When did tradition become first used as Tradition?

Your question is quite loaded, but I will try to answer it from an Eastern Orthodox perspective.

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I will take the first sort of tradition that you refer ("pious, informed, well-meaning") to as being equivalent to what Jesus accused the scribes and Pharisees of in Matthew 15:1-2:

Then came to Jesus scribes and Pharisees, which were of Jerusalem, saying, Why do thy disciples transgress the tradition of the elders? for they wash not their hands when they eat bread.

I will take the second sort of tradition ("divine, sacred, God-breathed") that you refer to as being equivalent to what Paul refers to in his second Epistle to the Thessalonians (2:14):

Therefore, brethren, stand fast, and hold the traditions which ye have been taught, whether by word, or our epistle.

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In both cases the Greek word being used is παράδοσις - demonstrating the same sort of ambiguity in Greek that you imply there is in English. But the word simply means that which is given over: δοσις means something given, παρά- is a prefix that means aside, or from the side, or by. Other languages have similar etymologies (Latin trāditiō, Russian предание).

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There is no New Testament (or Septuagint) Scripture that literally defines any kind of παράδοσις as being "Divine, sacred," or "God-breathed". The latter term, "God-breathed" - Greek θεόπνευστος - was a term coined by Paul in his 2nd Epistle to Timothy (3:16) in reference to Scripture (γραφή), not tradition (παράδοσις):

All scripture is given by inspiration of God [θεόπνευστος], and is profitable for doctrine, for reproof, for correction, for instruction in righteousness

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This imprecision in language makes it difficult to answer your question as phrased, but if what you mean is, "When did the Eastern Orthodox Church begin to accept that which was not necessarily in Scripture on an equal basis with that which was?" then I suppose I would have to answer more or less from the beginning. There is evidence of this not only in Paul's letter to the Thessalonians, but in the words of Christ Himself in the Gospels:

Matthew 28:19-20

Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost: Teaching them to observe all things whatsoever I have commanded you

The Gospel teachings were παράδοσις "passed on" from Christ. As far as we know, Christ Himself did not write a single word of Scripture. The Apostles "passed on" the same παράδοσις to those they ministered to; and those presbyters and overseers they appointed did likewise. At some point, what they taught was documented in writing in what has come to be known as the "New Testament", but this was merely written documentation of what they had been passing down and what their successors had continued to pass down. In this sense, Scripture is subservient to "Tradition".

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If the question, however, is when did the Eastern Orthodox Church begin to accept teaching that was not Apostolic παράδοσις as genuine Apostolic παράδοσις, then the answer would be never. The entire raison d'être of the Ecumenical Councils was precisely to defend the Church against teachings that were not consistent with that passed down by the Apostles. In fact, just about anything that the Orthodox Church is attacked for today by Christians outside the Church (e.g. neo-iconoclasm) has probably been addressed in one or more of these same councils.

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The notion proposed (that there was a time when tradition became Tradition,) is interesting. In Roman Catholicism the following article I quote from agrees with a certain progression in what is considered to be tradition while claiming it to be at the base of all faith, yet there is one apparent sticking point where the article admits to problems with the later Marian traditions. This could be the Achilles' heel of the article.

I simply quote parts of this weighty article that have a bearing on my introductory comments. You must judge for yourself if this answers your question.

The article is called 'Tradition' and is written by Karl-Heinz Weger in the Concise Sacramentum Mundi of the Encyclopedia of Theology edited by Karl Rahner (1981 printing, Burns & Oates)

THE CATHOLIC NOTION OF TRADITION ...The words and signs of the apostolic testimony form the permanent basis of all Christian tradition... One of the great achievements of Vatican II was to free the Catholic notion of tradition from the narrow limits to which it had been confined, chiefly in the post-Tridentine period. In the Dogmatic Constitution on Revelation, tradition does not appear primarily as a certain amount of matter, always the same, handed on in propositions and practices. The tradition of the Church is rather faith as lived: "The Church, in her teaching, life and worship, perpetuates and hands on to all generations all that she herself is, all that she believes. (Vebum Dei, art. 8) "

So, what does this liberated view of tradition amount to now? The word is never given a capital 'T' in the article. No Pope is invoked as progressing the 'new view' of tradition. It seems to become something altogether more fluid, or, to put it as an illustration, this is like trying to nail jelly to a wall. Here is a point raised in the article that demonstrates this difficulty.

The author admits that Protestants have raised the issue of comparatively recent Marian dogmas as needing to be addressed. He insists that those Marian dogmas of recent times,

"are permanently valid actualizations of Scripture. This poses a question for Catholics, which a priori they must answer in the negative, as to whether something 'new' has not here been defined as revelation, though it stems only from post-apostolic times and hence is no more than a pious custom, venerable perhaps by reason of its antiquity. ...But the true preaching of the faith always calls for a new assimilation and translation of the traditional faith as well as loyalty to revelation and its historical transmission."

