(לז) וַיֹּ֥אמֶר יְהוָ֖ה אֶל־מֹשֶׁ֥ה לֵּאמֹֽר׃ (לח) דַּבֵּ֞ר אֶל־בְּנֵ֤י יִשְׂרָאֵל֙ וְאָמַרְתָּ֣ אֲלֵהֶ֔ם וְעָשׂ֨וּ לָהֶ֥ם צִיצִ֛ת עַל־כַּנְפֵ֥י בִגְדֵיהֶ֖ם לְדֹרֹתָ֑ם וְנָֽתְנ֛וּ עַל־צִיצִ֥ת הַכָּנָ֖ף פְּתִ֥יל תְּכֵֽלֶת׃ (לט) וְהָיָ֣ה לָכֶם֮ לְצִיצִת֒ וּרְאִיתֶ֣ם אֹת֗וֹ וּזְכַרְתֶּם֙ אֶת־כָּל־מִצְוֺ֣ת יְהוָ֔ה וַעֲשִׂיתֶ֖ם אֹתָ֑ם וְלֹֽא־תָתֻ֜רוּ אַחֲרֵ֤י לְבַבְכֶם֙ וְאַחֲרֵ֣י עֵֽינֵיכֶ֔ם אֲשֶׁר־אַתֶּ֥ם זֹנִ֖ים אַחֲרֵיהֶֽם׃ (מ) לְמַ֣עַן תִּזְכְּר֔וּ וַעֲשִׂיתֶ֖ם אֶת־כָּל־מִצְוֺתָ֑י וִהְיִיתֶ֥ם קְדֹשִׁ֖ים לֵֽאלֹהֵיכֶֽם׃
The above is the original Scriptural source of the mitzvah of tzitzit. God tells Moses to convey to the Children of Israel the commandment to make tzitzit on the corners of their garments and tells them why. The pronouns are in the 2nd person plural, not using the word בניך or anything similar that would narrow the commandment to males exclusively. The use of the word בני in God's reference to the Israelites as בני ישראל is used through the Torah to refer to the entirely of the Israelite people, male and female. From this original source, the mitzvah appears to apply to both women and men.
(א) ויאמר ה' אל משה ועשו להם ציצית אף הנשים במשמע, ר”ש פוטר את הנשים מן הציצית מפי שמצות עשה שהזמן גרמא נשים פטורות, זה הכלל. אמר ר' שמעון כל מצות עשה שהזמן גרמא נשים פטורות. ונוהג באנשים ולא בנשים בכשרים ולא בפסולים. ר' יהודה בן בבא אומר ביחוד (פטרן נוטלים) [פטרו] חכמים את הרדיד של אשה מן הציצית ולא חייבו בטלית אלא מפני שפעמים שבעלה מתכסה בה.
(1) (Bamidbar 15:37-38) "And the L-rd spoke to Moses, saying … and they shall make for themselves tzitzith": Women, too, are included (in the mitzvah of tzitzith.) R. Shimon exempts women from tzitzith, it being a time-based (only in the daytime) positive commandment, from which women are exempt, this being the principle: R. Shimon said: Women are exempt from all time-based positive commandments. R. Yehudah b. Bava said: Of a certainty, the sages exempted a woman's veil from tzitzith, and they are required in a wrap only because sometimes her husband covers himself with it. "tzitzith": "tzitzith" is something which "protrudes" ("yotzeh") somewhat. And the elders of Beth Shammai and those of Beth Hillel have already entered the upper chamber of Yonathan b. Betheira and declared: Tzitzith have no prescribed size. And they declared, similarly: A lulav has no prescribed size. "and they shall make for themselves tzitzith." I might think that one string suffices; it is, therefore, written (Devarim 22:12) "Fringes (shall you make for yourself.") How many fringes? Not fewer than three. These are the words of Beth Hillel. Beth Shammai say: Three of wool and the fourth of tcheleth (blue linen). And the halachah is in accordance with Beth Shammai. When is this so (that a minimum size is required)? In the beginning (of its attachment). But for what is left over or lopped off any size (is sufficient). (Bamidbar, Ibid.) "and they shall make for themselves tzitzith." I might think that all of it shall be tzitzith; it is, therefore, written "fringes." If "fringes," I might think all of it shall be fringes. It is, therefore, written "tzitzith." How is this (to be implemented)? That its fringes protrude from the corner (of the garment), and tzitzith from the fringes. "in the corners of their garments": I might think, even garments that are three-cornered, five-cornered, six-cornered, seven-cornered, and eight-cornered; it is, therefore, written (Devarim, Ibid.) "on the four corners of your garment," to exclude the aforementioned. And whence is it derived that pillows and covers are (also) excluded (from tzitzith)? From (Ibid.) "wherewith you cover yourself." If from there, I would think that night-clothes are also included (as requiring tzitzith). It is, therefore, written (Bamidbar, Ibid. 39) "and you shall see it" — in the daytime and not at night. And if it were intended both for day and night, it requires tzitzith. I might think that this excludes both the above and the garment of a blind man; it is, therefore, written (Bamidbar, Ibid. 39) "And it shall be for you for tzitzith" — in any event (i.e., to include a blind man). (Ibid. 38) "and they shall place on the tzitzith (on) the corner a