...hath appeared to ALL men

Titus 2 is rich with spiritual and practical application for the believer to lead a "quite and peaceable life." (1Tim 2.2)
However, in morning devotion, the following verse from Titus 2 grabbed this believer's attention and focus. Titus 2.11 says: "For the grace of God that bringeth salvation hath appeared to all men."  How much debate has gone on with the little word, "all?" If we understand that not "all" will become saved or believers, then what does "all" men in this passage?
The Nelson Bible note for this verse says, "God's grace has provided salvation universally for all mankind through the unlimited atonement of Christ."
Well, there is no argument from this writer that His blood was enough for "all."  But the truth is, according to the doctrine of election, we understand that not "all" will believe.  (Mt 24.22, Mk 13.22,  Rom 11.5, IThes 1.4, Tit 1.1, IPet 1.2)  So then, what is meant by this salvation "appear(ing) to all?"
Is it simply the truth that "if He died for 'all' then 'all' were dead?" (2Cor 5.14) But one must go further with the words in this verse. "...hath appeared to all..."
If we are to take the word "appeared" literally rather than spiritually, what then?  How could He "appear" to all before and after the cross? Surely, "all" who encountered the Lord Jesus, saw Him, quite literally.  So one could say He "appeared to all" in that respect.  And before the cross we believe that He was seen in human form of many of the patriarchs. Abraham saw Him in Gen 16.14; Jacob saw Him in Gen 32.30; Moses saw Him in Exo 3.2, the children of Israel saw Him in a "cloud by day and a pillar of fire by night" in Exo 13.21; Gideon saw Him in Judges 6.22.
One might also note that the carnal eye has only to look around and see God's handiwork in all of nature.  And certainly, one must agree that His "grace" by virtue of letting us live and breath would be "grace appearing to all."  Thus, in this way, again, physically, He (i.e. His grace) appears to "all." 
But to "rightly divide" the scriptures (2Tim 2.15), one must dig a bit deeper for the meaning of "all."
John 5.39 encourages us to "search the scriptures." Obviously, "all" will not "search the scriptures."  But we KNOW, believers will. In this writer's mind, it's simple really.  The "grace of God that bringeth salvation to all men..." All of scripture is written to believers.  Since, "... the natural man receiveth not the things of the Spirit of God: for they are foolishness unto him: neither can he know them, because they are spiritually discerned,"(ICor 2.14) - it is but a step to understand "all" is written to believers.
Back to the blessed doctrine of election. Those who have come because "the Father has drawn them" (Jn 6.44) are the ones, I believe, who are referred to in the passage "hath appeared to all." (Rom 9.11, 11.5, 7, 28, IThes 1.4, 2Pet 1.10).
Grace and peace to all who study this blessed truth.