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 (I Timothy 4:10).
Herman Hoeksema
a. Saviour in the text means Preserver, as the Synod of 1924 evidently understood the word and the Dutch translation renders it. In that case, the text does not speak of grace at all, but merely of God’s providential preservation of all men, the wicked as well as the righteous, the reprobate as well as the elect. The text then means: God is a Preserver of all men, for He gives to all men their existence and life and all things necessary for the sustenance of their being; but especially of believers, for them and them only He preserves in His grace, leading them to eternal life.
Or:
b. Saviour has the usually meaning of Deliver from sin and death. In that case the text means: God is a Saviour of all men—more specifically speaking, of believers from among all men.
But whichever interpretation is preferred, the text does not support the theory of a common grace of God toward and upon the godly and the ungodly, the elect and the reprobate.
(Herman Hoeksema, Ready to Give an Answer: A Catechism of Reformed Distinctives [Grand Rapids, MI: RFPA, 1997] pp. 74-75)
Ronald Hanko and Ronald Cammenga
I Timothy 4:10 [is taken by many today] to teach that God, in addition to being the Savior of His people, is also in some sense the Savior of all men ...
As far as I Timothy 4:10 is concerned, it cannot mean that God is the Savior of all men in the usual sense of the word, because otherwise the passage would contradict the rest of the Scriptures and teach universalism, the teaching that no one will be damned. Notice that the verse does not just say that God sent His Son for all, but that He is the Savior of all. The explanation we prefer, though Calvin gives an alternative, has to do with the use of the word “specially.” The word “all” seems to indicate that “all men” is a larger and less exclusive group than “those that believe.” In fact, they are the same group. The idea of the verse is therefore this: "The Saviour of all men, that is, of those that believe.”
Three other verses in the New Testament use the same word translated “specially” and “chiefly” in that way. In Acts 25:26 “you” and “king Agrippa” are the same person, so that the verse can be read, “before you, that is, before thee, O king Agrippa.” In I Timothy 5:8 “his own” and “those of his own house” are also the same group, and the word “specially” again has the idea of “that is.” Thus, everyone is commanded to care for “his own, that is, for those of his own house.” Finally in II Peter 2:9,10 the “unjust” and “them that walk after the flesh” are the same group of people, and the word translated “chiefly” again has the idea of “that is.” God reserves “the unjust unto the day of judgment to be punished, that is, them that walk after the flesh.”
Insofar as the word has any other meaning, it indicates that the group referred to in each case has a special name, a name that reinforces what each passage says about them. In Acts 25:26 “you” is “king Agrippa.” In I Timothy 5:8 “his own” are “those of his own house,” reinforcing the command to care for them. And in II Peter 2:9, 10, the “unjust” are “those that walk after the “flesh,” emphasizing the reason that they are reserved unto judgment.
So in I Timothy 4:10 “all men” are especially “those that believe,” and the text is explaining by the second name why God is their Savior. Thus, the verse, instead of suggesting that God in some sense is Savior of all men without exception, actually shows that “all men” is the equivalent of “those that believe,” a limited number of persons.
(Ronald Hanko and Ronald Cammenga, Saved By Grace: A Study of the Five Points of Calvinism [Grandville, MI: RFPA, 2002], pp. 110-112)
Robert L. Reymond
Then later, when he describes the living God as the 'Savior of all men, that is believers' (I Tim. 4:10), [Malista, malista, can bear the sense of further definition ('that is'), according to J. C. Skeat, "'Especially the Parchments': A Note on 2 Timothy IV.13," Journal of Theologiccal Studies 30 (1979): 173-77] he doubtless presumes again that he will be understood, against the earlier contextual background, to mean that God is the Savior of believers, who are found among all categories of men."
(Robert L. Reymond, A New Systematic Theology of the Christian Faith [Nashville, TN: Thomas Nelson Publishers, 1998], pp. 693)