One kind reader of the Eastern Orthodox persuasion, using the handle "Orthodox," responded with a list of three quotations, which I've taken the liberty of beefing up by providing greater context. All of these come from the same work of John of Damascus, and we'll see a theme to them when we carefully examine them. I have maintained the order of the three quotations.
It is not without reason or by chance that we worship towards the East. But seeing that we are composed of a visible and an invisible nature, that is to say, of a nature partly of spirit and partly of sense, we render also a twofold worship to the Creator; just as we sing both with our spirit and our bodily lips, and are baptized with both water and Spirit, and are united with the Lord in a twofold manner, being sharers in the mysteries and in the grace of the Spirit.- John of Damascus, An Exact Exposition of the Orthodox Faith, Book 4, Chapter 12
Since, therefore, God is spiritual light [1 St. John i. 5.], and Christ is called in the Scriptures Sun of Righteousness [Mal. iv. 2.] and Dayspring [Zach. iii. 8, vi. 12; St. Luke i. 78.], the East is the direction that must be assigned to His worship. For everything good must be assigned to Him from Whom every good thing arises. Indeed the divine David also says, Sing unto God, ye kingdoms of the earth: O sing praises unto the Lord: to Him that rideth upon the Heavens of heavens towards the East [Ps. lxviii. 32, 33.]. Moreover the Scripture also says, And God planted a garden eastward in Eden; and there He put the man whom He had formed [Gen. ii. 8.]: and when he had transgressed His command He expelled him and made him to dwell over against the delights of Paradise, which clearly is the West. So, then, we worship God seeking and striving after our old fatherland. Moreover the tent of Moses [Levit. xvi. 14.] had its veil and mercy seat [Ibid. 2.] towards the East. Also the tribe of Judah as the most precious pitched their camp on the East [Num. ii. 3.]. Also in the celebrated temple of Solomon the Gate of the Lord was placed eastward. Moreover Christ, when He hung on the Cross, had His face turned towards the West, and so we worship, striving after Him. And when He was received again into Heaven He was borne towards the East, and thus His apostles worship Him, and thus He will come again in the way in which they beheld Him going towards Heaven [Acts i. 11.]; as the Lord Himself said, As the lightning cometh out of the East and shineth. The old translation gives occupat.even unto the West, so also shall the coming of the Son of Man be [St. Matt. xxiv. 27.].
So, then, in expectation of His coming we worship towards the East. But this tradition of the apostles is unwritten. For much that has been handed down to us by tradition is unwritten.
As you may have guessed, the particular part quoted was: "So, then, in expectation of His coming we worship towards the East. But this tradition of the apostles is unwritten. For much that has been handed down to us by tradition is unwritten"
Note, first of all, that this is appeal to tradition for a practice, not a doctrine. The claim that John of Damascus makes is that the apostles worshiped to the East and handed down this tradition of worshiping to the East.
Note, second of all, that John of Damascus explains the practice quite extensively from Scripture. Every doctrinal and symbolic basis for the practice has (at least in John of Damascus' view) Scriptural support.
Let's continue to the next quotation:
But besides this who can make an imitation of the invisible, incorporeal, uncircumscribed, formless God? Therefore to give form to the Deity is the height of folly and impiety. And hence it is that in the Old Testament the use of images was not common. But after God [St. John i. 14; Tit. iii. 4.] in His bowels of pity became in truth man for our salvation, not as He was seen by Abraham in the semblance of a man, nor as He was seen by the prophets, but in being truly man, and after He lived upon the earth and dwelt among men [Bar. iii. 38.], worked miracles, suffered, was crucified, rose again and was taken back to Heaven, since all these things actually took place and were seen by men, they were written for the remembrance and instruction of us who were not alive at that time in order that though we saw not, we may still, hearing and believing, obtain the blessing of the Lord. But seeing that not every one has a knowledge of letters nor time for reading, the Fathers gave their sanction to depicting these events on images as being acts of great heroism, in order that they should form a concise memorial of them. Often, doubtless, when we have not the Lord’s passion in mind and see the image of Christ’s crucifixion, His saving passion is brought back to remembrance, and we fall down and worship not the material but that which is imaged: just as we do not worship the material of which the Gospels are made, nor the material of the Cross, but that which these typify. For wherein does the cross, that typifies the Lord, differ from a cross that does not do so? It is just the same also in the case of the Mother of the Lord. For the honour which we give to her is referred to Him Who was made of her incarnate. And similarly also the brave acts of holy men stir us up to be brave and to emulate and imitate their valour and to glorify God. For as we said, the honour that is given to the best of fellow-servants is a proof of good-will towards our common Lady, and the honour rendered to the image passes over to the prototype. But this is an unwritten tradition, just as is also the worshipping towards the East and the worship of the Cross, and very many other similar things.- John of Damascus, An Exact Exposition of the Orthodox Faith, Book 4, Chapter 12
As you may have guessed, the quoted part was "But this is an unwritten tradition, just as is also the worshipping towards the East and the worship of the Cross, and very many other similar things."
Again, John of Damascus is alleging that the practice of giving honor to images is acceptable on the basis of it being an ancient practice of the church. Notice that John of Damascus is again appealing to tradition for the practice, not a doctrine.
The same can be seen from the next quotation which comes (in John of Damascus' book) directly after the quotation I provided above:
A certain tale [Evagr., Hist. iv., ch. 27.], too, is told [Procop., De Bellis, ii. ch. 12.], how that when Augarus [i.e. Abgarus.] was king over the city of the Edessenes, he sent a portrait painter to paint a likeness of the Lord, and when the painter could not paint because of the brightness that shone from His countenance, the Lord Himself put a garment over His own divine and life-giving face and impressed on it an image of Himself and sent this to Augarus, to satisfy thus his desire.- John of Damascus, An Exact Exposition of the Orthodox Faith, Book 4, Chapter 12
Moreover that the Apostles handed down much that was unwritten, Paul, the Apostle of the Gentiles, tells us in these words: Therefore, brethren, stand fast and hold the traditions which ye have been taught of us, whether by word or by epistle [2 Thess. ii. 15.]. And to the Corinthians he writes, Now I praise you, brethren, that ye remember me in all things, and keep the traditions as I have delivered them to you [1 Cor. xi. 2.].”
You will not be surprised that the quoted part this time is: "Moreover that the Apostles handed down much that was unwritten, Paul, the Apostle of the Gentiles, tells us in these words: Therefore, brethren, stand fast and hold the traditions which ye have been taught of us, whether by word or by epistle. And to the Corinthians he writes, Now I praise you, brethren, that ye remember me in all things, and keep the traditions as I have delivered them to you"
And again, the issue is one of orally transmitted practices, not doctrines. The legend of Jesus' supposed self-imaging is patently absurd, of course. Jesus' human appearance was ordinary. He took on a true human nature as well as a true divine naure. Can anyone seriously imagine that Jesus shone so brightly that a painter couldn't paint him, and yet Pilate would not be afraid to crucify him? Does anyone seriously think that Jesus shone so brightly that a painter couldn't paint him, but the Roman soldiers were not afraid to nail him to the cross? This foolish legend is a most desperate straw used by John of Damascus to try to bolster the fairly novel (though clearly not first-generation) use of images for worship (against the objections of Christians at that time).
Finally, John of Damascus' flawed reasoning has been picked up and expanded to matters not only of practice but also of doctrine by those who seek to deny the material and/or formal sufficiency of Scripture. Nevertheless, we do not - in any of the quotations provided above - see John of Damascus alleging that there are doctrines of the Christian faith that are not taught in Scripture and that are only transmitted orally from the apostles.