How plausible is a Midianite / Ishmaelite switchoff?

Please read part one and part two first. These posts argue forcefully for a position, put forth in Ibn Ezra, that in parshat Vayeshev, the Midyanim are the same as the Yishmaelim. Thus, Ibn Ezra says:

ויעברו-וכאשר עברו עליהם הישמעאלים הסוחרים, כי המדינים יקראו ישמעאלים. 
וכן אמר על מלכי מדין כי ישמעאלים הם.

From a pasuk in Shofetim, we see that Midyanim can be called Yishmaelim. What logically follows from this is the following scenario:

1) Yosef initially comes to his brothers and they aim to slay him directly.
2) Reuven intercedes, arguing that they should kill him indirectly by letting him perish in the pit.
3) The pasuk tells us, then and there, that Reuven's aim was to save Yosef and return him to Yaakov.
4) Reuven apparently disappears*, as a first step to carrying out this plan, and the brothers who stay to eat, at some distance from the pit, are a subset of all brothers.
5) In Reuven's absence, a caravan of Midianites appears, heading towards Egypt. The Torah refers to these Midyanim initially as Yishmaelim.
6) Yehuda does not know of Reuven's plan, and sets his own plan into motion, to save Yosef's life.
7) Yehuda suggests that they sell Yosef to the Yishmaelim / Midyanim who are passing by.
8) The brothers agree.
9) The Midyanim, who are the same as the Yishmaelim, arrive. Now is the time to carry out the plan the brothers have agreed to.
10) The brothers draw Yosef out of the pit and sell him to the Midyanim / Yishmaelim.
11) Reuven has let some time pass, so that he can sneak back to the bit and carry out his aforementioned plan. He returns to that pit and discovers that Yosef is gone!
12) Reuven then returns to his brothers (who are now away from the pit) and tells them that Yosef is gone.
13) Presumably at this stage, Yehuda tells Reuven what has transpired.
14) They carry out their earlier plan of covering up Yosef's disappearance, by staining his coat with blood.
15) The Midyanim (which is spelled here chaser as Medanim) sell Yosef to Egypt, to Potifar.

The objection raised to this is whether the equation of Midianites with Ishmaelites is indeed plausible. Why would the Torah go out of its way to confuse us so?!

Before addressing this question in its many forms, let us look again at the pesukim which explicitly do equate them. See Shofetim perek 8 pasuk 22 and 24, where Ishmaelites are exchanged for Midianites without second thought:

כב  וַיֹּאמְרוּ אִישׁ-יִשְׂרָאֵל, אֶל-גִּדְעוֹן, מְשָׁל-בָּנוּ גַּם-אַתָּה, גַּם-בִּנְךָ גַּם בֶּן-בְּנֶךָ:  כִּי הוֹשַׁעְתָּנוּ, מִיַּד מִדְיָן.	22 Then the men of Israel said unto Gideon: 'Rule thou over us, both thou, and thy son, and thy son's son also; for thou hast saved us out of the hand of Midian.'
כג  וַיֹּאמֶר אֲלֵהֶם, גִּדְעוֹן, לֹא-אֶמְשֹׁל אֲנִי בָּכֶם, וְלֹא-יִמְשֹׁל בְּנִי בָּכֶם: ה, יִמְשֹׁל בָּכֶם.	23 And Gideon said unto them: 'I will not rule over you, neither shall my son rule over you; the LORD shall rule over you.'
כד  וַיֹּאמֶר אֲלֵהֶם גִּדְעוֹן, אֶשְׁאֲלָה מִכֶּם שְׁאֵלָה, וּתְנוּ-לִי, אִישׁ נֶזֶם שְׁלָלוֹ:  כִּי-נִזְמֵי זָהָב לָהֶם, כִּי יִשְׁמְעֵאלִים הֵם.	24 And Gideon said unto them: 'I would make a request of you, that ye would give me every man the ear-rings of his spoil.'--For they had golden ear-rings, because they were Ishmaelites.

So the equating of Midianite and Ishmaelite in Vayeshev is possible. But is it plausible?

Let us try to deal with some facets of the question.

1)
Q: Why would the Torah refer to these traders sometimes as Midianites and sometimes as Ishmaelites? We should expect the Torah to choose a single term and stick with it!

A: I don't understand this question. It is the rule, rather than the exception, that the Torah switches off between synonyms. The Rishonim, who were pashtanim, even had a name for this: kefel inyan bemilim shonot. We see this in Biblical poetry. We see this when the name of Hashem is YKVK, Elokim, or Kel Shakkai. We see this when Pharaoh is sometimes referred to as Pharaoh and sometimes as Melech Mitzrayim. We see this in Vayigash when Yehuda says, in reporting his father's words:

כט  וּלְקַחְתֶּם גַּם-אֶת-זֶה מֵעִם פָּנַי, וְקָרָהוּ אָסוֹן--וְהוֹרַדְתֶּם אֶת-שֵׂיבָתִי בְּרָעָה, שְׁאֹלָה.