strand of tcheleth": spun and doubled. This tells me only of the tcheleth, that it is to be spun and doubled. Whence do I derive (the same for) the white (i.e., the wool)? You derive it by induction, viz.: Since the Torah said: "place" tcheleth and "place" white, just as tcheleth is spun and doubled, so, white is spun and doubled. "and they shall place": on the place of the weaving (i.e., the corner of the garment), and not on the place of the "growing" (i.e., the strands at the corner of the garment). If he did place it on the site of the "growing," it is (nonetheless) kasher. R. Eliezer b. Yaakov includes it both on the "growing" and on the very edge of the garment, it being written "on the corners of their garments." "and they shall place on the tzitzith (on) the corner": What is the intent of this? From "and they shall make for themselves tzitzith, I might think that he should weave it (the tzitzith) together with it (the garment; it is, therefore, written "and they shall place." How so? He ties it (the tzitzith) together with it (the garment). (Ibid. 39) "And it shall be to you for tzitzith": The four tzitzith are mutually inclusive (i.e., in the absence of one there is no mitzvah), the four being one mitzvah. R. Yishmael says: They are four mitzvoth. R. Elazar b. R. Shimon says: Why is it called "tcheleth"? Because the Egyptians were "bereaved" ("nitkelu" [like "tcheleth"]) of their first-born, viz. (Shemot 12:29) "And it was in the middle of the night, that the L-rd smote every first-born, etc." Variantly: Because the Egyptians were "destroyed" ("kalu") in the Red Sea. Why is it called "tzitzith"? Because the L-rd "looked" ("hetzith") over our fathers' houses in Egypt, as it is written (Song of Songs 2:9) "The voice of My Beloved, behold, it is coming … My Beloved is like a gazelle or a young hart … Behold, He stands behind our wall, looking through the windows, peering through the lattices." R. Chanina b. Antignos says: One who fulfills the mitzvah of tzitzith, what is said of him? (Zechariah 8:23) "In these days it will happen that ten men, of all the languages of the nations will take hold of the corner (i.e., of the tzitzith) of a Jewish man, saying 'Let us go with you, for we have heard that G-d is with you!'" And one who nullifies the mitzvah of "the corner," what is said of him? (Iyyov 38:13) "to take hold of the corners of the earth and to shake the wicked from it!" R. Meir says: It is not written (Bamidbar, Ibid. 39) "And you shall see them" (the tzitzith), but "And you shall see Him." Scripture hereby apprises us that if one fulfills the mitzvah of tzitzith, it is reckoned unto him as if he beheld the face of the Shechinah. For tcheleth is reminiscent of (the color of) the sea; the sea, of the firmament; and the firmament, of the Throne of Glory, as it is written (Ezekiel 1:26) "And above the firmament that was over their heads … (28) the appearance of the likeness of the glory of the L-rd." (Bamidbar, Ibid.) "and you shall see and you shall remember": See this mitzvah and remember another mitzvah, (which is contingent upon it.) Which is that? The recitation of the Shema — But perhaps (the reference is to) one of all the other mitzvoth of the Torah. It is, therefore, written (in the section of tzitzith, Ibid. 41) "I am the L-rd your G-d," which you find to be written only in (the section of) the recitation of the Shema. "and you shall remember": Remember (i.e., recite) the section with your mouth. I might think that the section "vehaya im shamoa" (Devarim 11:13-21) should precede all of the sections. — Would you say that? The section of Shema (Devarim 6:4-9), which contains acceptance of the yoke of the kingdom of Heaven should precede "vehaya im shamoa," which contains acceptance of the yoke of mitzvoth, and "vehaya im shamoa," which obtains both in the daytime and at night, should precede the section of tzitzith ("vayomer" [Bamidbar 15:37-41]), which obtains only in the daytime. And perhaps he should recite three (sections) in the evening as he does in the daytime. It is, therefore, written (of tzitzith [Bamidbar 15:39]) "and you shall see it" — in the daytime and not at night. R. Shimon b. Yochai