I do not think we can move on that. Many Calvinist that I heard from still say that God elects people before the foundation of the world. And that He elects them based on His own will alone.
I also think that from the definition "Grace alone" (without giving the man an option to choose to accept this amazing grace or reject it), follows logically that God elects people before the foundation. Since He already know to whom He wants to show His grace, and since Calvinists believe it is irresistible, follows logically, that to whom He will show His irresistible grace, he will be saved. And thus He already chose those who He wanted to be saved, in other words elected them before the foundation of the word.
I am still studying this subject. I am not here to debate it. Just sharing my humble thoughts with you. This is how I think salvation happen:
There was a nice image about Calvinism here in the forum, about a skeleton hand been lifted up by the Holy Spirit guiding it to Jesus. I agree with it totally. To God is all the glory, He did everything to save us. He is to be credited for His salvation, love and grace. He is sovereign. Without His grace we all will be lost, and cannot be found!
However, what I currently believe in and is not reflected in that image is:
1) Man is free to reject the Holy Spirit. (God's grace is not irresistible)
2) The atonement is not limited for a closed group of people. Every human can enjoy this precious atonement.
I think you misunderstand what Irresistible Grace means, and that is probably because of the unfortunate label. A better, more accurate label for the doctrine is "effectual calling".
Irresistible Grace does not aim to teach that God's grace cannot be resisted. In fact, the T in TULIP (Total Depravity) teaches that very thing: that humans are always resisting God's grace because they are unregenerate and by nature children of wrath.
What Irresistible Grace means is that everyone would resist God's grace all the way to hell, unless God steps in to change our hearts. And God never fails to do this because regeneration is the realm of the Spirit of God alone, per John chapter 3.
The elect stop resisting God's grace when God quickens us while we were spiritually dead. The non-elect effectually resist God's grace all their lives.
As for Christ's atonement, I think you are again misunderstand what is meant by "Limited". It does not mean that people cannot avail themselves of the atonement if they want to. So it is not limited in a practical aspect.
What it means is that Christ successfully saved and made perfect atonement for every single person he died for. And since this is not everyone (that would be universalism), it must be less than everyone, or Limited.
The distinction is drawn from realizing that the Bible never speaks of Christ's death as merely potentially or possibly securing salvation for us, but actually, and effectually doing so.
No where does the Bible talk about Christ's atoning work for us as merely making salvation "possible", but
actually saving us.
