Polhill:

Having thus debated the manner of conversion, I proceed to the last thing proposed, viz.;

Query 3. Whether the will of God touching conversion be always accomplished therein? For answer whereunto, I must first lay down a distinction as a foundation. God may be said to will the conversion of men two ways; either by such a will as is effective, and determinative of the event, or by such a d as is only virtual, and ordinative of the means tending thereunto: both parts of this distinction are bottomed upon scripture.

1. God wills the conversion of some by a will as is effective and determinative of the event. There are some chosen to holiness, (Eph. i. 4), called kata prothesin according to purpose, (Rom. vii. 28); predestinated to be conformed to Christ’s Image, (ver. 29); begotten of God’s own will to be first-fruits to him, (Jam. i. 18); and within that election of grace which doth ever obtain, (Rom. xi. 5, 1). Touching these, the will of God is effective and determinative of the event, in these, conversion is wrought after an irresistible and insuperable manner.

2. God wills the conversion of others by such a will as is only virtual and ordinative of the means tending thereunto. Thus God would have healed Israel, (Hos. vii. 1). Thus God wills “the turning of the wicked, who yet dies in his sin,” (Ezek. xxxiii. 11), because the true tendency of the means is to heal and turn them. Thus the apostle asserts, that God ” will have all men to be saved, and to come to the knowledge of the truth,” (1 Tim. ii. 4). In which place, as I take it, the word “all” extends further than to the elect; for those words of the apostle are laid down as a ground of that exhortation to “pray for all men,” (ver. 1); and that exhortation to prayer extends further than to the elect: wherefore, the ”all” whom God would have to be saved, being parallel and co-extensive to the “all” whom we are to pray for, must also extend beyond the elect. Wherefore, I conceive that the latter part of the words, viz., “and to come to the knowledge of the truth,” is a key to the former, viz, “that God would have all to be saved.” God would have all to be saved, so far, as he would have all to come to the knowledge of the truth, and he would have all to come to the knowledge of the truth, so far, as he wills means of knowledge unto them; for the true end and tendency of the means (and that from the will of God ordaining the same thereunto) is that men might be turned and saved: wherefore, in respect of that ordination, God may be truly said, by a kind of virtual and ordinative will, to will the turning and salvation of all men.

Edward Polhill, “The Divine Will Considered in its Eternal Decrees,” in The Works of Edward Polhill (Morgan, PA.: Soli Deo Gloria Publications, 1998), 208. [Some spelling modernized, and underlining mine.]