says: The section of Shema, which contains (the mitzvah of) learning (Torah), should precede "vehaya im shamoa," which speaks only of teaching. And "vehaya im shamoa" should precede the section of tzitzith, which is only to do (i.e., the final stage). For thus was Torah given: to learn and to teach, to keep and to do: "And you shall see it, and you shall remember (all the mitzvoth of the L-rd, and you shall do them."): Now does this not follow a fortiori, viz.: If one who fulfills the mitzvah of tzitzith, (which is only a sign and a remembrance towards the doing of mitzvoth,) is accounted as one who has fulfilled all of the mitzvoth, how much more so (is this true of) one who (actively) performs (any one of) all the mitzvoth of the Torah! "And you shall not go astray after your hearts": This is heresy, as it is written (Koheleth 7:26) "And I find more bitter than death 'the woman' (heresy), whose heart is snares and nets. Her hands are bonds. The good before G-d shall escape her." "and after your eyes": This is harlotry, as it is written (Judges 14:3) "Take her for me, for she is just in my eyes." "after which you go astray": This is idolatry, as it is written (Ibid. 8:33) "and they went astray after the ba'alim." R. Nathan says: that one not "drink" in this "cup" (i.e., his own wife), and cast his gaze at the "cup" of another. Variantly: "And you shall not go astray after your hearts and after your eyes": This teaches us that the eyes follow the heart. — But perhaps the heart follows the eyes! Would you say that? Are there not blind men who commit all the abominations in the world? What, then, is the intent of "And you shall not go astray after your hearts, etc."? That the eyes follow the heart. R. Yishmael says: "And you shall not go astray after your hearts": What is the intent of this? From (Koheleth 11:9) "Rejoice young man in your youth (… and walk in the ways of your heart"), (I would not know whether) in a way that is straight or in (any) way that you like; it is, therefore, written "And you shall not go astray after your hearts." (Ibid. 40) "So that you remember and you do (all of My mitzvoth): This equates remembering with doing. "and you shall be holy to your G-d": This refers to the holiness of all of the mitzvoth. You say the holiness of (all the) mitzvoth, but perhaps the holiness of tzitzith (is intended). — Would you say that? What is the (general) context? The holiness of all the mitzvoth. Rebbi says: The reference is to the holiness of tzitzith. You say the holiness of tzitzith, but perhaps the holiness of all the mitzvoth is intended. — (Vayikra 19:2) "Holy shall you be" already refers to the holiness of all the mitzvoth. How, then, am I to understand "and you shall be holy to your G-d"? As referring to the holiness of tzitzith — whence it is seen that tzitzith add holiness to Israel. (Ibid. 41) "I am the L-rd your G-d, who took you out of the land of Egypt.": Why is this mentioned here? So that one not say: I will take imitation-dyed threads (and attach them to my garment) as tcheleth, and who will know the difference? If (within the framework of) the measure of punishment, the lesser measure (of the L-rd) — if one sins in secret, He exposes him in public, (as He did in Egypt), then, (within the framework of) the measure of good, the greater measure (of the L-rd) — how much more so (does this hold true)! Variantly: Why is the exodus from Egypt mentioned in connection with every mitzvah? An analogy: The son of a king's loved one was taken captive. When he (the king) redeems him, he redeems him not as a son, but as a servant, so that if he (the son) does not accept his decree, he can say to him "You are my servant!" When they enter the province, he (the king) says to him: Put on my sandals and carry my things before me to the bath-house. The son begins to object, whereupon the king presents him with his writ (of servitude) and says to him: "You are my servant!" Thus, when the Holy One Blessed be He redeemed the seed of His loved one, He did not redeem them as "sons," but as servants, so that if they reject His decree He says to them: "You are My servants!" When they went to the desert, He began