29 and if ye take this one also from me, and harm befall him, ye will bring down my gray hairs with sorrow to the grave.

with the word בְּרָעָה while Yaakov actually said:

לח  וַיֹּאמֶר, לֹא-יֵרֵד בְּנִי עִמָּכֶם:  כִּי-אָחִיו מֵת וְהוּא לְבַדּוֹ נִשְׁאָר, וּקְרָאָהוּ אָסוֹן בַּדֶּרֶךְ אֲשֶׁר תֵּלְכוּ-בָהּ, וְהוֹרַדְתֶּם אֶת-שֵׂיבָתִי בְּיָגוֹן, שְׁאוֹלָה.

38 And he said: 'My son shall not go down with you; for his brother is dead, and he only is left; if harm befall him by the way in which ye go, then will ye bring down my gray hairs with sorrow to the grave.

with the word בְּיָגוֹן. (I didn't notice this myself. Some meforshim take up this question.)

We see this when one set of luchot has Shamor and the other set of luchot had Zachor. I could go on with hundreds of examples. We are conditioned by midrash to make the most of these slight differences.

However, it is not at all surprising that the Torah switches off in its language.

2)
Q: OK, the Torah will sometimes switch off language. But here, it is extremely confusing! Why would the Torah deliberately confuse us so? We only know that Midianites can be referred to as Ishmaelites from one small segment in sefer Shofetim.

A: You are not the target reader of the Torah. The ancient Israelite was the first intended reader. And for him, the synonym of Ishmaelite in place of Midianite was obvious.

It is hubris to think that, because some usage is only attested to once, it is rare, and so rare as to be non-obvious to the ancient reader. The Rishonim, expert grammarians of Biblical Hebrew, recognized that our knowledge of Biblical Hebrew is only partial. Thus, in Radak's, he writes that our knowledge of the Hebrew language is incomplete and reconstructed from the 24 books of Tanach, from Mishnaic Hebrew, and the like. So there could be a meaning which we would not know from other Biblical evidence.

We don't know how often Ishmaelite was used to refer to Midianite in every day speech. Tanach represents a tiny corpus, and one time happened to catch this synonym. But that does not mean that such usage must be rare, because it only occurs once in Tanach.

3)
Q: Ishmaelite is most often used in Tanach to mean Ishmaelite, and Midianite is most often used to mean Midianite. To seize upon the one rare usage and assert that this is what it means represents an incredible kvetch.

A: See the preceding question and answer.

More than this, I know a little bit about the field of computational linguistics. Let us say you wanted to build a machine translation program. A really rudimentary one might take two texts that are translations of one another (called a parallel corpus) and count up the occurrences in which word X was a translation for word Y.

It might discover that the word bank is most often used to mean a financial institution. Then, in any text it encounters, it will translate that word in that sense.

And then, when it encounters a sentence such as:

the river bank overflowed

, it would translate it as

the river financial institution overflowed.

A better machine translation program would also count, but would count based on context. What is the most frequent meaning of "bank" in the context of water? What is the most frequent meaning of "bank" in the context of dollars?

I don't care what the most frequent meaning of Ishmaelite and Midianite is. I care about the most plausible meaning in the current context. And the current context refers to both Ishmaelites and Midianites, in a way that adopting the synonymous meaning resolves quite a number of questions. (For example, what do you mean later that the Midyanim brought him to Egypt? What does Yosef mean that his brothers sold him?) And the current context sets us up to expect the brothers to be selling Yosef to the ones who are seen in the distance.

If we always adopted the most frequent meaning of any word, then we would stubbornly create theological problems where there are none. Et is most often used as the direct object marker. When Chava names her son Kayin, she does so because קָנִיתִי אִישׁ אֶת־ה. Will you say that she has aquired a man, namely she has acquired God? Or will you correctly say that Et less frequently means "with" and so she is saying that she has aquired a man with the help of God?

4)
Q: Is it too early to say Ishmaelite for Midianite?

To quote Hillel, a commenter on a previous post:

It's not clear what "Ishamelite" means in Shoftim exactly (a culture or ethnicity, perhaps?) but it would make sense that the descendants of the 'other' children of Avraham would be all lumped together culturally 800 years after their birth. It's no so convincing that would be true two generations later. Even assuming we're talking the time of Moshe, that's still perhaps three or four centuries later, so a term of art from the time of Gidon may not have applied.

