From this viewpoint, it follows that the one Christ has been divided into two things, into God and a man. But this is alien to the apostolic teaching and is in fact an invention of a demonic imagination. For the divine word proclaims to us that at the end of the ages, the Logos became man, not indeed that he was transformed into human nature, but that he took himself this nature.- Cyril of Alexandria, "Against Those Who are Unwilling to Confess that the Holy Virgin is Theotokos," Part 1, Section 2
What is implicit in Cyril's analysis is that if it is not in the Scriptures, it is not part of the apostolic teaching. We see him express the same thing negatively here:
But, if they say that the divine visitation has come upon a man born of a woman, then this is also what happened in the case of all the prophets. If this is true, then it is necessary to find in the divine Scripture two separate confessions, one, which praises God the Logos in himself, and another, which glorifies a man like us in words appropriate to human beings.- Cyril of Alexandria, "Against Those Who are Unwilling to Confess that the Holy Virgin is Theotokos," Part 1, Section 2
The same thing is repeated:
[After quoting John 1:1, John 1:14, and Hebrews 2:14] Do you hear then the one saying that the Logos was made flesh and the other that he partook of the same? But, if Jesus were born the man from a woman and afterwards the Logos descended upon him, as said before, it is necessary to find everywhere two completely separate confessions. Now, however, that the divinely inspired Scripture attributes to him conjointly the things, which belong by nature of man, the economy of the union is clearly seen.- Cyril of Alexandria, "Against Those Who are Unwilling to Confess that the Holy Virgin is Theotokos," Part 1, Section 3
Notice as well that in the quotation above Cyril says that the orthodox is "clearly seen" in Scripture, thereby affirming the perspicuity of Scripture on this issue.
Now consider Cyril's rather sharp remarks about his theological opponents:
But we recognize that their words are full of madness and delirium that it is as if they were spoken in sleep or drunkenness. We shall say to them the words of the Savior, "You err, knowing neither the Scriptures nor the power of God" (Matt. 22:29). You ought to sober up and stop sinning, because you have become sick through ignorance of God.- Cyril of Alexandria, "Against Those Who are Unwilling to Confess that the Holy Virgin is Theotokos," Part 1, Section 6
What is implied in Cyril's rather non-irenic comments is that ignorance of Scripture is ignorance of God. The two go hand in hand.
If, then, they apply the indwelling to him in a similar manner as in the saints, their blasphemy will be obvious to everyone, and it will be clear that their teaching is entirely alien to the apostolic teaching.- Cyril of Alexandria, "Against Those Who are Unwilling to Confess that the Holy Virgin is Theotokos," Part 1, Section 7
Notice that Cyril's emphasis is on the fact that their ideas are not part of the apostolic teaching. In fact, they are foreign to it.
However, of course, the heretics did try to argue from the Scriptures. So Cyril analyzed their arguments. Consider his approach:
But look, they say, the Apostle openly confessed Him to be a man. For, in a letter to Timothy, he writes this: "a man Christ Jesus" (1 Tim. 2:5). They say this, because they want to disturb the mind of the most sincere [believers]. But, if anyone prudently examines the apostolic verse, he will cast his vote against their impiety on the basis of this very verse. However, we shall not cut short the verse like they do, but taking into account a little of what precedes this verse, we shall be able to understand correctly the confession of the economy which is made here.- Cyril of Alexandria, "Against Those Who are Unwilling to Confess that the Holy Virgin is Theotokos," Part 2, Section 12
There are at least three things to note in the preceding quotation. First, the perspicuity of Scripture is shown in Cyril's comment about "if anyone prudently examines the apostolic verse." Second, the sufficiency of Scripture is shown by Cyril's comment, "on the basis of this very verse." Third, the hermeneutical principle that Scripture interprets Scripture is shown by Cyril's appeal to context.
It's not a lone appeal either, for he continues:
If this is the case, then, let us bring right into the middle of our discussion the Lord's statement, which they presumptuously say must be understood, as if in the Gospels he confessed that he was a mere man: "why do you seek to kill me a mere man, who has spoken the truth to you?" (John 8:40). But if one gives his mind as a love of truth to the verses of the Gospels and especially to the context, in which the Savior has spoken, then he will fully understand their cunning and will justly call them censorious and slanderous.- Cyril of Alexandria, "Against Those Who are Unwilling to Confess that the Holy Virgin is Theotokos," Part 2, Section 15
Notice again in the preceding quotation the double affirmation of Scripture's perspicuity and the necessity to read Scripture in context, letting Scripture interpret Scripture.