to decree upon them some "light" mitzvoth and some formidable ones, such as Shabbath, illicit relations, tzitzith, and tefillin, and Israel began to object — whereupon He said to them: "You are My servants! On that condition I redeemed you; on condition that I decree and you fulfill!" "I am the L-rd your G-d": Why is this stated again? Is it not already written (Shemot 20:2) "I am the L-rd your G-d who took you out of the land of Egypt"? Why state it again? So that Israel not say: Why did the L-rd command us (to do mitzvoth)? Is it not so that we do them and receive reward? We shall not do them and we shall not receive reward! As Israel said (Ezekiel 20:1) "There came to me (Ezekiel) men of the elders of Israel to make inquiry of the L-rd, and they sat before me." They said to him: A servant whose Master has sold him, does he not leave His domain? Ezekiel: Yes. They: Since the L-rd has sold us to the nations, we have left His domain. Ezekiel: A servant whose Master has sold him in order to return, does he leave His domain? (Ibid. 32-33) "And what enters your minds, it shall not be, your saying: We will be like the nations, like the families of the lands, to serve wood and stone. As I live, says the L-rd G-d. I swear to you that I will rule over you with a strong hand and with an outstretched arm and with outpoured wrath!" "with a strong hand": pestilence, as it is written (in that regard, Shemot 9:3) "Behold, the hand of the L-rd is in your cattle, etc." "with an outstretched arm": the sword, as it is written (I Chronicles 21:16) "with his (the angel's) sword drawn in his hand, stretched over Jerusalem." "and with outpoured wrath": famine. After I bring these three calamities upon you, one after the other, I will rule over you perforce!
(2) R. Nathan said: There is no mitzvah in the Torah whose reward is not "at its side." Go and learn this from the mitzvah of tzitzith. There was once a certain man who was particularly diligent in the mitzvah of tzitzith. Once, hearing of a ("famed") harlot in the cities of the sea, who took four hundred gold coins as her hire, he sent her that sum, and she set a time for him. When the appointed time came, he went there and sat at the door of her house. Her maid-servant went in and said to her: That man whom you appointed a time for is sitting at the door of the house. The harlot: Let him come in. When he came in, she spread seven beds for him, six of silver and one of gold, and she was on the uppermost. Between each one was a silver ladder, and the uppermost, of gold. When he came to the act, his four tzitzith came and struck him across his face. They seemed to him like four men. He immediately left off and sat upon the ground. She, too, left off and sat upon the ground. She said to him "'Gapa of Rome' (an idolatrous oath), I shall not let you go until you tell me what blemish you have seen in me!" He: I swear, I have seen no blemish in you. There is no beauty like yours in all the world, but there is one mitzvah (tzitzith) concerning which it is written two times (Bamidbar 15:41) "I am the L-rd your G-d." "I am the L-rd your G-d" — I am destined to reward; "I am the L-rd your G-d" — I am destined to punish. And now they appeared to me as four witnesses (testifying to the above). At this, she said: I swear that I will not let you go until you write for me your name, the name of your city, and the name of the place where you study Torah. He wrote for her his name, the name of his city, the name of his master, and the name of the place where he studied Torah — whereupon she arose and divided all of her wealth: a third to the authorities (for permission to convert), a third to the poor, and a third which she took with her, in addition to those spreads. When she came to R. Meir's house of study, she said to him: My master, convert me. R. Meir: Is it possible that you have "cast your eyes" upon one of my disciples! At this, she took out the note that she had with her, and he said to her: "Go and claim your purchase!" Those spreads which she had spread for him unlawfully, she now spread for him lawfully, This was her reward in this world. As to the world to come, I do not know how much.
