Are the terms Old Covenant or Old Testament used in reference to scripture? If so, how, why, and how so? Are they proper or right terms for scripture?
Does the Bible refer to a covenant in the Bible as old?
Is scripture, whether Torah or TaNaKh, properly referred to as the Old Covenant?
Does the term Old Covenant refer to the Torah while the term Old Testament refers to the TaNaKh with the arrangement into the 39 books ordered in a different way? I don't know this to be the case. The 39 books are either referred to as the Old Covenant or the Old Testament? Which came first? Are both used to refer to the 39 books, or just the term Old Testament? I heard once that the 39 books are the Old Covenant, I think, but I don't know if the first 5 books of the Bible have been referred to as the Old Covenant, or even if the term Old Covenant has ever been used in reference to Scripture. I believe the 39 books have been called the Old Covenant and the Old Testament. I am not certain of this, but I believe it to be true. I do not know why this is so.
Some believe the Old Covenant began with or involves a covenant God made with Adam and Eve. This makes a new covenant, or a second covenant, seen in a different way from what the writer of Hebrews appears to have intended, if I have read Hebrews correctly in the past. I have (also) wondered this before, but did not even think about this in my most recent reading of the book of Hebrews.
A first covenant and an old covenant are not the same thing, even if the first covenant is properly the covenant God made with the nation of Israel after the other covenants (first of the two not first in history), when speaking of the new covenant promised by God through the prophet Jeremiah and which came to be or alternatively came to be ratified in Yeshua or Jesus about 2000 years ago. If ratified either this means it came to be or that it had not yet come to be, the later of which I find highly unlikely or speculative. Scripture, or the Bible, reveals that the new covenant came to be in Jesus Christ and was spoken of afterward looking back in light of the present (and I believe the future as well, though not that it had not yet come to be even for the Jewish people or Israel) by Biblical writers or authors (a Biblical writer or author would be Paul, though he is not the only author or writer of New Testament books or letters to speak of the New Testament or even to make explicit mention of it). Consider, for example, the Gospel accounts. In these books we do find mention of the new covenant. The events recorded, of Jesus' life, refer to the new covenant in His own blood, which Paul came to understand later.
But, what is the new covenant according to the book of Jeremiah (the prophet Jeremiah, and what God had said through him in this book, and what we find in Jesus (Yeshua HaMashiach, Jesus the Christ) in His life recorded in the gospels (the gospel accounts) and about which was written afterward (writings afterward (other New Testament (Writings/)Scriptures), and even about Jesus' life though not in the same detail contained in the Gospels), and in teaching by the apostles to include Paul though the author of the book of Hebrews who mentioned what Jeremiah wrote or what we find in Jeremiah in reference to the new covenant was not mentioned by name in the book of Hebrews (found in the New Testament Writings or the New Testament Scriptures (New Testament Scripture or New Testament Scriptures, New Testament Writings) (Hebrews? for what is the New Testament and what is New Testament Scripture or the New Testament Writings, not necessarily). How the author of Hebrews meant, understood, or wrote what he did, and how it applied to his audience and us is important. But we must understand Jesus lived before this book was written, and the Gospels record Him speaking of the new covenant. So, to start, we need to look to or at Jeremiah the prophet to understand what the new covenant is and to whom it would come. It was to be a new covenant, not like the old which the people broke although God was a husband to them, but it would be for the house of Israel and the house of Judah and it would involve God's law being put within them and being written on their hearts, and He would be their (our if we are of Israel) God and they (us, if we are of Israel or are Israel) would be His people. It is important to be of Israel unless there are Gentiles or people from among the Gentiles grafted in(, and) whether they are called Gentiles any more or not. It is possible to be a believer, a member of the body of Christ, the church, and not be circumcised. This ends up being the same issue of whether or not you can be of Israel and not have been circumcised. Circumcision is not required to be a part of the church, the body of Christ, though it may or may not be required to be a part of Israel (according to the Law it (circumcision) is required to observe Passover and (as a part of the whole thing) be called among God's people Israel observing all of God's Law). The only other option for observing Passover, whether in the land (no, I think no) in Jerusalem (the requirement of the temple being there is there, and my understanding is that it is not there), or outside of the land, is that it would be a teaching Passover, whether Messianic or only or completely Jewish. That is, it may be true that some Gentiles have observed Passover without being circumcised though I have being a person who is circumcised. The question of whether or not Passover is to be continued to be observed, and if there will be a temple again one day, is there, in light of what Yeshua (Jesus) accomplished for us in dying for our sins (Christ our Passover (has been sacrificed for us (a picture of how He took our place as the lamb (from among the sheep or from among the goats (see Shemot (Exodus) 12:5))))) once for all (all time or all people, must read in context to understand and the reason for this question may not be apparent). Once was enough and all that is needed for you and I to be forgiven, given the Holy Spirit by faith in believing, and resurrected among the righteous to eternal life.
About the new covenant from Jeremiah... read Jeremiah 31:31-34 NASB or (edit- from) (an)other translation.