Notice as well Cyril's explanation for the faulty conclusion of the heretics:
But they are silent about all these verses and seize upon this word "man," and in this, they are similar to the Jews of that time. For the Jews waited for the Savior to teach, not really because they wanted to believe or to be taught, but because they were planning to seize upon something he would say, as the evangelist reports. These men too read or rather speculate about the divine Scriptures in order to find an accusation against him, who laid down his life for them.- Cyril of Alexandria, "Against Those Who are Unwilling to Confess that the Holy Virgin is Theotokos," Part 2, Section 15
This is the difference between exegesis and eisegesis. The latter seeks to seize the Word for its own purposes, the former comes to the Word seeking to learn.
He even gets stronger:
[After quoting John 5:17, 19, 22-23, 25, and 27-29 and John 6:35] But they bypass all these verses as if they do not hear or rather, because they intentionally pretend to be deaf. They carry on about this statement, "but now you are seeking to kill me, a man, who has told you the truth," in order to disturb the minds of the most sincere [believers]. But they should consider, if they are right, that he who spoke what was said before is he, who has said this statement also.- Cyril of Alexandria, "Against Those Who are Unwilling to Confess that the Holy Virgin is Theotokos," Part 2, Section 16
Notice how Cyril is bringing in the concept of tota scriptura - all of Scripture must be considered, not only a select verse or fragment of a verse. That is because Scripture interprets Scripture.
Cyril continues on with sola Scriptura:
We should be content with what we have said and seek nothing more. For those who are right thinking and instruct themselves by listening to the divine Scriptures will say in good faith that there is nothing absurd about him being at once God and man, if in saying these things sometimes he is called God and sometimes man. The one designation by no means annuls the other.- Cyril of Alexandria, "Against Those Who are Unwilling to Confess that the Holy Virgin is Theotokos," Part 2, Section 16
Notice that Cyril has proposed a self-magisterium. A person educates himself by reading the Bible. Such a person is "right thinking" to Cyril. When Cyril says that we should be content with what we have said and seek nothing more, he means that we should accept and limit ourselves to what Scripture teaches.
Cyril also addresses a counter-argument based on something akin to sola Scriptura:
If they insist on saying, "where the Virgin is called Theotokos in Scripture," let them clearly hear the angel proclaiming this piece of good news to the shepherd and saying: "For today to you a Savior is born, who is Christ the Lord" (Luke 2:11). He does not say, "Who shall be Lord" or in whom the Lord shall dwell," but "who is Lord."- Cyril of Alexandria, "Against Those Who are Unwilling to Confess that the Holy Virgin is Theotokos," Part 3, Section 23
Notice that Cyril doesn't answer: "well, we don't have to prove our doctrines from Scripture," nor does he make vague comparisons to the fact that the word "Trinity" is not in Scripture. Instead, he answers the argument by showing where the Scriptures teach that Christ was God-become-man, not a human that was later indwelt by God. He accepts the major premise of his objectors (if it is not in Scripture it is not orthodox) but he rejects the minor premise (it is not in Scripture).
In view of the above, it should not be surprising to hear Cyril describe Paul this way:
Again, they should not whisper about this by putting forward the passion and resurrection and the fact that God raised him up. For already the reasoning, which applies to the economy, has been proven by what we have already said. If, however, they want to learn more clearly who it was who was crucified, then let them hear the teacher of the whole world, when he writes in his epistle to the Corinthians, "for I received from the Lord and delivered to you, that our Lord Jesus Christ on the night, on which he was betrayed, took bread," etc. (1 Cor. 11:23). Do you observe that the one who suffered for us is openly declared to be Lord?- Cyril of Alexandria, "Against Those Who are Unwilling to Confess that the Holy Virgin is Theotokos," Part 3, Section 24
Is the quotation above itself a compelling proof that Cyril practiced sola Scriptura? Of course not. But it is not by itself. It is part of a larger context in which it becomes obvious that Cyril thinks that the Scriptures teach the reader important things plainly.
