Gemara

Question (Reish Lakish): "V'Chag ha'Katzir" - on which Chag do we harvest?

Answer (Reish Lakish): This is Shavu'os;

Surely we do not harvest on Yom Tov! Rather, it refers to the days of Tashlumim (to bring Chagigah and Olas Re'iyah).

Rejection (R. Yochanan): If so, you should say that "V'Chag ha'Asif", i.e. Sukos, is a Chag on which we gather (produce drying in the field into the house);

We may not gather on Yom Tov, nor on Chol ha'Mo'ed!

Rather, we must say that Chag ha'Asif is a Chag in the season in which we gather. Likewise, Chag ha'Katzir is a Chag in the season in which we harvest!

Question: Both of them forbid Melachah on Chol ha'Mo'ed. What is the source?

Answer #1 (Beraisa #1 - R. Yoshiyah): "Es Chag ha'Matzos Tishmor Shiv'as Yomim" forbids Melachah on Chol ha'Mo'ed;

R. Yonason says, a Kal va'Chomer forbids Melachah. There is no Kedushah before and after the first and seventh days, yet Melachah is forbidden on them. There is Kedushah before and after Chol ha'Mo'ed, all the more so Melachah is forbidden on them!

Question: The six days of the week disprove this! There is Kedushah (Shabbos) before and after them, yet Melachah is permitted on them!

Answer: Korban Musaf is not brought for the six days of the week, so we cannot learn from them to Chol ha'Mo'ed, for which there is Korban Musaf.

Question: Rosh Chodesh disproves this! There is Korban Musaf for Rosh Chodesh, yet Melachah is permitted on Rosh Chodesh!

Answer: Rosh Chodesh is not called 'Mikra Kodesh'. We cannot learn from it to Chol ha'Mo'ed, which is called Mikra Kodesh, so it is fitting that Melachah be forbidden.

Answer #2 (Beraisa #2 - R. Yosi ha'Gelili): "Kol Meleches Avodah Lo Sa'asu" forbids Melachah on Chol ha'Mo'ed;

R. Akiva says, we learn from "Eleh Mo'adei Hash-m (Mikra'ei Kodesh)";

It does not teach about (Isur Melachah) on the first or seventh days (of Pesach), for these are already called "Shabboson";

Rather, it forbids Melachah on Chol ha'Mo'ed.

Answer #3 (Beraisa #3): "Sheshes Yomim Tochal Matzos uva'Yom ha'Shevi'i Atzeres" - just like the seventh day (of Pesach) is Atzur (shut down) from Melachah, also the first six days.

Suggestion: Perhaps just like the seventh day is Atzur from all Melachah (except for Ochel Nefesh), also the first six days!

Rejection: "Uva'Yom ha'Shevi'i Atzeres" - the seventh day is Atzur from all Melachah, but the first six days are not;

The Torah empowered Chachamim to decide which days are forbidden and which are permitted, and which Melachos are forbidden and which are permitted.

Moed Katan 11b (Mishnah): If someone turned over his olives and became an Avel... he may load the beam onto them once, and leaves them for after the Mo'ed.

Question: The Mishnah initially discuss Aveilus, and then it discusses the Mo'ed!

Answer (Rav Ashi): The Mishnah teaches that Devar ha'Eved is permitted not only during Aveilus, when Melachah is forbidden mid'Rabanan, rather, even on Chol ha'Mo'ed, when it is forbidden mid'Oraisa.

Megilah 21a - (Mishnah): On Rosh Chodesh and Chol ha'Moed four read the Torah;

The rule is that four read on any day with Musaf that is not Yom Tov.

Rishonim

The Rif (Moed Katan 1a) brings the three Beraisos.

Rambam (Hilchos Yom Tov 7:1): Even though Chol ha'Mo'ed is not called Shabboson, since it is called Mikra Kodesh and it is when Chagigah is brought in the Mikdash, it is forbidden to do Melachah. This is so it will not be like weekdays without Kedushah. One who does forbidden Melachah on Chol ha'Mo'ed is lashed Makos Mardus, because the Isur is from Divrei Sofrim. It is not like Yom Tov, on which every Meleches Avodah is forbidden. Since Melachos were forbidden so it will not be like a weekday, some Melachos are forbidden and some are permitted.

The Rosh (Moed Katan 1:1) brings all of these teachings.

Rosh (ibid.): These teachings imply that the Isur Melachah on Chol ha'Mo'ed is mid'Oraisa. R. Tam asked, if so how were Chachamim able to permit Devar ha'Eved, or for a worker who has nothing to eat? We do not find mid'Oraisa Isurim that are partially permitted! A Mishnah (Megilah 21a) says that four read the Torah on Chol ha'Mo'ed because there is Musaf but it is not Yom Tov, i.e. Melachah is permitted.

Poskim

Shulchan Aruch (530:1): Some Melachos are forbidden on Chol ha'Mo'ed and some are permitted.

Rema: The permitted Melachos are those that Chachamim saw fit to permit.

