This is a muddled mess.
I am going to try to interject some clarity into this discussion.
Before I say anything, there are a couple things I want to point out.
1) Merely asking "Do Moses and Jesus Have Equal Authority Over the Believer?" is silly. I assume by "Moses" you mean the books that he wrote--the Torah/pentateuch/first 5 books of the Bible and by Jesus you are referring to the new covenant. No believer in this thread has advocated that the new covenant is inferior or subservient to the old covenant. No one.
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There are several different outlooks on the law and grace.
The first outlook is this: The new covenant is merely an addition to the old covenant. Therefore the old covenant law is binding upon a believer, but the sacrificial portions of it are fulfilled by Jesus. We still must rest on the Sabbath, tithe, and put fences on the roof of our house. We also should abstain from catfish, pork, etc. Righteousness, holiness, and salvation are gained by works and maintained by works. Faith is coupled with works and produces salvation.
An equation to sum up this view is this:
Faith + Works(Righteousness and Holiness) = Salvation
They view every stitch of scripture as rules by which to live.
No one on this thread is advocating this position. Not one single person.
The 2nd outlook is this: Jesus is a continuation of the old covenant. He has fulfilled the law in our stead and has revealed the true purpose and point of the law--proving that we are sinful. Righteousness and Holiness are gained through faith in Jesus Christ, which are a result of salvation. The law is written upon our hearts and by truly loving God and loving people, we walk in holiness.
This equation shows this position
Faith = Salvation(righteousness) + Works(Holiness)
The view of the scriptures is that all of them are binding upon the believer, but all of it is routed through the atoning work of Jesus Christ. So there must be a sacrifice for me to be atoned for--Jesus fulfilled that. I must honor the Sabbath and keep it holy--Jesus is the fulfillment of that. I must love my neighbor. Jesus is the fulfillment of that. I must not lie. Jesus makes that happen. The old covenant is fulfilled in Christ and the law and it's true intent and purpose are written on the hearts of believers so that by loving God and loving our neighbor, we fulfill all of the law through Jesus Christ.
A 3rd view is this: Jesus cancelled the old covenant totally and instituted a new one. The OT law has been abolished and the "Law of Grace" has been instituted. In this view salvation is gained by faith in Christ. None of the OT law is applicable to the believer. Only what is found in the new covenant counts.
This view is highly compatible with the 2nd view. However, I have NEVER in my life heard the idea that the entire OT was the law. Pslams, proverbs, Ruth, Lamentations, Micah, Daniel, all get lumped together as "Law". So if this is the standard stance for New Coventant Theologians, then this is where the breakdown occurs
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We can all agree that salvation is attained by faith alone.
We can all agree that righteousness comes through faith in Christ and by no means through the fulfillment of any moral actions (law or not).
We can all agree that those who are truly converted should not live by rules or regulations, but in Christ through the Spirit.
So we need to quit debating about whether the OT law is binding on the believer or not. No one in here says it is.
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The REAL issue is the authority of the scriptures.
Let me, once again, post what our brother Paul of Tarsus said to Timothy:
All Scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness, that the man of God may be complete, thoroughly equipped for every good work.
Let's not skip and dance around this anymore.
Everyone agrees that the OT is divinely inspired. However, this verse also says that it is:
1) Profitable for Doctrine
2) Profitable for Reproof
3) Profitable for correction
4) Profitable for INSTRUCTION IN RIGHTEOUSNESS
5) Makes us complete
6) Makes us equipped for every good work.
You can't avoid that. The OT is useful and I CAN derive doctrine out of it without being pegged a legalistic Christian.
So let's look at what Jesus said about fulfilling the law in it's context:
Do not think that I came to destroy the Law or the Prophets. I did not come to destroy but to fulfill. For assuredly, I say to you, till heaven and earth pass away, one jot or one tittle will by no means pass from the law till all is fulfilled. Whoever therefore breaks one of the least of these commandments, and teaches men so, shall be called least in the kingdom of heaven; but whoever does and teaches them, he shall be called great in the kingdom of heaven. For I say to you, that unless your righteousness exceeds the righteousness of the scribes and Pharisees, you will by no means enter the kingdom of heaven.
Saying that this simply means that Jesus came to live under the law is not accurate. Every stitch of the law AND the prophets has been / will be fulfilled once the end comes. All of it, but it will be fulfilled in Christ. Not in our own efforts. From Genesis to Malachi, all of it will be fulfilled in Christ. It hasn't all been fulfilled yet. Reading any of the OT prophets and the Psalms will prove that. Even Genesis 3:15 hasn't met it's entire fulfillment yet. Look at what the writer of Hebrews said in regards to the old covenant rest vs. the new covenant rest:
Let us therefore be diligent to enter that rest, lest anyone fall according to the same example of disobedience. For the word of God is living and powerful, and sharper than any two-edged sword, piercing even to the division of soul and spirit, and of joints and marrow, and is a discerner of the thoughts and intents of the heart. And there is no creature hidden from His sight, but all things are naked and open to the eyes of Him to whom we must give account.
According to the author of Hebrews, the word of God is a "discerner of the thoughts and intents of the heart." Sounds like he is deriving doctrine from it. As did Jesus and Paul and the other NT writers who made reference after reference and gave quote after quote of the first 39 books of the Bible. AGAIN AND AGAIN AND AGAIN AND AGAIN.
Also, dividing the law into moral, ceremonial, and judicial law is merely a means of explanation for how the law relates to believers. I never use it, personally. Just like using the water, steam, ice explanation for the Trinity can be useful, it doesn't totally explain how it all works.
As believers, the law is written on our hearts. They have been put into us.
I don't murder people. I just don't do it. Why? Because the law says not to? No! Because I love people and I love God.
I also don't seek vengence. Not because I am better than everyone, but because I love people and I love God.
I seek justice for the innocent. Is there a verse in the NT that says explicitly that I should do that? No. I do it because I love God and I love people.
This is the law written upon our hearts brothers and sisters and the OT is slap full of examples of how to live that out!!
God read Hebrews 11 and see how much the OT is refered to. He isn't taling about law! He is talking about the examples that God has given to us.
Paul said this same exact thing:
Now these things became our examples, to the intent that we should not lust after evil things as they also lusted. And do not become idolaters as were some of them. As it is written, "The people sat down to eat and drink, and rose up to play.” Nor let us commit sexual immorality, as some of them did, and in one day twenty-three thousand fell; nor let us tempt Christ, as some of them also tempted, and were destroyed by serpents; nor complain, as some of them also complained, and were destroyed by the destroyer. Now all these things happened to them as examples, and they were written for our admonition, upon whom the ends of the ages have come.
Not only is Paul appealing to the OT, he is appealing to the first 5 books of the Bible, wherin the Law is contained! Not only that, but Paul said, "they were written for our admonition, upon whom the ends of the ages have come."
You CANNOT escape the reality that the OT is useful for us.
You have to maintain BAD THEOLOGY in order to do so.