"Also women are logically included." Or "So, too, women are implied." R. Shimon exempts women from tzitzit since women are exempt from mitzvot that are time-bound. This is the general rule. R. Shimon said that women are exempt from every positive time-bound mitzvah. This [mitzvah] is the practice for men but not for women, for the ritually fit [men] but not the ritually unfit [men]. R. Yehudah ben Baba says says the Sages especially exempted the wrap of a woman from tzitzit and only obligated it as a tallit because sometimes her husband covers himself in it.
ת"ר איזוהי מצות עשה שהזמן גרמא סוכה ולולב שופר וציצית ותפילין ואיזוהי מצות עשה שלא הזמן גרמא מזוזה מעקה אבידה ושילוח הקן וכללא הוא הרי מצה שמחה הקהל דמצות עשה שהזמן גרמא ונשים חייבות ותו והרי תלמוד תורה פריה ורביה ופדיון הבן דלאו מצות עשה שהזמן גרמא הוא ונשים פטורות אמר רבי יוחנן אין למדין מן הכללות ואפילו במקום שנאמר בו חוץ דתנן בכל מערבין ומשתתפין חוץ מן המים ומלח ותו ליכא והאיכא כמהין ופטריות אלא אין למדין מן הכללות ואפילו במקום שנאמר בו חוץ: ומצות עשה שהזמן גרמא נשים פטורות: מנלן גמר מתפילין מה תפילין נשים פטורות אף כל מצות עשה שהזמן גרמא נשים פטורות ותפילין גמר לה מתלמוד תורה מה תלמוד תורה נשים פטורות אף תפילין נשים פטורות ונקיש תפילין למזוזה תפילין לתלמוד תורה איתקיש בין בפרשה ראשונה בין בפרשה שניה תפילין למזוזה בפרשה שניה לא איתקיש ונקיש מזוזה לתלמוד תורה לא סלקא דעתך דכתיב (דברים יא, כא) למען ירבו ימיכם גברי בעי חיי נשי לא בעי חיי והרי סוכה דמצות עשה שהזמן גרמא דכתיב (ויקרא כג, מב) בסוכות תשבו שבעת ימים טעמא דכתב רחמנא האזרח להוציא את הנשים הא לאו הכי נשים חייבות אמר אביי איצטריך סלקא דעתך אמינא הואיל דכתיב בסוכות תשבו תשבו כעין תדורו מה דירה איש ואשתו אף סוכה איש ואשתו
Our Sages taught in a beraitha: What is a positive time-bound mitzvah? Sukkah and lulav, shofar and tzitzit and tefilin. And what is a positive non-time-bound mitzvah? Mezuzah, a [roof] railing, [returning a] lost item, and sending [a mother bird from] the nest. And is this a general principle? Are not matzah and rejoicing [on a festival] and hakhel positive time-bound mitzvot for which women are obligated?! And furthermore, are not Torah study and procreation and redemption of the firstborn not positive non-time-bound mitzvot from which women are exempt? Said R. Yohanan: One does not learn from general principles even in a place where an exception is said.
The gemara goes on to give some examples of other exceptions. Then it explains the origin of the general principle of women's exemption from time-bound mitzvot, which is the example of tefilin, and its juxtaposition to Torah study in both the first and second paragraphs of the Shema. The reason that mezuzah is required of women (and therefore put in the positive non-time-bound mitzvah), despite it being juxtaposed to both tefilin (in paragraph one of the Shema) and Torah study (in paragraph two of the Shema), is that it is also juxtaposed to the verse למען ירבו ימיכם, and don't women need life as much as men?