Beis Yosef (DH v'Da'as): The Rambam holds like Tosfos and the Rosh that the Isur Melachah on Chol ha'Mo'ed is mid'Rabanan. The Nimukei Yosef (Moed Katan 1a DH Gemara) and Magid Mishnah (Yom Tov 7:1) cite the Ramban and Rashba to say that the Torah permits only what is needed for the Mo'ed, or Devar ha'Eved even if it is not for the Mo'ed and it is a great exertion. Chachamim forbade some of these things, but the primary Isur Melachah is mid'Oraisa.

Beis Yosef (DH ul'Aniyas): It seems that the Isur Melachah is mid'Oraisa, but the Torah authorized Chachamim to decide which Melachos are permitted and which are forbidden. This is like the Ran (Reish Yoma) says about Inuy on Yom Kipur (other than eating and drinking). The Gemara (Chagigah 18a) says so explicitly. Hagahos Maimoniyos (7:2) says that the Isur Melachah cannot be mid'Oraisa, for if so Chachamim could not make leniencies! This is wrong. Also Inuy of Yom Kipur is mid'Oraisa, yet Chachamim were lenient to allow a king or Kalah to wash the face!

Beis Yosef (536 DH u'Mihu): The Tur says that the Rif holds that Melachah on Chol ha'Mo'ed is mid'Oraisa. I do not know what is his source. The Rif (Moed Katan 1a) brings the Beraisos which expound the Isur Melachah, but these could be Asmachtos!

Bach (DH Chol and DH v'Hachi): On Yom Tov the Torah permits only Melachah of Ochel Nefesh. This implies that all needs of the Mo'ed are permitted on Chol ha'Mo'ed. This supports the Ramban and Rashba. Toras Kohanim expounds that Meleches Avodah is permitted on Chol ha'Mo'ed. Rashi (Vayikra 23:8) says that this is Melachah that is important to you, such as Devar ha'Eved. The Gemara says that the Torah authorized Chachamim to decide which Melachos are permitted, i.e. which are Devar ha'Eved.

Magen Avraham (1): Here the Shulchan Aruch connotes that the Isur Melachah on Chol ha'Mo'ed is mid'Oraisa, but the Torah authorized Chachamim to decide which Melachos are forbidden. Elsewhere he connotes that the Isur Melachah is mid'Rabanan.

Kaf ha'Chayim (1): The Beis Yosef (531 DH v'Chol) connotes that the Isur Melachah is mid'Rabanan.

Note: The Beis Yosef is lenient about shaving the mustache because it is a Safek mid'Rabanan. No one forbids shaving on Chol ha'Mo'ed mid'Oraisa (it is a need of the Mo'ed). Chachamim decreed to forbid it, lest one enter the Mo'ed unkempt (Moed Katan 14a). Perhaps the Magen Avraham and Kaf ha'Chayim mean that one who forbids Meleches Chol ha'Mo'ed mid'Oraisa (even sometimes) should be stringent about a Safek in every case.

Magen Avraham (1): In any case the Isur is very severe. Rashi says that 'one who disgraces the Mo'ados is like one who serves idolatry' refers to Chol ha'Mo'ed.

Machatzis ha'Shekel: The Magen Avraham brings this to show that even those who say that the Isur Melachah is mid'Rabanan agree that it is severe. But Rashi holds that Melachah is mid'Oraisa. The Rashbam (Pesachim 118a) says that 'one who disgraces...' refers to Melachah on Chol ha'Mo'ed, and Tosfos (Chagigah 18a DH Cholo) disagrees, for this implies that Melachah is mid'Oraisa! Perhaps the Magen Avraham means that if some equate it to idolatry, surely all agree that it is a severe Isur.

Note: 'Rashi' (really, the Rivan) on Makos 23a says that it refers to Chol ha'Mo'ed (but he does not say that it refers to Melachah). Rashi (Avos 3:11) says that 'one who disgraces the Mo'ados has no share in the world to come' refers to Melachah on Chol ha'Mo'ed, or eating and drinking on Chol ha'Mo'ed like on a weekday.

Gra (DH u'Mutar): There are five permitted Melachos: Devar ha'Eved, needs of the Rabim, Ma'aseh Hedyot (even for an individual), needs of the Mo'ed, and a worker who has nothing to eat.

Gra (DH l'Fi): R. Aba bar Mamal (Yerushalmi, Moed Katan 9a) says 'they forbade Melachah on Chol ha'Mo'ed so Yisrael will eat, drink and exert in Torah. They eat, drink and are frivolous! If Chachamim would join me, I would permit it'. This implies that the Isur is mid'Rabanan. The Ramban explains that it refers to those Melachos that Chachamim forbade even though they are needs of the Mo'ed or Devar ha'Eved.

Mishnah Berurah (2): R. Aba wanted to permit things that are not true Melachos, e.g. buying and selling. We learn that the Isur of frivolity during the Mo'ed is worse than Melachah.

Kaf ha'Chayim (8): Devar ha'Eved was permitted lest one's anxiety over what he is losing inhibit his learning.