This is manifestly not true. What on earth do you think Rome was persecuting in those first three centuries?
The best answer I can offer to your idea is from a Catholic - and so, he (logically enough) identifies the Church as the Catholic Church. But as this deals with the first millennium, it can equally be referred to as the Orthodox Church. So I replace the word "Catholic" with "Orthodox" and find no change in meaning.
The entire chapter (chapter 2) should be read for completeness of thought, but here is an excerpt that shows Belloc's razor-like mind and aptitude for history:
"A word as to the constitution of the Church. All men with an historical training know that the Church of the years 200-250 was what I have described it, an organized society under bishops, and, what is more, it is evident that there was a central primacy at Rome as well as local primacies in various other great cities. But what is not so generally emphasized is the way in which Christian society appears to have looked at itself at that time.
The conception which the Catholic Church had of itself in the early third century can, perhaps, best be approached by pointing out that if we use the word "Christianity" we are unhistorical. "Christianity" is a term in the mouth and upon the pen of the post-Reformation writer; it connotes an opinion or a theory; a point of view; an idea. The Christians of the time of which I speak had no such conception. Upon the contrary, they were attached to its very antithesis. They were attached to the conception of a thing: of an organized body instituted for a definite end, disciplined in a definite way, and remarkable for the possession of definite and concrete doctrine. One can talk, in speaking of the first three centuries, of stoic_ism_, or epicurean_ism_, or neoplaton_ism_; but one cannot talk of "Christian_ism_" or "Christ_ism_." Indeed, no one has been so ignorant or unhistorical as to attempt those phrases. But the current phrase "Christianity," used by moderns as identical with the Christian body in the third century, is intellectually the equivalent of "Christianism" or "Christism;" and, I repeat, it connotes a grossly unhistorical idea; it connotes something historically false; something that never existed.
Let me give an example of what I mean:
Four men will be sitting as guests of a fifth in a private house in Carthage in the year 225. They are all men of culture; all possessed of the two languages, Greek and Latin, well-read and interested in the problems and half-solutions of their skeptical time. One will profess himself Materialist, and will find another to agree with him; there is no personal God, certain moral duties must be recognized by men for such and such utilitarian reasons, and so forth. He finds support.
The host is not of that opinion; he has been profoundly influenced by certain "mysteries" into which he has been "initiated:" That is, symbolical plays showing the fate of the soul and performed in high seclusion before members of a society sworn to secrecy. He has come to feel a spiritual life as the natural life round him. He has curiously followed, and often paid at high expense, the services of necromancers; he believes that in an "initiation" which he experienced in his youth, and during the secret and most vivid drama or "mystery" in which he then took part, he actually came in contact with the spiritual world. Such men were not uncommon. The declining society of the time was already turning to influences of that type.
The host's conviction, his awed and reticent attitude towards such things, impress his guests. One of the guests, however, a simple, solid kind of man, not drawn to such vagaries, says that he has been reading with great interest the literature of the Christians. He is in admiration of the traditional figure of the Founder of their Church. He quotes certain phrases, especially from the four orthodox Gospels. They move him to eloquence, and their poignancy and illuminative power have an effect upon his friends. He ends by saying: "For my part, I have come to make it a sort of rule to act as this Man Christ would have had me act. He seems to me to have led the most perfect life I ever read of, and the practical maxims which are attached to His Name seem to me a sufficient guide to life. That," he will conclude simply, "is the groove into which I have fallen, and I do not think I shall ever leave it."
Let us call the man who has so spoken, Ferreolus. Would Ferreolus have been a Christian? Would the officials of the Roman Empire have called him a Christian? Would he have been in danger of unpopularity where Christians were unpopular? Would Christians have received him among themselves as part of their strict and still somewhat secret society? Would he have counted with any single man of the whole Empire as one of the Christian body?
The answer is most emphatically No.
No Christian in the first three centuries would have held such a man as coming within his view. No imperial officer in the most violent crisis of one of those spasmodic persecutions which the Church had to undergo would have troubled him with a single question. No Christian congregation would have regarded him as in any way connected with their body. Opinion of that sort, "Christism," had no relation to the Church. How far it existed we cannot tell, for it was unimportant. In so far as it existed it would have been on all fours with any one of the vague opinions which floated about the cultured Roman world.
Now it is evident that the term "Christianity" used as a point of view, a mere mental attitude, would include such a man, and it is equally evident that we have only to imagine him to see that he had nothing to do with the Christian religion of that day. For the Christian religion (then as now) was a thing, not a theory. It was expressed in what I have called an organism, and that organism was the Catholic Church."
http://cnqzu.com/library/Philosophy/neoreaction/Hilaire Belloc/Europe and the Faith (HTML).htm