Well, that seems to be the perfect illustration of a tradition that is admittedly not apostolic (otherwise evidence of the Apostles having adored Mary would have been forthcoming) being denied as a new revelation. This is a tradition that has not been developed from Scripture at all. This exposes as false the claim in the article that,

"tradition, in this sense, is not only prior in time to any crystallization of it in Scripture, but is also at the base of all faith."

To lend substance to this claim, the article goes on to quote from Die Verbum, art. 11 that the books of Scripture only teach

"faithfully, firmly and without error that truth, which God wanted put into the sacred writings for the sake of our salvation" This is ALSO TRUE OF THE INFALLIBLE UTTERANCES OF THE POST-APOSTOLIC TRADITION OF THE CHURCH." [Capitals mine]

This is the Achilles' heel of the article. The jump from denying that Catholic tradition is anything new to claiming that recent Marian traditions are "permanently valid actualizations of Scripture" fails. Of course, it does not fail in the view of the author of the article or in the view of Catholics who stick to their Church traditions as originating from the Apostles. It is simply the lack of Scriptural and/or Apostolic proof that Mary be venerated which shows such a tradition to have no actual validation from Scripture, or the Apostles. This would appear to be an example of what you are seeking - a time when, in church history, an idea of tradition apart from Scripture became equivalent to Scripture. That example would be when Mary began to be adored and prayed to. But there could be earlier examples of other traditions elevated to the status of equal to Scripture. I don't know. I simply highlight one provided in this article by the author.

However, the article gives this further quotation from Dei Verbum, art. 9, which appears to be worthy of 'the last word' on this question:

"Consequently, it is not from sacred Scripture alone that the Church draws her certainty about everything which has been revealed." Tradition (or its content) in the strict sense, which has been the subject of discussion up to now, that is, the doctrines of faith defined in post-apostolic times by the Church and its magisterium, must be clearly distinguished from the broad stream of traditions which also took form in other ways in the course of Church history."

This is actually a very interesting question, which we could rephrase as "When did Tradition [in the Catholic/Orthodox sense] became a Dogma?"

Every historical declaration of dogma/doctrine by the Catholic Church is recorded in the Enchiridion (usually cited as DS; English version online here). Therefore, we can search that document for "tradition". As can be seen from the quotes and the heading in the DS document however, this concept is in the beginning often found tied with that of "Infallibility of the Roman Pontiff". In effect, under the view of the Catholic Church these are inseparable because, as expressed in Lumen Gentium:

In virtue of his office, that is as Vicar of Christ and pastor of the whole Church, the Roman Pontiff has full, supreme and universal power over the Church. And he is always free to exercise this power. The order of bishops, which succeeds to the college of apostles and gives this apostolic body continued existence, is also the subject of supreme and full power over the universal Church, provided we understand this body together with its head the Roman Pontiff and never without this head. This power can be exercised only with the consent of the Roman Pontiff. For our Lord placed Simon alone as the rock and the bearer of the keys of the Church, and made him shepherd of the whole flock;(Jn 21,15f.) it is evident, however, that the power of binding and loosing, which was given to Peter,(Mt 16,19) was granted also to the college of apostles, joined with their head.( Mt 18,18; 28,16-20)

So, if we look for these concepts, we can find the following, in chronological order:

417 AD: Pope (saint) Innocent I, in the letter In requirendis, writes:

In seeking the things of God . . . preserving the examples of ancient tradition . . . you have strengthened the vigor of your religion . . . with true reason, for you have confirmed that reference must be made to our judgment, realizing what is due the Apostolic See, since all of us placed in this position desire to follow the Apostle, from whom the episcopate itself and all the authority of this name have emerged. Following him we know how to condemn evils just as (well as how) to approve praiseworthy things. Take this as an example, guarding with your sacerdotal office the practices of the fathers you resolve that (they) must not be trampled upon, because they made their decisions not by human, but by divine judgment, ...

418 AD: The letter Quamvis Patrum traditio by Pope saint Zosimus:

Although the tradition of the Fathers has attributed such great authority to the Apostolic See that no one would dare to disagree wholly with its judgment, and it has always preserved this judgment by canons and rules, and current ecclesiastical discipline up to this time by its laws pays the reverence which is due to the name of PETER, from whom it has itself descended . . . ; since therefore PETER the head is of such great authority and he has confirmed the subsequent endeavors of all our ancestors, so that the Roman Church is fortified . . . by human as well as by divine laws, and it does not escape you that we rule its place and also hold power of the name itself, nevertheless you know, dearest brethren, and as priests you ought to know, although we have such great authority that no one can dare to retract from our decision, yet we have done nothing which we have not voluntarily referred to your notice by letters . . . not because we did not know what ought to be done, or would do anything which by going against the advantage of the Church, would be displeasing.

422 AD: Pope (saint) Boniface I also wrote a doctrinal document with these issues, but it is a bit too long to put here. See the DS website linked above. It has the same type of "indirect" claims.

