The First Four Councils
The main, but only the main, conclusions of each of the first four Ecumenical Councils were specifically endorsed by both Calvin and Luther personally. These 4 councils are also mentioned by name in the (Calvinist) Second Helvetican Confession, Chapter 11 . The doctrines themselves are also in the Westminster Confession chapters 2 and 8, and the (Lutheran) AugsburgConfession Articles 1 and 3, amongst others.
Endorsing only the first four seems to imply there must have been some objection to the fifth. We may imagine Luther, in his Wittenberg study, going through the Councils in order and saying: Nicea, ok; First Constantinople , ok; Ephesus, ok, Chalcedon, ok; Second Constantinople, uh-oh, don't like this one.
But that would be a misunderstanding. The first four were particularly mentioned because of the great importance of the doctrines to which they bore witness. Pope Gregory the Great, who lived after the fifth Council, but before the sixth,wrote that he received and revered the first four Councils as he did the four gospels. He went on to say he also revered the fifth Council. It wasn't that Gregory had anything against the fifth, but it just wasn't, to him, such a big deal, doctrinally, as the first four. In this, Luther and Calvin concurred with him.
Furthermore, the Assyrian (Nestorian) Church accept only the first two Councils, objecting to the third; and the Oriental Orthodox (e.g. Coptic, not to be confused with Eastern Orthodox) accept the first three, objecting to the fourth. In accepting four the Reformers demonstrated their Catholicity in contrast to these groups.
Luther wrote On the Councils and the Church in 1539. In it he summed up the doctrines of the first four as follows.
The first, at Nicaea, defended the deity of Christ against Arius; the second, at Constantinople, defended the deity of the Holy Ghost against Macedonius; the third, at Ephesus, defended the one Person of Christ against Nestorius; the fourth, at Chalcedon, defended the two natures in Christ against Eutyches: — but they did not thereby establish any new article of faith. For these four articles are established far more abundantly and powerfully in St. John’s Gospel alone, even though the other evangelists and St. Paul and St. Peter had written nothing about them, though all these, together with the prophets, teach them and testify mightily to them.
Luther was adamant that these doctrines of these councils were fully proved in Scripture, and believed for that reason only. The Councils, per se, added nothing. It is convenient to refer to the doctrines by the names of the Councils, but they are not accepted merely by authority of the councils. At all councils there were bad mixed with good," like mouse-droppings in the pepper", as he put it. In any case, he said, he would "rather drink from the spring than the brook", by which he meant Scripture rather than Council.
Luther drew a distinction between the chief subject of a Council, that is the purpose for which the Emperor had called it, and the other matters it might take it upon itself to consider. He was quite scathing about most of the decrees of the even the first Ecumenical Council, that of Nicea.
The greater part of them is merely priests’ quarrelling : — there are not to be two bishops in one city; no bishop of a small church is to be ambitious for a greater one; clerics, or servants of a church, are not to leave their own church and slip hither and thither among other churches; no one is to ordain the people of any bishop without his knowledge and consent; no bishop is to accept a man who has been expelled by another bishop; the bishop of Jerusalem is to retain his ancient privilege of dignity above others; and more of that kind of talk.
Who can hold these things for articles of faith? What of them can one preach to the people in the Church? What difference do these things make to Church or people? Unless, of course, they are to be treated as a history from which one can learn that at that time, too, there were everywhere in the Church self-willed, wicked, disorderly bishops, priests, clergy, and people, who were more concerned about honours and power and wealth than about God and His kingdom, and that people needed to be on their guard against them.
Luther also ridiculed the Nicean canons on military service (12) and priestly castration (1). So it is clear that Luther did not regard any of the Ecumenical Councils as binding or even correct except as regards specific points which were, anyway, in the Bible, and accepted on that account alone.
In fact Luther goes further back, to the Council of Jerusalem in Acts 15 . The chief subject was whether Gentile Christians must obey the Mosaic Law. The decision: no. But to this was added a stipulation, proposed by James, about abstaining from blood. If people were to take that seriously, Luther pointed out, nobody would eat blutwurst. Since a ban on German sausages was so patently preposterous, it proved that the peripheral decrees of councils, even of the apostles never mind later bishops, could not to be taken seriously as having any permanent relevance. (Luther also moved James' epistle towards the back of German Bibles, but gave reasons unconnected with sausages.)
