Particular Atonement From Kingdom through Covenants (2/3)

Christs work as our great high priest is a unified work

His intent was not only to achieve the redemption of a particular people but also to secure everything necessary to bring those same people to the end for which his death was designed, namely, the full forgiveness of sin and all the blessings of the new covenant including the gift of the Spirit, who effectively  applies his work to those whom the Son represents... the problem with all general atonement views is that they must divide Christ's unified priestly work, redefine Christ's relation as priest to his people, and ultimately make ineffective his work as the head of a new covenant- all points that Scripture will not allow.

P1, God gives all things to those whom the Son dies for
P2, God has not given all things to all men
C, Therefore the Son has not died for all men.

The fault here is easy to see if we take the tacit premise and make it into it's own syllogism:
God either gives all things, or nothing whatever to men
God gave all things to the elect,

The non-elect therefore get nothing whatever.

The next bit of text which begins with "The priestly argument for definite atonement is nothing new. Almost every defense of particular redemption includes it. Yet it is rarely dealt with by its critics, or if it is discussed at all, only aspects of it are mentioned- aspects which are usually divorced from its full biblical-theological presentation..." is irrelevant and I can't make an argument out of it, so I've omitted it. We go on,

There is no evidence He intercedes non-salvifically for the non-elect. Three texts buttress this claim.

In John 17:6-19, our Lord effectively prays for His disciples, those whom the father has given him, but not for the world (9-10). In verses 20-26 Jesus then prays for all future believers, once again given to him by the father (v24, 6:37-44). This intercession is consistent with Jesus teaching previously: he is the good shepherd who dies for the sheep (10:11-15); his sheep are given to Him by his father (10:29) his sheep receive eternal life due to his death; but not all people are his sheep (10:26-27). All of this is consistent with his office as a priest who offers himself for a particular people and intercedes for those same people.

P1,  Jesus prays for His disciples only, and not all men equally,
P2, In the same way He does not die for all men equally.
C, Jesus has not made a way for the non-elect to be saved. 

I'm trying to be fair about how I summarize the argument, but this is just going terribly.

The problem with all general atonement views is that they fragment Christ's priestly work of offering and intercession. Either they must view Christ's work apart from these typological patterns and not discuss the atonement within the constraints of these biblical categories, or they must separate Christ's intercession from his death, thus dividing his priesstly work... 

P1, Christ's atonement and intercession are inseparable,
P2, Christ intercedes only for the elect,
C, Therefore Christ atoned only for the elect.

This is a bit harder to show the error in, but on the other hand it's much harder to prove, for you must first conclusively show that both these premises are bulletproof truths, not just statements. The authors must use the OT to show that in every instance there was never a time in the OT that God was concerned about the Gentiles, and then use the NT show Jesus never showed regard for the non-elect. The problems with doing this are manifold (Nineveh, the Rich Young ruler, Jerusalem etc). They then must prove Christ only intercedes for the elect, and has never kept the non-elect in His grip in any way. But that's a problem too because the only place that says anything like this is John 17. Note John 17:12 "I have kept all you have given me except..." Which means God gave Jesus Judas to keep as well. It's a problem again in v23 where Jesus says "...that the world may know..."
It's indicative that they came into this with the assumption that both points were true, and then tried to prove it. I'll show you why I think that with this next bit:

... What about Luke 23:34? Is it proof that Christ intercedes salvifically for the non-elect? No, and for four reasons: 

1. Such an interpretation goes against the entire scriptural presentation of the intercession of the priest.
2. ... One cannot conclude from a specific prayer for a handful of people that this is a prayer "for all and every man that ever were, are, or shall be"
3. ...Christ prays for a delay of judgment, thus allowing history to continue and God's ultimate purposes to save his people to be realized. Tied to this is God's common grace upon the non-elect who crucified him and, bu a delay in judgment, the salvation of the elect as evidenced in the thief on the cross and many people on the day of Pentecost. This prayer does not serve as evidence that Jesus intercedes salvifically for the non-elect. 
4. ...[if he did intercede for the non elect] it would mean Christ failed in His high priestly work, but this goes against everything scripture teaches about the priestly work of Christ as perfect and effective.

 Unless you were already committed to thinking that Christ hates the non-elect I can find no grounds for being swayed by any of these four points. If one cannot conclude from a specific prayer that Christ regards men in general with favor then whose word will convince us? If "common grace" is a tool to save the elect while condemning the non-elect then it's not grace. And then why must we conclude Christ has failed if the non-elect perish? Only if we first define His work a certain way first does that hold true.
Now for the arguments put forward in the last section.