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May one wear a cotton Tallis Katan?
A. The issues of concern:
Wearing a cotton Tallis Katan touches upon two Halachic issues 1) Is the material Biblically obligated in Tzitzis, and hence is one Biblically fulfilling the Mitzvah upon wearing it? 2) If the cotton garment has wool material Tzitzis tied to it [which is the case today], is it Kosher?
Issue 1: What materials are Biblically obligated in Tzitzis? A wool garment is Biblically obligated to have Tzitzis according to all opinions. If a Tallis is made of material other than wool or linen, it is disputed as to whether it is Biblically obligated in the Mitzvah of Tzitzis, or only Rabbinically. Practically, the main opinion follows those who rule that all materials are Biblically obligated. Nevertheless, being there are opinions who argue, those who desire to fulfill the Mitzvah of Tzitzis on its highest standard [i.e. according to all opinions] are to be careful to wear a pair of Tallis Gadol/Katan that is entirely made from sheep wool, meaning that both the garment and fringes are made from sheep wool, and by doing so one fulfills the Mitzvah of Tzitzis without any question.
Issue 2: The material of the fringes: Some Poskim rule that wool or linen fringes may be used as Tzitzis for a garment of any material. Other Poskim rule that the material of the fringes must be simialr to the material of the garment. Accordingly, a cotton Tallis Katan must have cotton material strings tied to it, and if wool material fringes are attached, the Tzitzis is invalid. Practically, although the custom is not like this opinion, nevertheless, it is proper for every G-d fearing Jew to be stringent upon himself like this opinion, and hence tie cotton material Tzitzis onto a cotton Tallis. Likewise, even those who are lenient like the first opinion, to tie wool strings to a cotton garment, it is proper not to recite a blessing upon wearing such Tzitzis. Thus, a blessing should not be recited over a cotton garment that has wool fringes. Rather, one is to recite a blessing over a different Tallis and have in mind to exempt also this Tallis. [Nevertheless, from the letter of the law, one may say a blessing over this Tallis, if he so chooses.]
B. The final ruling:
From the letter of the law, one may be lenient to wear a cotton Tallis, even if it contains wool fringes. Nevertheless, those who desire to fulfill the Mitzvah of Tzitzis on its highest standard are to avoid wearing a cotton Tallis [whether of a Tallis Katan or Tallis Gadol, if a wool Tallis is available] even if the fringes are made from cotton. [This applies even in the summer.] If however the fringes are made from wool [which is the case today being that cotton fringes are not manufactured], then although the custom is to be lenient, every G-d fearing Jew is to be stringent upon himself to avoid wearing it [whether it is a Tallis Katan or Gadol] and if he does wear it, it is proper that a blessing not be recited. Practically, the Chassidic custom is to be particular to only wear wool Taleisim.
It is permitted to wear a cotton Tallis Katan, and those who choose may even say a blessing over it. Nevertheless, every G-d fearing Jew is to avoid wearing a cotton Tallis, and is to rather wear a wool Tallis, and so is the Chassidic custom. Likewise, in the event that one needs to wear a cotton Tallis, it is proper that a blessing not be recited over it.
May one who is particular to wear a wool Tallis, wear a cotton Tallis during the nighttime:
Some learn that one may be lenient to wear cotton Tzitzis at night even if he is generally particular to only wear a wool Tallis, as stated above. The Chassidic custom is to be particular to wear wool Talleisim even at night.
 Admur 9:4; Michaber 9:1 and 6
 Admur 9:4; Michaber 9:1 and 6; Ketzos Hashulchan 6:1
 Some Poskim rule it is only Rabbinically obligated in Tzitzis. [Michaber 9:1; Rif; Rambam 3:2; Gemara Menachos 39b] Others rule all materials are Biblically obligated in Tzitzis. [Rama 9:1; Tosafus; Rosh; Smag; Mordechai]
 Rama 9:1; Admur in Kuntrus Achron 9:1 “and so is the main opinion”; Admur in 9:1 learns the verses in a way that shows all garments are Biblically obligated
 Lit. Mitzvah Min Hamuvchar. However, the Michaber ibid writes “Every G-d fearing Jew is to…” Vetzaruch Iyun as to what the difference is between the wording of Admur and that of the Michaber. The wording of the Michaber suggests that every G-d fearing Jew must do so, while the wording of Admur suggests that this matter is optional to each person. Perhaps the explanation is that in truth we [Ashkenazim] hold mainly like the opinions that rule that all materials are a Biblical obligation, as rules Rama 9:1 unlike the Michaber 9:1, and hence Admur does not use the same wording as the Michaber and rather uses a more lenient wording.
