Where the Reformed and the Arminian agree: Christ’s death is sufficient for each and every person.
“It is not asked with respect to the value and sufficiency of the death of Christ- whether it was in itself sufficient for the salvation of all men. For it is confessed by all that since its value is infinite, it would have been entirely sufficient for the redemption of each and every one… The question does not concern the fruits and efficacy of Christ’s death… our opponents acknowledge that these are to be extended to believers only.”
Where is the difference?
“The question properly concerns the purpose of the Father in delivering up his own Son and the intention of Christ in dying. Did the Father appoint his Son for each and every one and, did the Son deliver himself up to death with the design and intention of substituting himself in the place of each and every one to make satisfaction and acquire salvation for the same?… The question hinges upon this – not what is the nature and power of Christ’s death in itself, but what was the purpose of the Father in appointing him and the intention of Christ in undergoing it… The question refers to the design of God in sending His Son into the world and the purpose of Christ in his death.”
For Turretin, the key to limited atonement is the mission of the Son from the Father. For what purpose did God send Christ? We can all agree that Christ’s death is “for” every person in the sense that it can save every person and that every person is outwardly called to come. The primary distinction is that the Reformed affirm that the Father sent the Son for a particular people. Although Turretin does mention Christ’s intentions too, he primarily places the emphasis in the Father’s Will. The Father is most important in Limited Atonement. Rather than asking “For whom did Christ die?” we would be better to ask “For whom did God send Christ to die?” And John 6 suggests the Father sent the Son to die for and save a particular people.
Resisting the Winds 
IMHO John 6 is simply referring to prevenient grace of the Father that was responded to, not sending Jesus only for a “certain group”. Jesus came for all, fully knowing not all will come to Him.
LikeLiked by 1 person
The reason I do not think PG fits with John 6:
1) “All that the Father gives me will come to me, and whoever comes to me I will never cast out.”
Those given to the Son are guaranteed to come to Christ. They “will” come. PG cannot guarantee anyone comes, let alone everyone.
2) “‘But there are some of you who do not believe.’ (For Jesus knew from the beginning who those were who did not believe, and who it was who would betray him.) And he said, ‘This is why I told you that no one can come to me unless it is granted him by the Father.’”
Thought more subtle, I think Jesus does teach here that the reason the grumblers do not believe is because they were not given of the Father. In other words, Jesus explains their unbelief to them. Thus, not everyone is given to the Son and only some of those given come. Rather, John 6 teaches that all those given to the Son will come, and if someone never comes, we must be reminded that only those given come, which means they came not because they were given not.
LikeLiked by 1 person