Why don't Korach and his followers ask if an all Techeiles Beged is Patur from Techeiles?

Question

רש"י במדבר ט"ז:א' ד"ה דתן ואבירם. ... מֶה עָשָׂה? עָמַד וְכָנַס ר"נ רָאשֵׁי סַנְהֶדְרָאוֹת — ... וְהִלְבִּישָׁן טַלִּיתוֹת שֶׁכֻּלָּן תְּכֵלֶת, בָּאוּ וְעָמְדוּ לִפְנֵי מֹשֶׁה, אָמְרוּ לוֹ טַלִּית שֶׁכֻּלָּהּ שֶׁל תְּכֵלֶת חַיֶּבֶת בְּצִיצִית אוֹ פְטוּרָה? אָמַר לָהֶם חַיֶּבֶת, הִתְחִילוּ לִשְׂחׂק עָלָיו, אֶפְשָׁר טַלִּית שֶׁל מִן אַחֵר חוּט אֶחָד שֶׁל תְּכֵלֶת פּוֹטְרָהּ, זוּ שֶׁכֻּלָּהּ תְּכֵלֶת לֹא תִפְטוֹר אֶת עַצְמָהּ?! (תנחומא):

... What did he [Korach] do? He arose and assembled 250 men, fitted to be heads of the Sanhedrin... and he attired them in robes of pure purple wool. They then came and stood before Moses and said to him, “Is a garment that is entirely of purple subject to the law of Zizith or is it exempt”? He replied to them: “It is subject to that law”. Whereupon they began to jeer at him: “Is this possible? A robe of any different coloured material, one thread of purple attached to it exempts it, and this that is entirely of purple should it not exempt itself (i.e. ipso facto be exempt) from the law of “Zizith”? (Midrash Tanchuma, Korach 2).

Why are Korach and his followers asking whether it is Chayav in Tzitzis? There is no reason why it shouldn't be Chayav in Tzitzis (strings at the corner). All that they've proved is that it should be Patur from Techeiles. Why don't they ask him whether a Beged that is completely Techeles should be Chayav in having Techeiles strings?

Answer 1

While it is impossible to know with certainty what the Tanhuma was thinking, I think that the following is a likely explanation.

Numbers (15:38-9) states:

וְעָשׂוּ לָהֶם צִיצִת עַל-כַּנְפֵי בִגְדֵיהֶם, לְדֹרֹתָם; וְנָתְנוּ עַל-צִיצִת הַכָּנָף, פְּתִיל תְּכֵלֶת: וְהָיָה לָכֶם, לְצִיצִת, וּרְאִיתֶם אֹתוֹ וּזְכַרְתֶּם אֶת-כָּל-מִצְו‍ֹת יְהוָה, וַעֲשִׂיתֶם אֹתָם

That they make them throughout their generations fringes in the corners of their garments, and that they put with the fringe of each corner a thread of blue.

And it shall be unto you for a fringe, that ye may look upon it, and remember all the commandments of the LORD, and do them.

After describing the tekhelet, verse 39 states that it shall be tsitsit, and you shall see it and remember all the mitsvot.

This could be interpreted as saying that the tekhelet in particular serves as the reminder of all the mitsvot.

Now, this remembering of the mitsvot is presented as being the reason for the mitsvah. It seems likely that the originator of the arguement regarding a garment fully dyed tekhelet, read the verses thusly. Accordingly, since the whole reason for the mitsva is remembering the mitsvot, and since it is particularly the tekhelet which serves this purpose, it follows that a fully dyed garment should be fully exempt from the entire mitsvah! Not just just from tekhelet.

---

There is some corroboration for the above reading of the verses (although not evidence that this was the reading of the originator of the above argument) see the commentary of Rashbam to verse 39, who may be explaining that the singular it refers exclusively to the tekhelet:

והיה לכם לציצית - [פתיל] הציצית הזה יהיה לכם לראייה שתראו אותו. כמו מציץ מן החרכים. וכן מצאתי בסיפרי. [וגם] פתיל תכלת פירשו רבותינו לפי שהתכלת דומה לים וים דומה לרקיע ורקיע לכסא הכבוד

However, I am not sure if that is his intent, and it is difficult to determine given different versions of this passage, (note Sefarias minor variations).

Answer 2

This interestingly phrased question of Korach appears in two other sources.

Badmibar Rabbah 18:3

קָפַץ קֹרַח וְאָמַר לְמשֶׁה טַלִּית שֶׁכֻּלָּהּ תְּכֵלֶת מַהוּ שֶׁתְּהֵא פְּטוּרָה מִן הַצִּיצִית, אָמַר לוֹ חַיֶּיבֶת בְּצִיצִית. אָמַר לוֹ קֹרַח טַלִית שֶׁכֻּלָּהּ תְּכֵלֶת אֵין פּוֹטֶרֶת עַצְמָהּ, אַרְבָּעָה חוּטִין פּוֹטְרוֹת אוֹתָהּ

As well as Yerushalmi Sanhedrin 10:1

עמד ועשה טלית שכולן תכלת אתא גבי משה א"ל משה רבינו טלית שכלה תכלת מה שתהא חייבת בציצית אמר לו חייבת דכתיב גדילים תעשה לך וגו'

In both places as well it says Korach asked if this garment is obligated in tzitzis, where seemingly it being made of techeiles shouldn't make a difference to if it needs tzitzis or not. Your question is actually something that many commentaries were bothered by (Mizrachi to Numbers 16:1; Eitz Yosef (quoting Zayis Ra’anan), Maharzu, and Chiddushei HaRashash to Bamidbar Rabbah; Eitz Yosef (quoting Zayis Ra’anan) and Biur HaAmarim to Midrash Tanchuma Korach § 3; and it seems the Korbon HaEidah to Yerushalmi Sanhedrin).

Therefore, they explain that Korach wanted to know if he needed to dye the tzitzis in his garment techeiles or is the garment being that color sufficient. Moshe responded that he still needed to make some of the strings techeiles. This explanation fits better with Korach’s subsequent question, which is similar in nature: Does a house full of scrolls need a scroll on the doorpost, i.e. a mezuzah. What they have in common is I have X, why would I need another X. According to the plain meaning of the words, the two questions aren't as similar.

However, the Kesav Sofer ad. loc. understands the Midrash according to its literal wording. He seems to interpret it like @mevaqesh suggested, that Korach felt that a garment full of techeiles accomplished the purpose of the mitzvah of tzitzis, so there was no point in adding tzitzis to it.

Now, this sounds like Korach is doresh ta'amah dekra, that he applies the reason behind the mitzvah to its laws. There are late achronim who explicitly suggest that this was Korach's opinion. It's actually a dispute if we are doresh ta'amah dekra, and some of these achronim suggest that this was the dispute between Korach and Moshe, where the latter held we aren't doresh ta'amah dekra. These achronim are, inter alia, Avnei Eliyahu parshas Chukas s.v. ובזה י"ל ‎[#1], Harei BaShamayim ad. loc. s.v. במדרש מה ראה ‎[#2], Chavatzeles HaSharon parshas Ki Seitzei s.v. וסמך נחמד (although he provides an alternative explanation), and Chakel Yitzchak parshas Korach s.v. והנה לר' שמעון. If you look at these sources inside, you'll see some go with the literal understanding of the Midrash, and some go with the explanation of the above commentaries. Either way, it seems Korach was doresh ta'amah dekrah.