Well, I have just finished up a book by Francis Turretin entitled The Atonement, which I would like to share some quotes here, especially with regards to the Neo-Amyraldian teaching prevalent within so-called "Reformed" churches.
The version of the book here is translated by the Reverend James R. Wilson, D.D., and edited, updated, and revised by C. Matthew McMahon. It is published by Puritan Publications © 2005 A Puritan's Mind, Inc. And the modernizing of the words used done by Dr. McMahon is greatly appreciated, as even with it, the text itself requires focus and concentration to absorb its meaning as Turretin was a Calvinistic scholastic theologian who taught very logically, which mean that the way or writing tend to be more factual and logical and less engaging.
Anyway, here are the interesting quotes from the book:
On God desiring the salvation of the reprobates
It [the Amyraldian position] represents Christ as saying, I wish to obtain salvation for all, to the end that it may be applied to them, will they but believe, however, I am resolved not to reveal this redemption to all, and to refuse to innumerable multitudes to whom it is revealed, that condition which is the only means by which it can be applied to them. Shall men make the infinitely wise and holy Jesus say, I desire that to come to pass, which I know neither will nor can take place, and I am even unwilling that it should, for I refuse to communicate the only means by which it can ever be brought to pass, and the granting of this means depends upon myself alone? What a shameful indignity does this offer to the wisdom of Immanuel! It would be an insult to the understanding of frail man. Nor will the matter be amended by saying that the failure of the application is not to be attributed to Christ, but to the wickedness and unbelief of man. This is not less injurious to the honor of Christ, for it represents Him as either not foreseeing, or as not capable of the salvation He obtained, and thus make it fruitless. They indeed allege that it was not in vain, though it fails of success, because, however men treat the salvation offered them, Christ will not miss the prime object which He had in view in His death, that is, to provide pardon and salvation for every man if He will only believe and repent — a thing which before was prevented by the inexorable rigor of divine justice. All this does not remove the absurdity. The object in procuring salvation could be none other than its application, and it cannot but be in vain, if it fails to accomplish this object. Christ needed to die for men, not to procure them pardon and salvation under a condition which it is impossible for them to comply with but to obtain for them actual pardon and redemption. (p. 119, Chapter 5: The Extent of the Atonement)
Absurdities of Universal Atonement, or the Universal aspect of Atonement
If Christ died for all men universally, it will follow that:
1. That He died, on condition they would believe, for multitudes innumerable, to whom His death has never been made known, and hence it was impossible that they could believe.
2. That He died for those whom He knew to be children of perdition, whom God had passed by, and who wold never, to all eternity enjoy any of the fruits of His death, and so exercised ineffable love towards those whom both He and the Father will cause to suffer eternally under the effects of their wrath.
3. That He died for those, who previously to His death were actually condemned without all hope of reprieve, and were in hell suffering His avenging wrath, and that as their surety He suffered punishment in the place of those who were suffering punishment for themselves, and must suffer it without end.
4. That Christ is the Savior and Redeemer of those who not only never will be, but never can be saved or redeemed. Or otherwise He must be an imperfect Savior, having obtained a salvation which He never applies, for He indeed cannot be properly called a Savior of any but those whom He makes to be partakers of salvation, and who are actually saved.
(p. 126-127, Chapter 5: The Extent of the Atonement)
Answering the objection that unless He died for all, the Gospel Offer cannot be sincere
For the Gospel which is preached to those who are called, does not declare that, in the eternal decree of God, it has been ordained that in Christ redemption has been procured for each and every man, It rather announced to sinners a divine command, with a promise annexed, and teaches what is the duty of those who wish to be made partakers of salvation. (p. 146, Chapter 5: The Extent of the Atonement)
On Assurance of Salvation, linked to the Offer of the Gospel
Christ is not revealed in the Gospel as having died for me in particular, but only as having died in general for those who believe and repent. Hence I reason from that faith and repentance which I find actually to exist in my heart, that Christ has, indeed, died for me in particular. I know that He died for all who fly to Him, I find that I have fled to Him, hence I can and should infer that He died for me. (p. 138)
To express it in a word, the faith which the Gospel demands of those who hear it is, the flying of the sinner for refuge to God as the fountain of grace, and to Christ as the ark of safety which is opened in the Gospel. If I am conscious to myself that I have done this, which is the formal act of faith, then I can and ought to exercise the other act by which I believe, that for me, who repent and fly to Him, Christ hath died. (p. 140)
And although I cannot yet assure myself that Christ has died for me [based upon the fact that Christ died for those who believe], it does not follow that I must always remain in a state of doubt and anxiety, and that my faith must be weak and unstable. My faith may firmly rest upon the general promises of the Gospel to every believing and penitent sinner. Hence by certain consequence, when I find that I possess faith and repentance, I may assure myself that these promises belong to me. (p. 143)
As it can be seen, these quotes show how Turretin handled the issues. He did not sell out the Gospel offer just because the Amyraldians twist it (following Hyper-Calvinism), and neither did he allow the Amyraldians space to defend their unbiblical theory of universal atonement. Furthermore, he applied it to the Gospel offer in order to show that denying universal atonement in its varied forms does not imply that the Gospel offer is not a sincere offer in the sense that such an offer is not false. As we can see Turretin's words, he states that "It rather announced to sinners a divine command, with a promise annexed, and teaches what is the duty of those who wish to be made partakers of salvation". Rather than it being well-meant as God desiring all Man to be saved (the Neo-Amyraldian error), it is 'sincere' or unreserved/unconditional in the sense that the promise annexed to the command will apply to anyone who fulfil the command, be they elect or reprobate (decree of election-blind conditional). That is all that it means, not actually stating God's desires towards all Man per se.
As it can be seen also from Turretin's masterful argumentation, postulating a desire in God to save all Man (Universal Atonement) would result in blatant logical contradictions and absurdity. That is why it is mentioned that all Amyraldians and Neo-Amyraldians are illogical, for if they be truly logical, they would either embrace orthodox Calvinistic Christianity, or they would be Arminians or even Semi-Pelagians or even degenerate into Open Theism. That they do not do so show their irrationality. May God open their eyes and minds to show them the errors of their ways.