A: This just seems to me to be looking for problems. "May not have applied?" So too, it may have applied. One can cast doubt on anything, after theorizing as to the reason a term applies.

Is this really only two generations later, at the time of the sale of Yosef? Recall that Yishmael was born before Yitzchak, and was to have prolific progeny הַרְבָּה אַרְבֶּה אֶת-זַרְעֵךְ, וְלֹא יִסָּפֵר, מֵרֹב. And we are told עַל-פְּנֵי כָל-אֶחָיו, נָפָל.

Meanwhile, Yitzchak waited a while before marrying, and Rivkah was initially barren. Yitzchak only had two children, Yaakov and Esav, while Yishmael had twelve sons.

Then, Yaakov waited until he was eighty-four years old before he first married Leah. And then Rachel was barren, such that it was a number of years from then before Yosef was born. And Yosef was sold at the age of 17.

Do you really think that there were only two generations of Ishmaelites in all that time?!

Let us assume it is from the time of Moshe. Is that only three or four centuries later, meaning from Yishmael's birth? Add to all the above that they stayed 400 years in Egypt, rather than Chazal's 210. Add another 40 years in the midbar. Does it work out now? We are talking about more than half a millennium.

And of course, for those who would posit post-Mosaic authorship of the Torah, the question entirely falls away.

5)
Q: What purpose does the switch-off between Midianite and Ishmaelite serve? If it serves no purpose, then the switch-off does not make any sense!

A: The best answer is that I don't know and I don't care. See the answer to question #1. Many meforshim posit reasons for specific alternations, but that is irrelevant. There may be a reason. There may not be a reason, in the general and specific case. If you want to explore this question, feel free to.

Some answers which appeal to me:

i) See the Documentary Hypothesis, but with my slight emendation. That is, there are multiple voices / streams in the text, all written by Moshe Rabbenu. These voices stress different facets of the story and use slightly different language. At the end, Moshe assembled these all together into a single unit:

בְּעֵבֶר הַיַּרְדֵּן, בְּאֶרֶץ מוֹאָב, הוֹאִיל מֹשֶׁה, בֵּאֵר אֶת-הַתּוֹרָה הַזֹּאת לֵאמֹר. 

In one voice, they were referred to as Ishmaelites; in another, Midyanites. And the blended account refers to them as both.

Unlike the classic Documentary Hypothesis, I am saying that these two voices do not need to be contradictory.

ii) They were called Yishmaelim due to some aspect that deserved to be stressed in that pasuk, that they were a caravan, expert at traversing the desert.

6)
Q: Midianites may be referred to as Ishmaelites, but these are Ishmaelites! How can you say to refer to them as Midianites?

A: Huh? How do you know that these are true Ishmaelites? Say that they are Midianites, and your question does not begin!

7)
Q: What about the Medanites who appear later? To cite Hillel again:

To take the exception and apply it when the common explanation works is not p’shat. It is further complicated since you must then deal with the Medanites who appear later. Are they also interchangeable? Why does the Torah toss around these nationalities without regard for specificity?

As I write in response to this comment:

It is called a variant spelling. We are not learning midrash here, that we make sure a big deal of a missing Yud. (Even though indeed there are Medan and Midyan in Bereshit 25:2.) See the Samaritan Torah which spells it malei yud. See Onkelos as well who translates Medanim there as Midyanim.

I would just reassert that indeed, not making a big deal of slight variations is indeed sometimes (often) peshat. Making a big deal of these fine details is a mark of midrash. Thus, this is the midrash:

After identifying these Hebrew names, Rabbi Judah claims that Joseph was sold four times: First his brothers sold Joseph to the Ishmaelites (Yishma'elîm), then the Ishmaelites sold him to the Midianite traders (ʼnāshîm midyanîm sōĥrîm), the Midianite traders to the Medanites (m‘danîm), and the Medanites into Egypt. Rav Huna adds one more sale by concluding that after the Medanites sold him to the Egyptians, a fifth sale occurred when the Egyptians sold him to Potiphar.

_____________________
Footnote to item 4 in the scenario above:
* Alas, the Torah does not tell us this directly, and this is an admitted weakness in the theory. But it is obvious from his later surprise, and that he has gone by himself to the pit; explainable as his excusing himself to eventually carry out his plan, where the plan had been explicitly stated; and this reading of his absence is already traditional, in that Chazal were willing to say this, albeit with their typical midrashic twist. And perhaps that a subset of the brothers stayed to eat was the novel point. Even much simpler narratives have such surprising seeming contradictions or omissions, and one such should not derail the theory, especially when it answers all questions both local and foreign. For example, why/where did the third angel disappear when it left Avraham? If Sarah prepared cakes, why weren't they served?