A reader asked about the origin of the biblical word be'ir בעיר, meaning "cattle" or "domesticated animals." Let's take a look.
It appears only six times in the Tanach: Bereshit 45:17; Shemot 22:4; Bamidbar 20:4,8,11, and Tehilim 78:48. In each case it refers to animals owned by humans. One verse in particular (Shemot 22:4) can perhaps shed light on where the word comes from:
כִּי יַבְעֶר־אִישׁ שָׂדֶה אוֹ־כֶרֶם וְשִׁלַּח אֶת־בעירה [בְּעִירוֹ] וּבִעֵר בִּשְׂדֵה אַחֵר מֵיטַב שָׂדֵהוּ וּמֵיטַב כַּרְמוֹ יְשַׁלֵּם׃
When a man lets his livestock loose to graze in another’s land, and so allows a field or a vineyard to be grazed bare, he must make restitution for the impairment of that field or vineyard.
Be'ir is translated here as "livestock." But in addition to be'ir we also have the verb בער bi'er, rendered here as "graze." In and of itself, that's not so surprising - animals do graze, and verbs and nouns are often related. The question is did the noun be'ir come from the verb בער, or did the verb provide us with the noun? I haven't found a conclusive answer to that question. Some sources say that the noun is the source (like Klein), others say the verb is the source (like Gesenius), and a surprising number aren't really sure (BDB, Ben Yehuda, Kaddari.)
One thing that is clear is that the verb בער has more than one meaning. In fact, another meaning is found in the very next verse!
כִּי־תֵצֵא אֵשׁ וּמָצְאָה קֹצִים וְנֶאֱכַל גָּדִישׁ אוֹ הַקָּמָה אוֹ הַשָּׂדֶה שַׁלֵּם יְשַׁלֵּם הַמַּבְעִר אֶת־הַבְּעֵרָה׃
When a fire is started and spreads to thorns, so that stacked, standing, or growing grain is consumed, he who started the fire must make restitution. (Shemot 22:5)
In this verse, בער means "to start a fire," and we also find the noun b'erah בערה - "burning, fire." The verbs in each verse have very different meanings (aside from some ancient Aramaic translations suggest that 22:4 is also talking about fire, not grazing). And as Cassuto put it in his commentary on Shemot, "there is clearly noticeable here a word-play in the use of the verb בער ba'ar in two different senses ['graze' and 'burn'] and in its proximity to the substantive בעיר be'ir ['cattle', 'beast']."
We've discussed the the possibility of biblical word play before, most famously in my post about ish and isha. But while that theory is subject to some controversy, these two verses make it very clear that the Torah is willing to use two words in proximity, with similar spellings but different meanings, even though it might lead to some confusion.
The verb בער has a number of meanings aside from "burn" (or "kindle, light") and "graze." It can also mean "to remove, eliminate, destroy." Which meaning is used in the phrase bi'ur chametz ביעור חמץ? Is it the removal of chametz from the home before Pesach, or the burning of that chametz? At first glance it would seem that this is the source of the debate in the mishna:
רַבִּי יְהוּדָה אוֹמֵר, אֵין בִּעוּר חָמֵץ אֶלָּא שְׂרֵפָה. וַחֲכָמִים אוֹמְרִים, אַף מְפָרֵר וְזוֹרֶה לָרוּחַ אוֹ מַטִּיל לַיָּם:
Rabbi Judah says: there is no removal of chametz except by burning; But the sages say: he may also crumble it and throw it to the wind or cast it into the sea. (Pesachim 2:1)
However, the halacha is that the chametz can be removed by any method, and the commentaries say that the disagreement between Rabbi Judah and the Sages is only about the ideal method to destroy the chametz. And while the Torah doesn't mention bi'ur in connection with chametz, it does mention removing the consecrated ma'aser food by using the verb בער (Devarim 26:13-14). In that case, it clearly means "removal", not "burning."
As I mentioned above, the linguists aren't certain about the origins and connections between the various meanings of בער. One possible line that runs between all of them is the sense of "consume," which could apply to both the grazing of animals and the burning of fire, and then be extended metaphorically to all removal or destruction.
One other meaning of בער is "to be brutish or foolish." This is actually related to the words we just discussed. It comes from be'ir, and so would literally mean "to act like an animal." The adjective ba'ar בַּֽעַר means "foolish, ignorant." As Philologos points out here, ba'ar is unrelated to both the Hebrew bur בור - "ignoramus" (connected to bar בר, which we discussed here) and the English "boor" (which also aren't related to each other.)