Question: But (contrary to R. Chiya's teaching that Shiurim [along with Chatzitzos and Mechitzos] are Halachah l'Moshe mi'Sinai) we find that Shiurim are d'Oraisa!?

The Pasuk in Devarim (8:8) praises Eretz Yisrael for its fruits (Eretz Chitah u'Se'orah v'Gefen...).

The Pasuk is understood to list each food item in order to instruct us regarding Shiurim.

Chitah- the time Shiur for becoming Tamei in a house afflicted with Tzara'as (stated as the time needed to eat a Peras) is made shorter owing (among other things) to the bread being made of wheat (and not barley, which takes longer to eat).

Se'orah- the amount of human bone which would create Tum'ah upon contact or being borne.

Gefen- the measure of a Revi'is for a Nazir is made using wine (which, due to its viscosity, will spill out less than water under the same pressure).

Te'eina- the Shiur of food for Hotza'as Shabbos.

Rimon- the Shiur of a breach for Taharas Kelim.

Zeis Shemen- All of the Land's Shiurim use a k'Zayis. (1) Question: All Shiurim!? (2) Answer: We mean the great majority.

Devash- the plump date is the Shiur for eating on Yom Kipur.

The implication from these derivations being that these are d'Oraisa.

Answer: These do not present the Shiurim, they only provide the basis for Asmachata, the Shiurim are, indeed, Halachah l'Moshe mi'Sinai!

Question: How could R. Chiya have taught that Chatzitzos are Halachah l'Moshe mi'Sinai given that they are derived from the Pasuk V'Rachatz BaMayim!

Answer: We need the Halachah l'Moshe mi'Sinai for the Chatzitzah of hair (as taught by Rabah bar bar Chanah).

One hair (tied to itself) is a Chatzitzah.

Three hairs (tied together) are not a Chatzitzah.

Two hairs (tied together) are questionable.

Question: But hairs are also derived from the Pasuk!?

The Derashah is made from Es Besaro.

This comes to include that which is Tafel to the body, namely, hair.

Answer: The Halachah l'Moshe mi'Sinai teaches us Chatzitzah as taught by R. Yitzchak (Rov and Makpid).

Mid'Oraisa (meaning from the Halachah l'Moshe mi'Sinai), only Rov with Makpid create a Chatzitzah (not Rov alone).

Chachamim added Rov without Makpid and Makpid without Rov as Chatzitzos.

Question: Why did they not add not Makpid without Rov (Mi'ut v'Eino Makpid) lest it be confused with Makpid without Rov?

Answer: That would be a Gezeirah l'Gezeirah.

R. Chiya taught that it is Halachah l'Moshe mi'Sinai.

Question: Unlike R. Yehudah (who needs the Halachah l'Moshe mi'Sinai since his five-Tefach Amah does not let him learn Mechitzos from the Aron plus Keruvim), why would we need a Halachah l'Moshe mi'Sinai according to R. Meir?

Answer: The Halachah l'Moshe mi'Sinai is needed to teach the Halachos of Gud (Asik and Achis- Halachically drawing the Mechitzah up or down), Lavud, and Dofen Akumah.

(Tana Kama): There must be two proper walls, at right angles to each other, and a third may be only a Tefach.

(R. Shimon): There must be three proper walls and the fourth may be a Tefach.

Question: What is their Machlokes?

Answer: Chachamim give priority to the way the word is written in the Torah (Eim LaMasores) while R. Shimon gives precedence to the manner in which the word is read (Eim LaMikrah).

(Chachamim): The word BaSukos is written defectively twice (no Vavin, as though singular) and fully once (two Vavin, plural) for a total of four walls.

One reference is needed for the actual Mitzvah of Sukah.

This leaves three, two of which must be proper, and the third may be a Tefach owing to the Halachah l'Moshe mi'Sinai.

(R. Shimon): All three occasions of BaSukos are read the same way, as plural, giving us six walls.

One reference is subtracted for the actual Mitzvah of Sukah, leaving four Mechitzos.

Three of which must be proper, and the Halachah l'Moshe mi'Sinai allows the fourth to be a Tefach.

Alternate Answer: While all hold Eim LaMikrah, they argue whether an additional reference must be deleted (Chachamim) to teach the Mitzvah of Sechach itself, or not (R. Shimon).

Alternate Answer: While all hold Eim LaMasores, they argue over whether the Halachah l'Moshe mi'Sinai is coming to allow one to diminish the third wall to a Tefach (Chachamim) or to require the addition of a Tefach of a fourth wall to the stated three (R. Shimon).

Alternate Answer: While all agree that the Halachah l'Moshe mi'Sinai comes to diminish the wall, and while all agree to Eim LaMasores, and they are arguing over whether we are to be Dorshin Techilos (R. Shimon-inferring from the opening reference, giving us four walls) or not (Chachamim).

Alternate Answer (R. Masnah): R. Shimon derives his position (of four walls) from the Pasuk in Yeshayah (4:6) which speaks of a Sukah as protection from the air-stream (only possible with four walls).