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In Numbers 24:17 Balaam says to Balak that all the children of Sheth will be destroyed. Who are these children?
In Genesis I read Enosh is a child of Sheth, and Noah is a grand-grand-grand-child so everyone living now is a descendant of Sheth. But what does Balaam mean?
The phrase you reference in the NASB (same wording in KJV, others) appears to come from וְקַרְקַר כָּל-בְּנֵי-שֵׁת (copied from the Hebrew University of Jerusalem, same text found elsewhere too). שֵׁת is almost always translated as Sheth or Seth, but there are those who have translated it differently. The meaning of the name is tumult. The meanings of names in Hebrew scripture will sometimes have more relevance than the actual names of the individuals (Naomi of Ruth fame being one example). Other suggestions, even less common (name of an otherwise unknown city, one of the specific princes that was sent to fetch Balaam, others) can be found here. There is meaning to be had from stripping the individuality from this particular word, but enough people seem to dispute that this meaning is the intended meaning (including the translators of your sourced translation, who used the word tumult often but Sheth only once in the entire text), that we will continue.
Yes, Sheth (or Seth) was a very famous son of Adam and Eve, and if it is the same one, then all the sons/children of Seth would in fact refer to every person born on earth in postdiluvian times, including speaker and listener. I find this conclusion plausible, as the topic of conversation here is decidedly not local or recent in scope, discussing an event far into the future that will impact the greatest (known to the speakers/listeners) military, political, and cultural organizations the world over.
The impetus of this question probably comes from the fact that the understanding for most believers of Hebrew scripture of the actions and intents of כּוֹכָב מִיַּעֲקֹב (translated Star ... come forth from Jacob in the sourced NASB above) are anathema to the "destroying every person" verbiage found in the NASB, and many other English translations of this passage. Frankly, some of the other English translations are gruesome and disturbing, and at a minimum lead one to doubt the identity of Sheth.
I don't have access to the notes of the various translators into English, so perhaps they had more information than I have, but the verb destroy appears to be translated out of the Hebrew קַרְקַר. A definition found here gives definitions of digging out (as in a well), breaking down (as in walls of a fortification), and refrigerate (probably not relevant here). Translation is both a science and an art, so I won't give an authoritative translation of this phrase, but others have. In this light, the verbs break down, uproot, and undermine seem plausible alternatives. To me, those verbs even convey similar ideas to Psalms 34, 51, and 147, for example, but now we are coming dangerously close to individual interpretations, which are always colored by personal beliefs.
Now, your second question, what does Balaam mean? Can't be completely sure, since I didn't say it, I didn't write it, and I wasn't even there... maybe ask someone who was? :)
The children of Sheth are carriers of the bloodline of the tainted Nephilim seed among the Moabites. In II Samuel 8:2 David gets them down to the ground and measures them with a line like a tape measure ( 6ft. Line?? ). One line you are normal size and can live, two lines you are a giant (nephilim) and must die.
Out of Jacob shall come he that shall have dominion, and shall destroy him that remaineth of the city.
-- Numbers 24:19 KJV
David was all about carrying out God's plan of Israel killing off all remaining Nephilim seed.
The Sheth in Numbers 24:17 could refer to an actual person who was a carrier of the Nephilim seed and also a well known giant as well as his family ( similar to Anak and the sons of Anak ) or just another reference to giant Nephilim relatives in general as I understand Sheth means 'tumult'
Given the larger context of the prophesy, it seems clear that this Sheth was a Moabite:
A star shall come forth from Jacob,
A scepter shall rise from Israel,
And shall crush through the forehead of Moab,
And tear down all the sons of Sheth.