Calvin, in his Institutes of the Christian Religion, Book 4, Chapter 9, addresses "Councils and their Authority". In section 8 of this chapter he said of the four councils, and later ones:
Thus those ancient Councils of Nice, Constantinople, the first of Ephesus, Chalcedon, and the like, which were held for refuting errors, we willingly embrace, and reverence as sacred, in so far as relates to doctrines of faith, for they contain nothing but the pure and genuine interpretation of Scripture, which the holy Fathers with spiritual prudence adopted to crush the enemies of religion who had then arisen. In some later councils, also, we see displayed a true zeal for religion, and moreover unequivocal marks of genius, learning, and prudence. But as matters usually become worse and worse, it is easy to see in more modern councils how much the Church gradually degenerated from the purity of that golden age
While praising the four he is very much opposed to the seventh, which condemned iconoclasm and mandated images in church. This Second Council of Nice (757) is condemned by Calvin in Book 1, Chapter 11, section 14 of the Institutes. He ridicules some of the arguments used by the Council in "the absurd defence of the worship of images", and quotes approvingly from a refutation of the seventh council said to have been written by Charlemagne.
Protestant Doctrinal Standards On Councils Generally
The Westminster Confession states in Chapter 31, article 4
All synods or councils, since the apostles' times, whether general or particular, may err; and many have erred. Therefore they are not to be made the rule of faith, or practice; but to be used as a help in both
The first two articles of the Epitome of Concord in the Lutheran doctrinal standard say (abridged):
We believe, teach, and confess that the sole rule and standard according to which all dogmas should be estimated and judged are the prophetic and apostolic Scriptures of the Old and of the New Testament alone. ..... Other writings, whatever name they bear, must not be regarded as equal to the Holy Scriptures, but all of them together be subjected to them, and should not be received otherwise or further than as witnesses.
Article 21 of the Church of England says
General Councils may not be gathered together without the commandment and will of Princes. And when they be gathered together, (forasmuch as they be an assembly of men, whereof all be not governed with the Spirit and Word of God,) they may err, and sometimes have erred, even in things pertaining unto God. Wherefore things ordained by them as necessary to salvation have neither strength nor authority, unless it may be declared that they be taken out of holy Scripture.
So, to summarise, Protestants acknowledge the truth of the principal dogmas of the first four councils. They do not accord any power to any council to declare any doctrine by its own authority. They believe Councils can err, and have erred. Calvin, in particular, asserts that the Seventh Council erred.
The fifth and sixth, dealing with obscure and long-forgotten controversies of no particular interest, were simply not mentioned.
This was the position in the time of the Reformation.
Twentieth Century Lutheran/Orthodox Statements
In the latter half of the twentieth century a dialogue between the Lutheran World Federation and representatives of the Eastern Orthodox churches resulted in a series of agreements.
The Seventh Joint Declaration, 1993, refers to all seven Ecumenical Councils accepted by the Eastern Orthodox. These are First Nicea, 325; First Constantinople, 381; Ephesus, 431; Chalcedon, 451; Second Constantinople, 553; Third Constantinople, 680; and Second Nicea, 757. Paragraph 4 says the teachings of these Councils are normative for the Churches today.
Paragraph 5 includes the recognition that not all decisions on canonical matters have the same authority as the doctrinal decisions, and their reception and use in the Orthodox and Lutheran Churches differs.
Paragraph 6 says that the statements at the Councils went through a process of "reception" in the years after them, across the Church's life, worship, catechesis and service even when the councils were not explicitly named.
Paragraph 7 says that the teachings of the Ecumenical Councils are authoritative for both Lutherans and Orthodox, but goes on that the seventh was not part of the tradition received at the Reformation, and that it does not have the same significance for Lutherans as it does for Orthodox.
The Eighth Declaration in 1995 in paragraphs 5a and 5b, is perhaps clearer.
We agree on the doctrine of God the Holy Trinity, as formulated by the Ecumenical Councils of Nicea and Constantinople, and on the doctrine of Christ formulated by the first four Ecumenical Councils. The Fathers of the four Councils rejected the Arian and Eunomian notion that the Logos, the Angel of the Great Council, was created before the ages, and insisted that the Logos is "homoousious to Patri". They also rejected the Nestorian notion that the One born of the Virgin Mary was not the Logos himself and that the Logos only dwelled in the One who was born of the Virgin Mary. In short, the Fathers of these Councils affirmed that he who was born of the Virgin Mary is God by nature and not just by the will of the Father, and that he became homoousious with us in his humanity. The union of the divine and human natures in the hypostasis of the Logos is, according to the Council of Chalcedon, "without confusion, without change, without division and without separation". The Ecumenical Councils which followed continued this teaching and applied it to new challenges to the faith.
The Fifth accepted as orthodox two theological terminologies in the confession of the one Lord Jesus Christ. The Sixth affirmed the two natural wills and energies with their natural properties of the one person of the Logos incarnate. The Seventh drew conclusions from affirmation of the hypostatic union in Christ in order to confirm the veneration of icons. ..... We agree in these fundamental teachings.
Perhaps the most striking thing about this, for the purposes of this Question, is how very little there is to say about the Fifth Council, in comparison with the first four.