"Not according to the covenant that I made with their fathers in the day when I took them by the hand to lead them out of the land of Egypt, because they continued not in My covenant, and I regarded them not, saith the Lord." - Heb. 8:9 KJV
In the introductory study, we examined that only one of God's covenants was an 'agreement' between two parties--after the manner of ancient treaties. The above words can be spoken only of the covenant made at Sinai. All of the other covenants of God are wholly promissory. In reference to these covenants, the words 'they continued not in My covenant' are an impossibility. God alone fulfills the conditions of the promissory covenants. See Galatians 3:15-29.
In contemplating the facts about covenant, we see that it is impossible for God to do certain things. He cannot lie, he cannot fail, he cannot deny himself, he cannot sin. This illustrates the utter futility of the modern 'evangelical' theology of paradox, which proposes that almost any proposition is true to some extent. The Bible proposes that certain ideas are true and opposite ideas are false. Any apparent 'paradoxes' in the scriptures are to be resolved with much study, prayer, and reliance upon the Holy Spirit.
The theme of Hebrews 8:6-13 is the contrast between the Sinai covenant and the covenant promised in Jeremiah 31. In order to focus on what the New Covenant is, it is fruitful to examine all of the things that it is not: "not according to the covenant." All of the established denominations try and impose one or more of these false requirements from the Old Covenant on New Covenant believers. Don't go for it!
The New Covenant is not sabbatarian. Since there are so many laws attached to the covenant with Israel, it is easy to overlook the fact that it did not merely require the Sabbath to be kept: it was the Sabbath! (Ex. 31:16, 34:28; Deut. 4:13, Isa. 56:4-6). The covenant was in fact the decalogue, however, not all of the 10 commandments were of equal essence or meaning. The nine moral commands (applicable in any generation) were a hedge around the 'seal' of the Sabbath. That is why the words 'covenant' and 'Sabbath' are used interchangeably--in the same way that 'covenant' and '10 commandments' are so used.
When the New Testament says that the law-covenant is ended (2 Cor. 3, Gal. 3 & 4, Eph. 2:14-16, Col. 2:13-17, Heb. 10:1), it is saying that the Sabbath is ended! Many persons will argue that in doing away with the Sabbath, we are abolishing the other commandments. But it must be emphasized that the nine were simply a 'hedge' around the seal of the covenant--the fourth commandment. Disassociated from the law-covenant, the nine are still are applicable to us as laws to be written in the heart. There are no doubt some exceptions in letter--such as the apparent forbiddance of pictures.
In spite of this clear teaching of God's word, the centuries of Christendom are filled with continued attempts to impose first-day or seventh-day sabbatarianism upon believers. The whole Reformed movement has been devoted to a confessional and legalistic emphasis on Sunday as the Sabbath. We can't afford to compromise the implications of the gospel by allowing ANY form of sabbatarianism to be imposed upon us. Let us not raise again the 'wall of hostility' that separated the Jews from the nations.
The only Sabbath in the grace-covenant is Jesus and his everlasting rest! (Col. 2:17, Heb.4:9,10)