
What do we mean by "All Men"
First of all, then, I urge that requests, prayers, intercessions,
and thanks be offered on behalf of all people, 2 even for kings and
all who are in authority, that we may lead a peaceful and quiet life
in all godliness and dignity.
--1 Timothy 2:1-2
Paul, writing to Timothy, teaches him that prayers should be offered on behalf of all people. This is to ask for God to intercede and allow all to have a peaceful life. This is especially pertinent when you have an evil king or leader. This is because God can change the heart of a king.
The king's heart is in the hand of the Lord, as the rivers of water:
he turneth it whithersoever he will.
--Proverbs 21:1

This is why we should pray for all people, even those who are in authority over us. This is because God can change their hearts and allow us to live in peace.
Well, obviously not all people are saved, are they?
Notice for reference that Paul says "all people" and not just the believer. When Paul speaks of "all people" he is literally speaking of all people. This includes the believer and the non-believer. This is because God wants all to be saved.
Such prayer for all is good and welcomed before God our Savior, 4
since he wants all people to be saved and to come to a knowledge of
the truth.
--1 Timothy 2:3-4
So Here is what I want to caution you about as we go forward. There are teachers out there who like to fly on the high wire trapeze. And they will do several things to get you to see scripture in a manner that it was not written.
One method is by asking leading questions. They will begin with a question that leads you by the bit wherever they want to take you.
Another method, which is similar, is to say something that appears to be irrefutable fact, so that they can continue to lead you down the path they want you to go.
So as an example in 1 Timothy 2:4 above, they will take the phrase "since he wants all people to be saved" and will then lead you with the statement: "Well, obviously not all people are saved, are they? And God never fails in what he wishes to do. So what we are talking about is the efficacy of the redemption." In other words, they want to force the subject of a predetermined elect by raising a flag of efficacy (efficacy means the ability to produce the desired result).
Efficacy -- or what is effective?
So what is the desired result? The desired result is that all people are saved. But if all people are not saved, then the redemption is not efficacious. So the redemption must be efficacious. It must be effective. It must produce the desired result. And the desired result is that all people are saved. So if all people are not saved, then the redemption is not efficacious. And if the redemption is not efficacious then God is not omnipotent. And if God is not omnipotent, then he is not God. And if he is not God, then we are all in trouble.
The reality is that Paul actually says: "since he wants all people to be saved and to come to a knowledge of the truth." This is not a statement of efficacy, but a statement of desire. God desires all to be saved.
So why are they not? If God is omnipotent (all powerful) then he could make (force) everyone to be saved? That's an intersting question in the face of a predetermined elect. For if God "wants all people to be saved" then, being omnipotent, and if the individual election were true, then he would in fact make all people saved. This woule be effective for the elect, but not for "all people."

So is Paul a liar? Does God not really "want all people to be saved"? One or the other is true here. If God controls an election, and he "wants all people to be saved" then all people would be saved.
What am I saying then? Well, I'm saying the doctrine of individual election is not true. It is not damning, mind you. Calvinists are not going to hell by believing this. It simply is not salvific.
What would stop "all people" from being saved? It is because God has given us a choice. We can choose Life, or we can choose death. We can choose Blessing, or we can choose the curse. It is a choice that he has set before us and allows us to choose. And obviously, there are many people who have chosen not to accept God's offer of salvation. God wants all people saved, but in his sovereignty he allows us to choose. And some people choose not to be saved, not to accept; not to confess, not to believe in their heart.
Today I invoke heaven and earth as witnesses against you that I have
set life and death, blessing and curse, before you. Therefore choose
life so that you and your descendants may live!
--Deuteronomy 30:19
In fact all of heaven and earth were witness to the offer. Life or death. They've been set before you. And you are told that you get to choose. God even gives a hint: choose Life!
So did I just make up the stuff about efficacy of the redemtion? Nso, it came from a recent teaching from none other than John Piper. He is a Calvinist and he teaches that the redemption is efficacious. That is, it is effective. It is not a matter of desire, but a matter of fact. If God wants you saved, you will be saved. If he doesn't, you won't. It is not a matter of choice, but a matter of God's will.
Put another way, God "wants all people to be saved." But obviously they are not, So John's reasoning is that God must have set up an elect and a non-elect; so "all people" gets redefined to a subset of "all people." The term "all people" doesn't mean "all people." It's a trapeze act.
If you'd like to hear the message, you can find it here: One God, One Mediator, One Ransom for All. You'll get to the "effective" part around the 5:30 mark of the talk.
I like Piper's teachings on many subjects. But him being a Calvinist, I'm very careful about listening to him. Calvin's doctrines are in error in many places -- and not in error in many others. Remember, Calvin taught clearly that the only way to salvaiton is through Christ Jesus. He just have a different method on how that gets done.

