1 Tim 2:4 is one of the most popular "proof-texts" used against Reformed theology. In the NASB (1995 update), it reads:
[God] wills everyone to be saved and to come to knowledge of the truth.
The underlying Greek reads:
ὃς πάντας ἀνθρώπους θέλει σωθῆναι καὶ εἰς ἐπίγνωσιν ἀληθείας ἐλθεῖν.
There are no major textual variants in this verse; all of the variants are reflective of spelling mistakes by scribes and do not affect the meaning at all (e.g., Codex Alexandrinus has ανθρωπου, without the terminal sigma [ς]). An alternative translation could be:
Who wills all men to be saved and to come into a knowledge of the truth. (my translation)
One can understand why, based on a prima facie reading of this verse, many conclude that this verse refutes Reformed theology, as Calvinistic soteriology states that God, while commanding all people, without distinction, to repentance, only grants the ability to repent to a select few (the “elect”); that Christ only died efficaciously for the elect and only intercedes for the elect; and that men can only be saved by the efficacious (salvific) calling of God (“irresistible grace”)--all these theological concepts are refuted if such a prima facie reading holds true.
John Calvin, in his commentary on the Pastoral Epistles, echoes both the historical and modern Reformed approach to this verse when he writes:
[We] see the childish folly of those who represent this passage to be opposed to predestination. "If God say they, "wishes all men indiscriminately to be saved, it is false that some are predestined by his eternal purpose to salvation, and others to perdition." They might have had some ground for saying this, if Paul were speaking here about individual men; although even then we should not have wanted the means of replying to their argument; for, although the will of God ought not to be judged from his secret decrees, when he reveals them to us by outward signs, yet it does not therefore follow that he has not determined with himself what he intends to do as to every man.
But I say nothing on that subject, because it has nothing to do with this passage; for the Apostle simple means, that there is no people and no rank in the world that is excluded from salvation; because God wishes that the gospel should be proclaimed to all without exception. ow the preaching of the gospel gives life; and hence he justly concludes that God invites all equally to partake salvation. But the present discourse relates to classes of men, and not to individual persons; for his sole object is, to include in this number of princes and foreign nations.
In other words, for Calvin and most Reformed interpreters of this passage (e.g., R.C. Sproul; D.A. Carson; James R. White), God desires members of all classes of men to be saved, not all individuals within those categories. There are a host of exegetical issues with this response.
Firstly, some Reformed interpreters appeal to vv.1-2 to support the Calvinist interpretation of v.4; they read as follows:
I exhort therefore, that, first of all, supplications, prayers, intercessions, and giving of thanks be made for all men; for kings, and for all that are in authority; that we may lead a quiet and peaceable life in all godliness and honesty.
As “kings” and “[those] that are in authority” are classes of men, thus, they reason, the “all men” that God desires to be saved in v.4 are members of all categories of mankind, not all the individuals of humanity.
Such an interpretation is without merit, especially based on the Greek. The idea that πας ("all") can alone mean "all kinds" in a restrictive sense like Calvin et al. demands is simply false--they are playing as fast and loose with πας as the New World Translation of Jehovah's Witnesses does vis-a-vis Col 1:16. Furthermore, v.4 is not grammatically related to vv.1-2, as the former contains what Paul wants Christians to do, while v.4 contains what God wants for the world--even allowing the restrictive reading Calvinists desire for vv.1-2, the texts have different contexts; only by engaging in gross eisegesis and fallacious reasoning can one read vv.1-2 into v.4.
Indeed, with respect to πας, only when used in conjunction with numerals, ever has the "restrictive" sense Calvinists need it to have in 1 Tim 2:4, according to lexical sources such as Liddell and Scott.
Additionally, there are several words Paul could have used if he wanted to convey the meaning that only "kinds" of men will be saved, but none appear in the context; indeed, Paul goes out of his way to avoid such a notion, as seen in v.6, when he writes about the extent of Christ’s atonement:
Who gave himself a ransom for all, to be testified in due time.
The phrase "for all" is υπερ παντων, and literally means "for/on behalf of all," without any qualifications to the meaning of παντων (the genitive plural form of πας).
Had Paul wanted to "limit" the atonement, terms such as "some" (τινες) could, and should, have been used, but Paul did not. Interestingly, Calvinists who try to play fast-and-loose with 1 Tim 2:4 proves they only play superficial lip-service to the "perspicuity of Scripture."
Moreover, there is no place in the entirety of the Bible where Paul or any other inspired author teaches that God desires "all kinds" of men, as opposed to all men without exception, to be saved. One rule of interpretation, forwarded by those who hold, as Calvinists do, to Sola Scriptura, is that an "unclear" verse is to be read in light of the "clear," "explicit" verses--unfortunately for the Calvinist, there is no verse that is as explicit or clear as this "difficult" text (i.e., 1 Tim 2:4), so yet again, the Reformed lip-service to a key tenet of sola scriptura is displayed with great perspicuity (pun intended!)
Finally, Calvinists tend not to consider the possibility that Paul's initial expression "all men" in v.1 is for the purpose of saying that Christians should pray for all men without distinction, and that it logically follows that, when he mentions "kings" and "those in authority," such is merely a request for us to especially pray for those in positions of government in our lands, as they are in direct control of whether on can lead a peaceable life and live one's faith without persecution, which was a major problem for the New Testament church. This grammatical possibility is given short-shrift from many Reformed interpreters as their hermeneutic demands they do such do their theology is not caught in a blatant contradiction to the biblical texts.
Much more could be said, but it should be obvious that the Reformed interpretation of 1 Tim 2:4 is based on reading a series of man-made traditions back into the text (eisegesis) as opposed to meaningful exegesis based on the historical-grammatical method of interpretation.