Hear then Cyril's conclusion to his work:
He did, indeed, show that the one who was born from the Virgin, that is himself, was both son of David and Lord. However, those who heard this testimony were confounded and did not contradict him, as the evangelist says in the narrative: "For no one was able to reply to his word and dared from that time to ask him any more questions" (Matt. 22:46). May the same thing happen to these [heretics] as well. May they somehow abandon their madness and come to know the preaching of true religion. As for us, beloved, let us hold this faith forever, keeping it in mind, preaching it plainly and boldly with our mouths, being prepared willingly to suffer everything for it. For this is the prediction of the prophets, the preaching of the Apostles and the cause of the Kingdom of Heaven. This is the guide of eternal life. This is the wealth of the Fathers. This is our own true treasure, for the sake of which it is right that we sell and give away all things. If anyone ever wanted to steal this from us, let us despise him as an enemy of Christ and of our salvation, because we are persuaded by the commandment of the Apostle: "Whether we ourselves or an angel was to preach to you a different gospel from that which we preached let him be anathema" (Gal. 1:8).- Cyril of Alexandria, "Against Those Who are Unwilling to Confess that the Holy Virgin is Theotokos," Part 3, Sections 29-30.
For Cyril, as we have seen, it was crucial to keep doctrines Scriptural, and it was right to call down the anathema of Galatians 1:8 on those who were departing from Scripture's teaching on an important point.
Someone might wonder, "perhaps TurretinFan has simply cited the portions of the rebuttal relating to Scripture, but has left out the rebuttal from the Fathers and from the authority of the Church." Do not fear, I have not left out such items. In fact, the church is only rarely mentioned in the treatise. There is, of course, no mention of the Roman bishop (Cyril of Alexandria was no Romanist, after all) - and there is only a limited reference to councils. I think the limited reference to councils is illuminating, because Cyril is dogmatically condemning as heretics those against whom no counsel has yet proclaimed. He compares them to condemned heretics, and argues that his own position is founded on the unshakable rock. In the context of the work, that means Scripture, not the see of Peter, or apostolic succession generally:
These things and things like them are common to all those, who attempt to scatter the flock of true religion, as indeed the end of the aforementioned heresies has shown. What advantage did the deceit of Arius bring him? What advantage was there in the heresy of Eunomius and those, who blaspheme against the Holy Spirit? What profit in the heresy of Paul of Samosata or in the madness of the one called Apollinaris? All these men had a shameful end to their present life and were thrown out of the boundaries of the Church. They shall be thrown out of "the Church of the first-born in heaven" (Heb. 12:23), because their names have been erased from "the Book of the Living and shall not be inscribed with the just" (Ps. 68:29). The same end will come upon these current blasphemers, especially those, who have become the leaders of this perversity, if they do not quickly become aware of their madness and attempt to return to the place, from which they have fallen. For they shall hear from the Savior, "Just as a piece of cloth stained with blood is not clean, so you also will not be clean. Because you lost my land and killed my people, who shall not remain forever" (Isaiah 14:19-20). As for us, who have build our faith firmly upon the unbreakable rock, let us keep the true religion to the end. Let us not be disturbed at all by our opponents, but rather we will have the love of the Lord as an invincible weapon. Let us boast in Him for all things and laugh at the lowliness of our opponents and say the words of the prophet: "God is with us: Know all nations and be dismayed, be dismayed in your strength. If you regain your strength, you shall be dismayed; if you deliberate, the Lord will scatter your deliberations. And whatever words you might speak; it shall not persist among you, because the Lord God is with us" (Isaiah 8:8-10).- Cyril of Alexandria, "Against Those Who are Unwilling to Confess that the Holy Virgin is Theotokos," Part 1, Section 11.
So, quite the contrary, although Cyril believes that the Church will vindicate him, Cyril is bold to call these men heretics prior to any ecclesiastical decision on the matter. He doesn't wait for a council to condemn them, but argues that their positions are heretical on the strength of Scripture alone. May we be stirred up to follow this example of Sola Scriptura that we have seen in Cyril.
P.S. The following excerpt may also be interesting from the standpoint of a discussion on penal substitution:
When, therefore, this is the case, obviously, he demonstrated his love for us by means of a great philanthropy and has partaken of our own nature in order that he might raise it up and deliver it from bondage to the devil. No one, then, should be ashamed in hearing about a child and a baby and anything else that has been written about him in a purely human fashion. For he underwent all things not for his own sake, but for our sake. He preserved everywhere what is proper to human nature in order that the economy might not be regarded as a mere fiction.- Cyril of Alexandria, "Against Those Who are Unwilling to Confess that the Holy Virgin is Theotokos," Part 3, Section 26.