive, because we have fixed our hope on the living God, who is the Savior of all men, especially of believers." - 1 Timothy 4:10
This verse has had many interpretations. Here are a few of them:
(1) The idea that "God is the Savior of all men" means that all who have ever lived will be saved. This of course is contrary to all sound doctrine. If this was true, the rest of the verse would have no meaning when it says "especially of believers."
(2) God wants to save everyone but His desire is many times thwarted by the obsinate free will of man (the Arminian view). Note though that the passage does not say He wants to save, but that He actually saves: He is actually the Savior (in some sense) of all men. Also, God's will is never frustrated (Isaiah 46:10).
(3) God is able to save all men, but though all can be saved, only believers actually are. Again, this is not what the text says.
(4) God is the Savior of all men (in one sense) and especially of those who believe (in another sense).
I believe this is the correct interpretation....
As we study the terms "salvation" and "Savior" we find many nuances - many different ways God saves. The most important aspect of salvation is to be "saved" from the wrath of God (Romans 5:6-9), but salvation also includes the idea of rescue from enemy attack (Psalm 18:3); preservation (Matt. 8:25); physical healing (Matt. 9:22; James 5:15) etc. God "saved" not only Paul but everyone else on board ship with him in Acts 27:22, 31, 44. There are numerous ways that "salvation" takes place, but that's a complete Bible study all in itself.
When we study the word Savior (Greek: soter) in the LXX version (Greek translation of the Old Testament) we see the word used in a way that is far less grandiose than that which we generally think of the word. One example is Judge Othniel is called a Soter (Savior) or deliverer because he delivered the children of Israel from the hands of the king of Mesopotamia (Jud. 3:9). 2 Kings 13:5 talks of God giving Israel a "Savior" so that they were delivered from the hands of the Syrians. The judges of Israel were "saviors" as Nehemiah 9:27 states, "in the time of their suffering they cried out to you and you heard them from heaven, and according to your great mercies you gave them saviors who saved them from the hand of their enemies."(see also Psalm 36:6)
A great deal more could be said to substantiate this idea of a savior, but I think the above would make the point. God provides food (Psalm 104:27, 28) sunlight and rainfall (Matt. 5:45), as well as life and breath and all things (Acts 17:25), for "in Him we live and move and have our being" (Acts 17:28). God preserves, delivers and supplies the needs of all who live in this world, and it is in this sense that He extends grace to them, saving them from destruction every day they live.
God is also gracious in allowing many to hear the proclamation of the Gospel.
All of these mercies are refered to as "common grace." It is common only in the sense that every living person gets it. This grace should actually amaze us because God is under no obligation whatsoever to give it to anyone. God sustains the lives of His sworn enemies, often for many decades! However, as wonderful as it is, it is only a temporal grace because all unregenerate people eventually die and will face the judgment (Heb. 9:27).
I believe then that 1 Timothy 4:10 teaches that we have our hope set on the living God, who is the Savior (Soter - preserver, sustainer, deliverer) of all people (showing mercy to all each and every day they live), especially of those who believe (who receive full salvation from His wrath and everlasting life).