Who did Jesus die for?
Key scripture in their message comes from a number of places. One key scripture for the individual election is in Ephesians. John will cover it in his talk.
Blessed is the God and Father of our Lord Jesus Christ, who has
blessed us with every spiritual blessing in the heavenly realms in
Christ. 4 For
he chose us in Christ before the foundation of the world that
we should be holy and blameless before him in love. 5 He did this by
predestining us to adoption as his legal heirs through Jesus
Christ, according to the pleasure of his will— 6 to the praise of
the glory of his grace that he has freely bestowed on us in his
dearly loved Son. 7 In him we have redemption through his
blood, the forgiveness of our offenses, according to the riches of
his grace.
--Ephesians 1:3-7
Look at the bolded phrases in the above scripture quote. He chose us in Christ. Sure does look like predestination, doesn't it. But what is the context of the scripture? It is not about individual election. It is about the church.
Watch out for yourselves and for all the flock of which the Holy
Spirit has made you overseers, to shepherd the church of God that he
obtained with the blood of his own Son.
--Acts 20:28
Luke (the accepted author here) tells us that what or who is "obtained with the blood of his own Son"? The church. While it is true that an offer of salvation is set before you and me, if we accept we are added to the church. We are added to the Body of Christ. It is the Bride that Christ is coming back for: not you individually, you prideful thing. He is returning for the church.
Husbands, love your wives just as Christ loved the church and gave
himself for her 26 to sanctify her by cleansing her with the washing
of the water by the word, 27 so that he may present the church to
himself as glorious—not having a stain or wrinkle, or any such
blemish, but holy and blameless.
--Ephesians 5:25-27
Oh my, doesn't God just go on and on about individuals here? He does actually, elsewhere; I'm being just a little fecetious. But here in Ephesians he tells us that Christ loved the Church. He gave himself for the Church. He sanctifies the Church. He washes the Church with the water of the Word. He is making the Church to be without stain or wrinkle--blameless.
You? Individually? Yes, you too, but because you have been accepted into the Body of Christ, the Church, when you confessed with your mouth, and believed in your heart that Jesus is Lord (see Rom 10:9-10 again).
Election is corporate, not individual. You become elect when you are ushered into the Church as a believer in Jesus Christ. You are not elect before that.
he himself is the atoning sacrifice for our sins, and not only for our sins but also for the whole world.
So go back up to Ephesians 1:3-7 above and re-read the bolded parts with corporate election in mind. He chose us in Christ. Who? The Church. Predestining us to adoption. Who? The Church. We have redemption through his blood. Who? The Church. And you as part of the Church are washed in his blood. Your sins are forgiven. The sins of all who make up the Church are forgiven because the Church has been redeemed, it has been washed in the water of the Word.
For this is the way God loved the world: He gave his one and only
Son, so that everyone who believes in him will not perish but have
eternal life.
--John 3:16
For God loved the whole world. But is the whole world saved? No. It will be whosoever believes. It is "everyone who believes in him will not perish." But many will reject this and not believe. When we speak of the efficacy of redemption, it is efficient for those who believe. God will not lose you. You are in his hand, sealed by the Holy Spirit until the day of redemption -- when Christ returns for...the Church (with you in it; you making up part of the Body). And with you sealed and in his hand, he won't lose you. You're saved adn you are saved forevermore. If you think you can fall away from that, then answer me why God lied and said that his Spirit sealed you until the day of redemption? Did you break God's promise? Silly you.
So if you are still not sure about this predetermination thing. If you still think that God only atoned for the sins of the elect, and only a prechosen elect will be saved. Then listen to John once more.
But if anyone does sin, we have an advocate with the Father, Jesus
Christ the Righteous One, 2 and he himself is the atoning sacrifice
for our sins, and not only for our sins but also for the whole
world.
--1 John 2:1b-2
There is no confusion here. Jesus atoned for the sins of"not only for our sins [believers] but also for the [sins of the] whole world. Kind of clear who Jesus died for, isn't it? For us, the believers, and for the whole world.
So what of efficacy? Yes, it is here: for those who accept God's offer of salvation, he will save them and not lose them. But that's for another article. We'll do one on the Perseverance of the Saints. Calvin got that one right (perhaps for the wrong reasons, but we are OSAS).