I bring the previous paragraph to illustrate that the rabbis have admitted that one cannot blindly go by the general principle. See the next comment.
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Elizabeth Shanks Alexander, Gender and Time-Bound Commandments in Judaism
"As far as I can tell, however, the process of conceiving the category and formulating the rule did not require the sages to reflect on the social implications exempting women from tefillin. Rather, the category and the rule seem to have emerged when the sages reflected on the relationship between the tefillin verses and the tefillin instructions (of which women's exemption was one)." (p. 33)
"I further argue that the act of naming tefillin as a "timebound, positive commandment from which women (and slaves) are exempt" had implications beyond being a useful description of tefillin. Naming tefillin as a "timebound, positive commandment from which women are exempt" apparently suggested that a broader category of timebound positive commandments existed, for which there might be other exemplars. (p. 37)
רב יהודה רמי תכילתא לפרזומא דאינשי ביתיה ומברך כל צפרא להתעטף בציצית מדרמי קסבר מצות עשה שלא הזמן גרמא הוא אמאי מברך כל צפרא וצפרא כרבי דתניא תפילין כל זמן שמניחן מברך עליהן דברי רבי אי הכי כל שעתא נמי רב יהודה איניש צניעא הוה ולא שרי ליה לגלימיה כוליה יומא ומאי שנא מצפרא כי משני מכסות לילה לכסות יום ת"ר הכל חייבין בציצית כהנים לוים וישראלים גרים נשים ועבדים ר"ש פוטר בנשים מפני שמצות עשה שהזמן גרמא הוא וכל מצות עשה שהזמן גרמא נשים פטורות אמר מר הכל חייבין בציצית כהנים לוים וישראלים פשיטא דאי כהנים לוים וישראלים פטירי מאן ליחייב כהנים איצטריכא ליה ס"ד אמינא הואיל וכתיב (דברים כב, יא) לא תלבש שעטנז צמר ופשתים יחדיו גדילים תעשה לך מאן דלא אישתרי כלאים לגביה בלבישה הוא דמיחייב בציצית הני כהנים הואיל ואישתרי כלאים לגבייהו לא ליחייבו קמ"ל נהי דאישתרי בעידן עבודה בלא עידן עבודה לא אישתרי ר"ש פוטר בנשים מאי טעמא דר"ש דתניא (במדבר טו, לט) וראיתם אותו פרט לכסות לילה אתה אומר פרט לכסות לילה או אינו אלא פרט לכסות סומא כשהוא אומר (דברים כב, יב) אשר תכסה בה הרי כסות סומא אמור הא מה אני מקיים וראיתם אותו פרט לכסות לילה ומה ראית לרבות כסות סומא ולהוציא כסות לילה מרבה אני כסות סומא שישנה בראיה אצל אחרים ומוציא אני כסות לילה שאינה בראיה אצל אחרים ורבנן האי אשר תכסה בה מאי עבדי ליה מיבעי להו לכדתניא (דברים כב, יב) על ארבע כנפות כסותך ארבע ולא שלש אתה אומר ארבע ולא שלש או אינו אלא ארבע ולא חמש כשהוא אומר אשר תכסה בה הרי בעלת חמש אמור ומה אני מקיים על ארבע ארבע ולא שלש ומה ראית לרבות בעלת חמש ולהוציא בעלת שלש מרבה אני בעלת חמש שיש בכלל חמש ארבע ומוציא אני בעלת שלש שאין בכלל שלש ארבע ור"ש מאשר נפקא ורבנן אשר לא משמע להו ורבנן האי (במדבר טו, לט) וראיתם אותו מאי עבדי ליה מיבעי להו לכדתניא וראיתם אותו וזכרתם ראה מצוה זו וזכור מצוה אחרת התלויה בו ואיזו זו זו קרית שמע דתנן מאימתי קורין את שמע בשחרית משיכיר בין תכלת ללבן ותניא אידך וראיתם אותו וזכרתם ראה מצוה זו וזכור מצוה אחרת הסמוכה לה ואיזו זו זו מצות כלאים דכתיב (דברים כב, יא) לא תלבש שעטנז צמר ופשתים יחדו גדילים תעשה לך תניא אידך וראיתם אותו וזכרתם את כל מצות ה' כיון שנתחייב אדם במצוה זו נתחייב בכל מצות כולן ור"ש היא דאמר מצות עשה שהזמן גרמא היא תניא אידך וראיתם אותו וזכרתם את כל מצות ה' שקולה מצוה זו כנגד כל המצות כולן ותניא אידך וראיתם אותו וזכרתם ועשיתם ראיה מביאה לידי זכירה זכירה מביאה לידי עשיה ורשב"י אומר כל הזריז במצוה זו זוכה ומקבל פני שכינה כתיב הכא וראיתם אותו וכתיב התם (דברים ו, יג) את ה' אלהיך תירא ואותו תעבוד
