This is probably more of a request for clarification than a suggestion for translation change. I wonder why 1000's of translators, including Berean Patriot, have chosen to render the last sentence "Against such things there is no law"? It seems to mean that there is significant evidence that "ou" could mean "nothing" given proper context. Further, in my limited understanding, "kata" strongly suggests a sense of prioritization or ordering. It is commonly rendered "down" or "accordingly" rather than "against." Even the English word "against" carries connotations of "as opposed to," "versus" or " compared to."
Then the context of the passage. Paul has just spent all of Galations 3, 4, and 5 contrasting grace versus law and demonstrating how grace, faith, spirit and freedom are superior in every way. Then, he is essentially wrapping up his theological argument and he goes for the power punch and says, " By the way, these things are also not forbidden by that law that you are not supposed to be obsessed with anyway" Or maybe he's saying it in a super snarky, sarcastic way. But, that doesn't really seem very Paul-like even after he's just wished castration on the pro- circumsicion crowd. Nobody really believed that the law required you to not do all those spiritual fruit things, so it can't be that, right?
It seems much more likely to me and fitting to the context that he is saying "In any comparison of the two, the law is so inferior, that it doesn't even measure, it's nothing". Therefore, my extremely uneducated perspective is that a better reading would be "(Compared) against such things the law is nothing."
So, why does almost no one but extreme paraphrasers do that?
So, to ou/ouk, remember that Greek does have a word which means "nothing". It's "οὐδείς" (oudeis). Paul didn't use oudeis in Galatians 5:23. He uses it in plenty of places, but not there. The reason almost no one translates ouk as "nothing" is because it doesn't mean "nothing". Ouk functions as a negating word, like "not" in English. It would be a rare case indeed where ouk could be translated "nothing" and accurately capture the sense of the verse.
Consider a simple English sentence like "He did not fight." Rendering "not" as "nothing" would look like this: "He did nothing fight." That's pretty nonsensical, and the same principle can be applied to ouk in Greek.
Now, looking at the passage you have: "ouk estin nomos", or "not is law". Looking at the placement, ouk (not) is modifying estin (is), so "isn't a law" would be woodenly literal. Making it readable, "there isn't a law" would be the most accurate way to translate it and be readable. I realized after reading your comment that I put the negation on the wrong word ("is not" vs. "no law") and I've thus changed the translation to be "there isn't a law against such things.", with a phrase order change for readability.
To kata, "against" is actually a primary meaning/usage of the word. Look at Thayer's definition I.2.b. which specifies that when paired with a genitive - which it is here - and used in a metaphorical sense - again which it is here - "against" is the proper understanding. Remember that the meaning of Greek prepositions like kata are dependent on the grammatical case they are paired with. Thus, "against" fits here.
Does that makes sense and answer your question?
Compare 1 Cor. 7:19, where Paul actually uses "is nothing". This would be used in Gal. 5:23 too, if that was the intended meaning. Also compare Mark 9:40 and Luke 9:50, where both expressions are used. This is their meaning in Gal. 5:23 too. Gal. 1:11 uses "according to", but it has different grammatical case. Therefore, Berean Patriot is correct from the language perspective.
From the perspective of interpretation (i.e. the wider context), saying that the law is nothing would be unbiblical. Jesus was bold on it (Luke 16:17). The spirit of the law (Rom. 7:14) has always been and will always remain the same (Heb. 9:14). When Paul says that the fruit of the spirit is love, he basically echos both Jesus (Mat. 22:40) and himself (Rom. 13:8), that the spirit of the law is love. Therefore, the law is not nothing (Ps. 119:97) and is not compared against love. The law is closely related to love, as a written expression of it. More specifically to Galatians (especially 5:6), the practice of circumcision is nothing (1 Cor. 7:19), but the spirit of circumcision remains unchanged (Rom. 2:29).
So it should indeed be obvious that the law doesn't oppose love (Jam. 2:8), however Paul may be making a rephrasing of verse 18, that the spirit is not under the law (1 Tim. 1:9). Given that the fruit of this spirit is in every righteousness (Eph. 5:9), it automatically fulfills the law (Rom. 8:4). It is not that the law vanishes, but that it finds its proper position (Jer. 31:33).
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