Is it saying the sabbath "is an everlasting covenant for the sons of Israel" OR what he does "before the LORD"?
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The translation "everlasting" is of the hebrew word
olam which comes from the primitive root word
alam meaning concealed or hidden. Not in all cases but in many cases the hebrew word
olam should have been translated as "a hidden or concealed time" and in some cases "a long time" or "long lasting".
Just look at some of the other scriptures where "
olam" was translated as "everlasting". We know by reading further along that many of the incidents where "everlasting" is used, have already ended, especially those concerning the Aaronic and Levitical priesthood and their practices.
The sabbath itself was just a antitype or shadow of something which was to come sometime later, which is Christ Jesus.
In the scripture that you posted, Leviticus 24:1-8,
olam would be better transalted to "long lasting" covenant. But regardless of how one wants to translate it, the fact is we now know that according to the writer of Hebrews that God had not intended that covenant to be everlasting.
Hebrews 8:7-13
7*
If the first covenant had been faultless, there would have been no need for a second covenant to replace it. 8 But God himself found fault with the old one when he said:“
The day will come, says the Lord,
when I will make a new covenant
with the people of Israel and Judah.9* This covenant will not be like the one
I made with their ancestors
when I took them by the hand
and led them out of the land of Egypt.
They did not remain faithful to my covenant,
so I turned my back on them, says the Lord.
10* But this is the new covenant I will make
with the people of Israel on that day, says the Lord:
I will put my laws in their minds
so they will understand them,
and I will write them on their hearts
so they will obey them.
I will be their God,
and they will be my people.
11* And they will not need to teach their neighbors,
nor will they need to teach their family,
saying, ‘You should know the Lord.’
For everyone, from the least to the greatest,
will already know me.
12* And I will forgive their wrongdoings,
and I will never again remember their sins.”*
13*
When God speaks of a new covenant, it means he has made the first one obsolete. It is now out of date and ready to be put aside.