Rav Yehudah would attach blue threads to the apron of his wife and bless every morning להתעטף בציצית. From his affixing, he really thinks that it is a positive non-time-bound mitzvah [and therefore women are obligated in it]. Why did he recite the blessing every morning? As Rabbi taught in a beraitha,every time one puts on tefillin, one blesses over them. If so, he should also [have recited the blessing] every time [he took the garment off and put it back on]. Rav Yehudah was a modest man and he didn't remove his cloak the entire day. How is this different? [Why is this unique?] When he changed from a nighttime garment to a daytime garment. The Sages taught in a beraitha: Everyone is obligated in tzitzit, Priests, Levites, Israelites, converts, women, and slaves. Rabbi Shimon exempts women due to its being a positive time-bound mitzvah and women are exempt from all positive time-bound mitzvot.
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Another beraitha is taught: "That you may look upon it and remember all God's commandments" (Numbers 15:39). Once a person [אדם] is obligated in this mitzvah, he is obligated in every one of the mitzvot. And this is compatible with the opinion of Rabbi Shimon that this is a positive time-bound mitzvah.
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Another beraitha is taught: "That you may look upon it and remember all the mitzvot of Adonai." This mitzvah is equivalent to all the other mitzvot together.
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Another beraitha is taught: "That you may look upon it and remember all of God's mitzvot" (Numbers 15:39) is equal to all the mitzvot together. Another beraitha is taught: "That you may look upon it and remember and do" - looking leads to remembering, remembering leads to do doing. Rashbi says: anyone who is zealous in this mitzvah merits and receives the presence of the Shechina. It is written here: "That you may look upon it [אותו]" (Numbers 15:39) and it is written there "You shall fear Adonai your God and serve him [אותו]" (Deut. 6:13).
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By the number of times it is mentioned that women are obligated in the mitzvah of tzitzit, and then afterwards only Rabbi Shimon is mentioned as having the opinion that women are exempt because of the time-bound nature of the positive mitzvah, it appears that the conventional thinking was the former and that Rabbi Shimon's opinion was the minority position.
There is much discussion on the details of fulfilling the mitzvah of tzitzit - which garments are proper, what time of day (day or day and night) are necessary, blessings, material, responsibility of other individuals - and some of these seem to be brought out to justify a strict opinion on women's exemption. I was particularly struck by the equating of the mitzvah of tzitzit to all mitzvot in general, and since, because of the general principal of women being exempt from positive time-bound mitzvot (stemming from the "penultimate mitzvah of tefillin" (in Alexander's words), women are therefore not obligated in tzitzit. With this argument, it would seem that women are not obligated in any mitzvot - but I suppose this is just one line of reasoning and אין למדין מן הכללות.