433 AD: Pope (saint) Sixtus III says (in the Latin version, sorry):

De Dei autem Genetrice Virgine quemadmodum et sapimus et dicimus et de modo humanationis unigeniti Filii Dei necessariae, non additamenti causa, sed ad satisfactionem proprie desuper tam de divinis scripturis quam de traditione sanctorum patrum adsumentes habuimus, breviter dicimus, nihil omnino addentes fidei sanctorum patrum, quae in Nicaea exposita est.

The key is where he says (my translation) that the Truth about the human nature of Jesus through Virgin Mary, "has been received from old, both from the sacred Scriptures and the tradition of the Holy Fathers".

There are plenty of these - some might argue - "indirect" mentions. Yet, the issue seems to become clearer over time. One of the last examples is from Pope (saint) Simplicius, in 476 AD, and found under the heading of "The Unchangeableness of Christian Doctrine":

Those genuine and clear [truths] which flow from the very pure fountains of the Scriptures cannot be disturbed by any arguments of misty subtlety. For this same norm of apostolic doctrine endures in the successors of him upon whom the Lord imposed the care of the whole sheepfold [John 21:15 ff.], whom [He promised] He would not fail even to the end of the world [Matt. 28:20], against whom He promised that the gates of hell would never prevail, by whose judgment He testified that what was bound on earth could not be loosed in heaven [Matt. 16:18 ff.]. (6). . . Let whoever, as the Apostle proclaimed, attempts to disseminate something other, than what we have received, be anathema[ Gal. 1:8 f.]. Let no approach to your ears be thrown open to the pernicious plans of undermining, let no pledge of revising any of the old definitions be granted, because, as it must be repeated very often, what has deserved to be cut away with the sharp edge of the evangelical pruninghook by apostolic hands with the approval of the universal Church, cannot acquire the strength for a rebirth nor is it able to return to the fruitful shoot of the master's vine, because it is evident that it has been destined to eternal fire.

Yet, what seems to be the first direct treatment of this as doctrine (i.e. in the DS), occurs in the acts of the Council of Constantinople, in 553 AD. We read, under the heading of "Ecclesiastical Tradition" :

We confess that (we) hold and declare the faith given from the beginning by the great God and our Savior Jesus Christ to the Holy Apostles, and preached by them in the whole world; which the sacred Fathers both confessed and explained, and handed down to the holy churches, and especially [those Fathers] who assembled in the four sacred Synods, whom we follow and accept through all things and in all things . . . judging as at odds with piety all things, indeed, which are not in accord with what has been defined as right faith by the same four holy Councils, we condemn and anathematize them.

From all this, I conclude that, just as so many other dogmas, and without diminishing the value of such clarified truth (see below), the Church came to realise about the dogma of Tradition over several centuries, and was declared as such in 553 AD. Importantly, this does not mean that other Early Church Fathers did not write about it (even in dissimilar ways like Irenaeus or Augustine). It only means that it was not "entrenched" as doctrine until later.

I think it is worth adding here perhaps the clearest doctrinal declaration on the issue of the sources of Revealed Truth. It comes (perhaps unsurprisingly) from the fourth session (1546) of the Council of Trent. The entry in the DS is as follows:

The sacred and holy ecumenical and general Synod of Trent, lawfully assembled in the Holy Spirit, with the same three Legates of the Apostolic See presiding over it, keeping this constantly in view, that with the abolishing of errors, the purity itself of the Gospel is preserved in the Church, which promised before through the Prophets in the Holy Scriptures our Lord Jesus Christ the Son of God first promulgated with His own mouth, and then commanded "to be preached" by His apostles "to every creature" as the source of every saving truth and of instruction in morals [Matt. 28:19ff., Mark 16:15], and [the Synod] clearly perceiving that this truth and instruction are contained in the written books and in the unwritten traditions, which have been received by the apostles from the mouth of Christ Himself, or from the apostles themselves, at the dictation of the Holy Spirit, have come down even to us, transmitted as it were from hand to hand, [the Synod] following the examples of the orthodox Fathers, receives and holds in veneration with an equal affection of piety and reverence all the books both of the Old and of the New Testament, since one God is the author or both, and also the traditions themselves, those that appertain both to faith and to morals, as having been dictated either by Christ's own word of mouth, or by the Holy Spirit, and preserved in the Catholic Church by a continuous succession.

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Having said this, the way you put the question is loaded, particularly knowing that you do not believe Tradition is a valid concept at all. Why is it loaded? Because for someone who does not believe in it, tradition became [wrongly] Tradition at a given time, because of non-supernatural inspired human decision. The answer to this perspective is then (if correct), the one given above. For someone who believe Tradition is Revealed Truth however, we know that the Catholic Church (Orthodox?) tells us that the establishment of a Dogma is not the creation of new truths, but the clarification of already Revealed Truths, made possible through the passage of time. Thus, in this sense, tradition never really became Tradition, since it always has been (as in the other answer).