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The Rambam (Hilchos Tefillin 3:19) wrote as follows: "A strap that tore — one may not knot it and one may not sew it; rather, one removes it and stores it away [in genizah] and makes another. And the remnants of the strap are invalid unless its length and width are like the [required] measure or more than it. And one must always be careful that the face of the strap be facing upward at the time he ties them on his hand and on his head" — end quote. And see in the Kesef Mishneh, who brought that the Rosh (Hilchos Tefillin siman 11) disagrees with the Rambam and holds that this speaks only of the parts of the strap that encircle the head and the upper arm, which are part of the tying of the batim upon him, for there we require specifically kesherah tamah, but for the remaining parts of the straps sewing is effective^[1].

Now, the Tur (OC siman 25) wrote as follows: "And I saw regarding my father, my master, of blessed memory, that immediately after he tied the shel yad on the upper arm he would put on the shel rosh before he would wind the strap around his arm, for he would say: since the second bracha relates also to the shel yad, and for this reason one may not make an interruption between them, one should minimize the interruption as much as one can, and the winding around the arm is not part of the mitzvah" — end quote. And so too the Mechaber ruled (se'if 11) that one should put on the tefillah shel rosh before he winds the strap around the arm — see there.

And to explain the basis of their dispute, it was written in the responsa Mishkenos Yaakov (OC siman 29) that the Rosh follows his own approach in this, for he holds that this that we have established — that knotting and sewing are not effective in a strap that tore — is specifically in the parts of the strap that encircle the head and the arm, as above, because these parts of the straps are part of the fulfillment of the mitzvah of tefillin; however, in the remaining length of the straps, which are not part of the body of the mitzvah, sewing is effective, and therefore he holds that the winding of the strap around his hand is not part of the mitzvah and one should give precedence to putting on the tefillah shel rosh.

And on this premise the Mishkenos Yaakov raised a difficulty on what the Mechaber wrote (siman 33 se'if 5) as follows: "If the strap tore, there are some who permit sewing it from the inner side; and some say that the part of it that encircles the head, and in the shel yad the amount that encircles the arm — to tie the tefillah with the arm and so that it should extend to the middle finger and one winds from it three windings around that finger and ties — have no remedy, neither by knotting nor by sewing, etc." — end quote. And it is explained that the Mechaber ruled like the opinion of the Rambam, that in the entire measure of the straps sewing is not effective; and according to his reasoning one is forced to say that the Rambam disagrees with the Rosh on two counts and holds that the entire measure of the straps is part of the body of the mitzvah. And accordingly, how did a single document win for two parties — to adopt in siman 25 like the Rosh and in siman 33 like the Rambam?

Now, see in the responsa of the Rambam (Machon Yerushalayim siman 82), where he wrote as follows: "The winding of the strap on the kibbores is the knot concerning which tying is stated, and then one must recite the bracha. However, the tying of the strap on the finger is to be after the bracha, and in it is the complete tying [kesheirah tamah], and the knot on the finger is not obligatory" — end quote. And one must be precise in what the Rambam wrote, that the winding of the strap on his fingers is not obligatory — that is, that it does not invalidate the fulfillment of the mitzvah; and nonetheless in his halachos he ruled that sewing and knotting are not effective if the strap tore, as above. And behold, according to what the Mishkenos Yaakov wrote, the Rambam contradicts himself, for on one hand he holds that this is not essential as part of the mitzvah, and nonetheless he holds that sewing is not effective in it.

And one is forced to say that the Rambam holds that the law of sewing in the straps of the tefillin is a law in the essence of the straps themselves, and does not depend on the mitzvah of winding the strap on his hand; and even though by law there is no need at all for this part of the strap, since he has long straps they must be in accordance with their halacha, just like the parts of the straps that do invalidate the fulfillment of the mitzvah.

And furthermore it appears to say that even if there is a fulfillment of a mitzvah in winding the straps on his arm, and even on his fingers, nonetheless one cannot conclude from this that it is the body of the mitzvah, but rather a merit and an additional mitzvah beyond the obligation. And with this the question of the Mishkenos Yaakov on the Mechaber is removed, for even if you say that the Rambam disagrees with the Rosh, it is not necessary to say that the two laws depend on one another.

And there is a clear proof to be brought for what we have written, from the Gemara in Zevachim (daf 19a): Rabbi Zeira inquired — tefillin, what is [the law] regarding whether they constitute a chatzitzah? According to the one who says that night is not the time for tefillin, you need not raise the question, since at night they interpose, by day too they interpose; when you should raise the question is according to the one who says that night is the time for tefillin — see there. And it is explained that according to all opinions, if there is a scenario in which the tefillin rest upon him but he does not fulfill a mitzvah with it, this is obvious that it interposes. And if you say that there is no mitzvah at all in the entire length of the straps that are wound on his hand, then even according to the one who says that night too is the time for tefillin, there is a part of the tefillin that is not part of the mitzvah, and accordingly even according to that opinion it is obvious that it interposes. And one is forced to say that even though this does not invalidate the fulfillment of the mitzvah, there is in it the aspect of an extra mitzvah^[2].

And so too it is forced according to the opinion of the Geonim, brought by the Rashba in his chiddushim to Yevamos (daf 4b) and by Rabbeinu Yerucham (brought by the Beis Yosef OC siman 11), that in a linen tallis it is permitted to make only the techeiles from wool and not the white threads. And it is obvious that according to them it is permitted to lengthen the techeiles itself beyond the measure, even though one does not need the entire length of the thread in order to fulfill the mitzvah, since by lengthening it he thereby adds to the mitzvah. And so too one may say regarding tefillin, that even though one does not need the entire length of the strap, nonetheless there is in it a fulfillment of a mitzvah in its own right.

And again I saw that Rabbi Reuven Margolios (in Be'er Miriam on the Haggadah, beginning "Amnam al kol panim") proved along the lines of what we have written, that as long as one has not interrupted, he thereby fulfills the mitzvah even in a place where he has already discharged his obligation of eating matzah on the night of Pesach. And so too he brought a proof from this — that even according to the one who says a person discharges his obligation of Krias Shema with the first verse, nonetheless there is a mitzvah in reciting the entire Shema. And so too if one made a sukkah of four walls there is holiness upon the entire sukkah; and so too that which we sound several tekios on Rosh Hashanah more than is needed to discharge the obligation of the mitzvah, even though in a non-mitzvah context this would be a shevus — see there.

Now, the Gri"d HaLevi Soloveitchik raised a difficulty on the Rambam from what we learned in the Gemara in Menachos (daf 35b): Rav Pappa said — gardumei retzuos are valid. For this is well according to the opinion of the Rosh — one may say that just as with tzitzis, since it already had its measure, even though now it tore, it nonetheless remains in its valid state; so too regarding the straps there is in it a framework of a measure, and since at its outset it had the measure, now too it has not become invalidated^[3].

However, according to the opinion of the Rambam, per the explanation of the Mishkenos Yaakov that there is a specific mitzvah in the entire length of the straps, how can we say that frayed remnants of straps are valid? And even though Rav Pappa's opinion was rejected from the halacha, the reason is because the law of gardumin applies only to tashmishei mitzvah, and tefillin are tashmishei kedushah — implying that were it not for this we would have accepted Rav Pappa's reasoning — such is the gist of his words. And according to what we have written it is settled, for one may say that the Rambam too concedes that it is a law of measure that exists specifically in the straps; and so too it is obvious that even in a place where there is grounds to validate on account of gardumi, there is still a fulfillment of a mitzvah through it, and the two matters do not depend on one another, as we have explained.