15 But as he which hath called you is holy, so be ye holy in all manner of conversation;
16 Because it is written, Be ye holy; for I am holy.
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God's call "be ye holy; for I am holy", was heard for the first time in the second part of the book of Leviticus, which, according to what is known of the history of the text of the Pentateuch today, was written in the ecclesiastical environment of Jerusalem in IX s BC. Before (and it is very visible from the first part of the same Book of Leviticus) the main task of the believers was the conservation of the ritual purity: because it is in particular it that gave the possibility to man to approach the altar, take part in the sacrifice and in the sacrificial meal, to be sanctified, entering in the presence of God, what was the main sense of all the yahviste sacrifices.
But such sanctifications in the spiritual life of Yahvistes of the early period were only episodes, although key episodes: for dwelling at the altar for a more or less extended period of time could only priests, and all the rest, at best could be there just for a few hours a week. And at that time, when appeared the second part of the book, if not to all, at least to some, was revealed that the state of sanctification ("the holiness") has to become for the people of God a norm, although how to reach this norm or at least to approach it, the book of Leviticus does not say, proposing only a little changed and partially widened norms of the ritual purity, mainly not distinguishing itself from what was applied in the earlier period.
There is nothing surprising here: because the task to live in the state of sanctification, to be in it constantly, was in fact the task of "room for growth": it could fundamentally be solved only in the Kingdom and only with the coming of the Messiah, although even it at the time, when sounded the call to holiness, was apprehended still quite vaguely. Centuries of the history of revelations, accomplished with the coming of Christ, were needed in order that the solution of the given task could become completely possible, without reductions on human sinfulness and indulgences connected to it.
And here is now the apostle returns to the call which sounded for the first time in the book of Leviticus, and certainly, well known to the first generation of the Christians knowing perfectly the Torah. He calls his coreligionists so that in their life there is no act which is incompatible with the state of sanctification ("the holiness"), as there was not in the life of the Savior Himself. And this call, of course is not a fate: because it is about the life in the Kingdom, which entirely is a sacred space, sanctified by the breath of God. The space, where will now live the Christians.