 Michaber ibid
 Admur ibid; Michaber 9:6 in name of Igur and Rabbeinu Yeshaya and Maharil; M”B 9:5; Kitzur SHU”A 9:12; Ben Ish Chaiy Noach 1; Kaf Hachaim 9:5; Halichos Shlomo 3 footnote 25; Or Letziyon 2:2 footnote 3; Igros Moshe 1:2; 2:1; 3:1; Yoreh Deah 3:52
 9:1; Michaber 9:2
 Stam opinion in Admur and Michaber ibid
 The reason: One verse states “Venasnu Al Tzitzis Hakenaf Pesil Techeiles”, while a previous verse states “Veasu Lahem Tzitzis Al Kanfei Bigdeihem”. What was the necessity of repeating the word “Kenaf/corner” in the latter verse? This is coming to teach us that the Tzitzis must be made of the same material as the corners of the garment. Another verse however states that “Lo Silbash Shatnez Tzemer Upishtim Yachdav, Gedilim Taaseh Lecha Al Arba.” This verse seems to imply that the fringes may be made of only wool or linen, and not of any other material. Hence the two verses seem contradictory. The explanation is as follows: Strings of wool or linen are valid to be used for garments of any material, whether of wool, linen or any other material, and on this it says “Tzemer Upishtim Gedilim Taaseh Lecha”. However, strings of other materials are only valid for garments made of that same material. [Admur ibid]
 Maharam 444; Hagahos Maimanis 3:6
 As is seen from the fact we allow tying wool strings to a silk garment. [Admur ibid; Terumos Hasdeshen 44]
 Admur ibid; M”A 9:3
Other opinions: Some Poskim rule it is better to attach wool strings to a silk garment. [Beir Heiytiv 9:1 in his understanding of M”A 9:4; Admur in Kuntrus Achron 9:2 negates his understanding of the M”A.] Some Poskim are lenient to even initially allow one to wear a cotton Tallis Katan, even if the fringes are made from wool. [Gra in Maaseh Rav 17 and in M”B 9:6; Chazon Ish brought in Orchos Rabbeinu 1:18]
 Admur 9:5; M”A 9:3 in name of Bach and M”A 8:16 as explained in Kuntrus Achron 9:2
Is one to say the blessing if he does not have another Tallis available? Tzaruch Iyun if according to Admur even in such a case one should not say a blessing, or only when he in any event has another Tallis available is he not to say a blessing.
Other opinions: See Beir Heiytiv 9:1 brought in previous footnote who implies a blessing is recited on a silk Tallis with wool Tzitzis!
 As we do not apply the rule of Safek Brachos Lihakel against a Minhag, and the custom is like the first opinion, as stated above in Rama and Admur ibid; Likewise, Admur only writes that it is proper not to say a blessing, and does not prohibit doing so.
 As according to all, cotton material is at least Rabbinically obligated in Tzitzis, and it is only a Mitzvah Min Hamuvchar to wear wool. [Admur 9:4] Likewise, even if the fringes are made of wool, the custom is to be lenient to tie even wool strings to a cotton pair of Tzitzis, and only a G-d fearing Jew is to be stringent. [Admur 9:4]
 Admur 9:4; Michaber 9:6; M”B 9:5; Kitzur SHU”A 9:12; Ben Ish Chaiy Noach 1; Kaf Hachaim 9:5; Halichos Shlomo 3 footnote 25; Or Letziyon 2:2 footnote 3; Igros Moshe 1:2; 2:1; 3:1; Yoreh Deah 3:52
 Igros Moshe brought in previous footnote
 Admur 9:5 as brought in Halacha 2A!
The reason: If the fringes of the cotton Tallis is made of wool [as is the commonly sold material of all Tzitzis today] then some Poskim [Maharam Merothenberg] rule that the Tzitzis is invalid, and it is as if one is wearing a four-cornered garment without Tzitzis. Now, although in conclusion we rule that the custom is to be lenient, nevertheless every G-d fearing Jew is to be stringent. [9:4]
Other opinions: Some Poskim are lenient to even initially allow one to wear a cotton Tallis Katan, even if the fringes are made from wool. [Gra in Maaseh Rav 17 and in M”B 9:6; Chazon Ish brought in Orchos Rabbeinu 1:18]
 See Igros Kodesh 14:229 [brought in Shulchan Menachem 1:44 footnote 14]
 Piskeiy Teshuvos 9:2, based on Ashel Avraham 21 that states “I was accustomed to wear a Tallis Katan of linen at night” and hence certainly he would allow one to wear cotton, of which from the letter of the law is obligated in Tzitzis at least Rabbinically. However, Tzaruch Iyun as how one can learn from this anything, as he himself writes that he is disturbed if this is proper, being that perhaps this makes it appear like Baal Tosif.
 Heard from Rav Eliyahu Landa Shlita