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The conclusion to the council's canons says:
After grace has been received through baptism, all baptized persons have the ability and responsibility, if they desire to labor faithfully, to perform with the aid and cooperation of Christ what is of essential importance in regard to the salvation of their soul.
This was the wording that I missed earlier. In other words, while God provides the initial impetus for salvation through grace, man is only saved thereafter "if they desire." This is clearly not consistent with "irresistible grace," or what Warfield terms "certain efficacy" of grace. Dialogist's answer is therefore more or less correct to say that what "troubled Warfield was that the Council of Orange ascribed any importance at all to man's free will," though Warfield, as a Calvinist, would affirm "free will" in a certain compatibilist sense.
John Leith says in Creeds of the Churches, page 37:
At the Council of Orange ... double predestination is repudiated and irresistible grace is omitted.
Similarly, Charles R. Biggs says in an article that the council "failed to articulate Augustine's teaching on predestination and irresistible grace." Biggs says in another article that "problems with the Synod of Orange" are the following:
(1) The irresistibility of grace is not affirmed. (2) Predestination to evil is condemned. (3) The reception of grace is so bound to baptism that the sacramental quality of grace and the merit of good works are put in the foreground.
Herman Bavinck says in Reformed Dogmatics: Vol 1:
The Synod of Orange ... accepted prevenient grace but did not decisively adopt irresistible grace and particular predestination. In the years following, not much Augustinianism was left intact."
So we can summarize the reformed objections to the council as follows:
Upvote:3
In defending the Church against Pelagianism, Augustine took the extreme stance of denying any role at all of man's free will in his salvation. He once wrote, for example:
Will you dare say that even when Christ prayed that Peter's faith might fail, it would still have failed if Peter had willed it to fail? As if Peter could in any measure will otherwise than Christ had wished for him that he might fail.
Although Augustine appeared not to be fanatical about his views, others in the Church - especially Prosper of Aquitaine - adopted his extreme anti-Pelagian views. Other Church Fathers such as John Cassian argued that grace and free will must be viewed in the context of a sort of synergy between God and man, but Prosper and others dismissed this view altogether. Prosper wrote, for example,
By a sort of contradiction, there is taught that ... [some] from the endowments of free will, have this desire to seek, to ask and to knock ...
Contra Collatorum, Chs 2:2, 2:4
Augustine himself modified his views in later works. In The Call of All Nations he writes that he sought "to investigate what restraint and moderation we ought to maintain in our views in this conflict of opinions" (Book I.1). He emphasized that grace does not compel man but acts in harmony with man's free will:
If we give up completely all wrangling that springs up in the heat of immoderate disputes, it will be clear that we must hold for certain three points in this question. First, that God wills all men to be saved and to come to knowledge of truth. Secondly, there can be no doubt that all who actually come to the truth and to salvation, do so not in virtue of their own merits but of the efficacious help of divine grace. Thirdly, we must admit that human understanding is unable to fathom the depths of God's judgments.
Book II.1
This was a considerable modification of his previous view that grace was not only a help, but the sole agent in man's salvation. The Canons of the Council of Orange reflect Augustine's modified views. While firmly emphasizing the role of God's grace, they do not explicitly deny that the actions of man himself also have a role in his salvation. The Canons simply state that man cannot be saved solely through his own will, which was essentially the Pelagian thesis. What probably troubled Warfield was that the Council of Orange ascribed any importance at all to man's free will.
[Most of the above follows the explanation of the Pelagian controversy found in Seraphim Rose's book, The Place of Blessed Augustine in the Orthodox Church]