Granted, the LXX is important in researching meaning. But of course it is only a translation, not the inspired original. I've compared many verses of the LXX to the Hebrew in many of the Psalms and in Proverbs 1-10 in my translation work, and it is quite often completely mistaken.I am not saying there is. 100% equlivance. To be fair, I don't know that there could be or of that should be our expectation.
My point with the LXX is not a 100% equlivance but a usage contemporary to the authorship of the NT.
I believe that Paul wrote 2 Corinthians to the Christians who lived in Corinth in the mid 1st century AD. So their understanding of word usage, even if not "proper", determines the meaning.
We have to allow for less than academic usages of words if common usages were sometimes less than academic.
The question is not whether the word should have been used for "sin offering" in the common language but if it was.
Did the people use the word for "sin" to mean "sin offering"?
Example - What does calling a person "nimrod" mean? It means they are a great hunter. But does it really?
Contemporary usage is certainly a factor--but not the most important one. New Testament usage trumps all other factors in determining NT Greek meaning. What you must do to prove your point, then, is to find a NT verse where hamartia by itself actually means "sin offering."
So, you did not deal with Hebrews 10:8, in which hamartia certainly does not mean "sin offering" since there is a Greek phrase of three words for that very meaning.
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