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Steve said,

Jer 31:31-34 (cf. Heb 8:8-12). '"Behold, the days are coming", says the LORD, "When I will make a new covenant with the house of Israel and with the house of Judah- not according to the covenant that I made with their fathers in the day that I took them by the hand to lead them out of the land of Egypt. But this is the covenant that I will make with the house of Israel after those days," says the LORD: "Iwill put My law in their minds, and write it on their hearts; and I will be their God and they shall be My people. No more shall every man teach his neighbour, and every man his brother, saying, 'Know the Lord', for they shall all know Me from the least of them to the greatest of them," says the LORD. "For I will forgive their iniquity and their sin I will remember no more"'.

This text says that the New Covenant will not be like the Old Covenant. The specific differences which are mentioned are:-
1. In the New Covenant, God's laws are written on the heart rather than on tablets of stone.
2. Everyone in the New Covenant knows the Lord
3. They all have their sins forgiven.
Steve,

In Jer 31 we see Jeremiah, under the inspiration of the Holy Spirit, picking up themes first expounded by Moses (Deut 30:1-10). Jeremiah prophesied that God would make a New Covenant with His people. As the institution of the Old Covenant (Exod 19-24) had followed the redemption from Egypt (Exod 12-15), so the formulation of the New Covenant would follow the redemption from exile (vs. 34). New Testament passages (1 Cor 11:15; 2 Cor 3:6; Heb 9:15, 12:24) reveal that the new covenant is fulfilled in Christ, who brought to fruitrition the Lord's desire for a renewed covenant relationship with His people. Even so, Christ in His first coming only inaugurated the new covenant. He continues to establish it during the time between His first and second coming and will establish it fully only at His return in glory. Please look at the text you selected, No more shall every man teach his neighbor, and every man his brother, saying, 'Know the Lord', for they shall all know Me from the least of them to the greatest of them. This promise will not be completely fulfilled until Christ returns. Only then will the Church be composed entirely of believers! Until then Christ says we see wheat and tares in His Church (Matt 13:24-30).

To apply your interpretation of these verses to the Church of today would entail believing everyone in the visible Church, without exception (2. Everyone in the New Covenant knows the Lord, 3. They all have their sins forgiven) is saved, a case which we both know is incorrect. cheers2

Reformed and Always Reforming,