Are the Ten Commandments Written on Our Hearts?

Sadly many people think that Jeremiah 31:31-34 (see below), and then Hebrew's quoting of it, is referring to the Ten Commandments / the law of Moses, when it doesn't say that at all. And in fact the law of Moses is called "the ministry of death" and "the ministry of condemnation" (2 Cor 3:7-9), and Paul says that the purpose of the law is to shut mouths and make people guilty (Rom 3:19). The passage in Jeremiah says that God will remember their sins no more, which is the opposite of what happened through the law. Paul says that the law is the strength of sin (1 Cor 15:56) and that the law entered so that sin might abound (Rom 5:20).

Because of all this - because the law was "against us" and "contrary to us" (Col 2:14) - Paul writes that the law was "wiped out," "taken out of the way" and "nailed to the cross" (also Col 2:14), and Eph 2:15 says that the law of commandments was "abolished in His (Jesus') flesh." And on top of all this, the very passage in Hebrews in which the passage from Jeremiah is quoted says that it was made obsolete, and it says that the New Covenant is "not according to the covenant that I made with their fathers."

So the law written in the hearts is not the law of Moses / the Ten Commandments. That would be God writing the ministry of death, condemnation, guilt and bondage in the hearts of men, and would go against the entire New Covenant! The "laws" that are not according to the Old Covenant are the "law of faith" (Rom 3:27) and the "law of the Spirit of life in Christ Jesus," which has "made me free from the law of sin and death" (Rom 8:2). We know that the law of Moses is "not of faith" (Gal 3:12) and again we know that the law of sin and death (and guilt, bondage and condemnation) is the law of Moses.

So this really is a new Covenant! It really is a "new and living way!" It's nothing like the Old. It doesn't derive anything from the Old. It's new, and the meaning of the Greek word for new in this case is "of a new kind, unprecedented." It's something that has never been before. Be default and by definition it cannot be based upon the Law of Moses / the Ten Commandments. The Old has gone and the New has come!

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Jer 31:31-34
31 "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 —  32 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, My covenant which they broke, though I was a husband to them, says the Lord. 33 But this is the covenant that I will make with the house of Israel after those days, says the Lord: I will put My law in their minds, and write it on their hearts; and I will be their God, and they shall be My people. 34 No more shall every man teach his neighbor, and every man his brother, saying, 'Know the Lord,' for they all shall 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."
NKJV

Heb 8:7-13
7 For if that first covenant had been faultless, then no place would have been sought for a second. 8 Because finding fault with them, He says: "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 —   9 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 did not continue in My covenant, and I disregarded them, says the Lord.  10 For this is the covenant that I will make with the house of Israel after those days, says the Lord: I will put My laws in their mind and write them on their hearts; and I will be their God, and they shall be My people.  11 None of them shall teach his neighbor, and none his brother, saying, 'Know the Lord,' for all shall know Me, from the least of them to the greatest of them.  12 For I will be merciful to their unrighteousness, and their sins and their lawless deeds I will remember no more."

13 In that He says, "A new covenant," He has made the first obsolete. Now what is becoming obsolete and growing old is ready to vanish away.