The four species that are taken on sukkot consist of the lulav, etrog, hadassim and aravot. How many of each of the species is the subject to debate (3:4). R' Yishmael maintains that it is three hadassim, two aravot, one lulav and one etrog. R' Akiva however understands that one of each is sufficient.
A further debate ensues regarding the hadassim. According to R' Yishmael, if two of the three are ketumim (cut at the top) it is still valid. The Bartenura cites the Gemara that questions this position. If ketumim presents a problem and R' Yishmael requires three hadassim, then none of the hadassim can be ketumim. If however ketumim does not present a problem, then all three should be able to be ketumim. The Gemara explains that according to R' Yishmael, ketumim is an issue. However, R' Yishmael retracted from his initial position, and maintained that only one hadas is required.
R' Tarfon however argues that all three can be ketumim. In other words, R' Tarfun does indeed require three hadassim, yet argues that hadassim that are ketuimim are valid. The Bartenura explains that R' Tarfon understands that the law of hadar (beauty) mentioned by the etrog does not apply to the hadassim. The Tosfot Yom Tov cites R' Yeshaya who explains that since the leaves of the hadassim cover the stem, if it is cut at the top, it would not be as noticeable.
The Misregot Zahav cites the Rosh who explains that all the quantities mentioned are minimums, and one could add more without violating the prohibition of baal tosif (adding to a mitzvah). The Rambam, however, only allows one to increase the number of hadassim but not any of the other minim (species). The Rosh finds this difficult considering that the number of hadassim is derived from the three words "anaf etz avot". The number of aravot is derived from the reference to "arvei nachal" with arvei being a plural implying that more than one is taken. The Misregot Zahav explains the debate as follows. When deriving a quantity from the use of a plural word, the Rambam also considers the danger of violating baal tosif. Consequently, the minimum plural -- two -- is derived. The Rosh however understands that any number more than one is implied by the passuk.
Rav Soleveichik (Harerei Kedem 130) presents a different understanding of the Rambam. He explains the quantities derived for the lulav, etrog and arava all relate to the laws of lekicha -- taking the species. Those quantites are implied in the pasuk and derived from the use of singular or plural terms. The hadassim are different. The quantity is learnt from the use of the three terms "anaf etz avot" -- no actual number is mentioned. Rav Soloveitchik understands that this does not define the number required when taking the four species (as it does regarding the aravot). Instead, the Torah is providing a definition for the hadassim. The myrtle branches are only defined as anaf etz avot as required for the mitzvah, when there are three branches. Put differently, the requirement of three hadassim is not a law in the maaseh mitzvah -- the action of taking the four species. Instead, it is a law in the cheftza -- the definition of what the hadassim are. That being the case, since there is no law regarding the quantity of hadassim that should be taken (as part of the maaseh mitzvah) there is no issue with adding more hadassim.
Rav Soloveichik provides another implication of this understanding. The Rambam rules (7:6) that one can fulfill the mitzvah by taking each of the minim one at a time. It would seem that this would also be true if one took one aravah at a time considering that, in the end, two aravot were taken. With the hadassim however, since the definition of the object that must be taken is three branches together, if one takes each of the branches one after the other, they never took once took the hadassim as required.
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