ראב"ע במדבר טו:לט
והיה לכם לציצת. והנה ישוב הפתיל להיותו בקצה כמו הציצית. והפירוש השני כאשר העתיקו חז''ל. ובעבור שיש עדים נאמנים על הפירוש השני בטל הראשון. והם העתיקו, כי זאת המצוה עם בגד שיש לו ארבע כנפים. והציצית הם הגדילים, ועוד אפרשנו. והנה מצוה על כל מי שיש לו בגד בארבע כנפים שיתכסה בו ביום תמיד, ולא יסירנו מעליו, למען יזכרו. והמתפללים בטלית בשעת התפלה, יעשו זה בעבור שיקראו בקריאת שמע, והיה לכם לציצית, ועשו להם ציצית,רק לפי דעתי יותר הוא חייב להתעטף בציצית בשאר השעות משעת התפלה,למען יזכור ולא ישגה ולא יעשה עבירה בכל שעה, כי בשעת התפלה לא יעשה עבירה. וראיתם אותו. מצוה להיות נראה, אחרי לבבכם. המתאוה והעין רואה והלב חומד. והנה יהיה הציצית לאות ולסימן שלא ירדוף אדם אחר הרהור לבו וכל אשר שאלו עיניו. אשר אתם זונים. כי מי שילך אחרי תאותו הוא זונה מתחת עבודת אלהיו.
And it shall be to you as fringes....And it is a mitzvah upon everyone who has a garment with four corners, that he should cover himself with it during the entire day and not take it off, so that he [they] will remember. Those who pray with a tallit during prayer [only], do it because they read in the recitation of the Shema "and you shall have for yourself tzitzit, and make for yourself tzitzit," but in my opinion one is more obligated to wrap in tzitzit during times other than prayer, in order to remember and not forget and not commit a sin at any time, because during the time of prayer one doesn't sin. And you may look upon it. It is a commandment [for the tzitzit] to be seen. After your own heart. The one who desires: the eye sees and the heart covets. And so the tzitzit will be as a sign and a symbol that a person should not chase after the thoughts of his heart and what his eyes seek. After which you go astray [lust]. As someone who goes after his desire is going astray from service to his God.
38 Speak to the Israelite people. Literally, "to the sons of Israel," not to the women; the subject to which this commandment alludes is too profound for women's flighty intelligence to attain it (Gersonides).
From The Commentators' Bible: The JPS Miqra'ot Gedolot, Numbers (Michael Carasik), p. 113.
See below. I later found the original source for Rabbi Levi ben Gershom's comments above. It is clear he has taken a very conservative view of the mitzvah of tzitzit and its observance by women. First, in an almost exceptional literary interpretation, he sees the words בני ישראל as referring to "the sons of Israel." Second, he expresses the belief in the inferior intellectual and spiritual nature of women such that they are not capable of observing the mitzvah of tzitzit, or more specifically, "the subject to which the mitzvah alludes," a little murky, but perhaps the process of linking a physical object to a reminder to action, which in this case refers to the entire body of mitzvot. Are women "too flighty" to understand what tzitzit stand for or are they "too flighty" to observe all the mitzvot?
רלב"ג, במדבר טו:לט
וראיתם אתו......והנה מפני הצוואה הזאת ל"בני ישראל" למדנו שאין הנשים חייבות בציצית וראוי היה להיות כן, כי הענין אשר תעיר עליו זאת המצוה הוא רב העומק ולא יתכן שיגיע אליו שכל הנשים, לקלות דעתם.
That you may look upon it... And here, because of this commanding to "the sons of Israel," we learn that women are not obligated in tzitzit and it is fitting that it should be thus, because the matter about which the mitzvah awakens one is very deep and it is not possible that the intelligence (understanding) of women will reach it, due to their frivolity.
Tamar Ross, Expanding the Palace of Torah: Orthodoxy and Feminism
The second part of Ralbag's commentary above is in contrast to one of the arguments presented by Ross in chapter 2 of her book (" Sources of Discontent and the Conservative Response"). While the perspectives of Ralbag and this specific one presented by Ross both focus on the nature of women in justifying why the mitzvah of tzitzit, among others, is not required of women, the bases for this justification comes from quite different views of women. Ross summarizes Rabbi Samson Raphael Hirsch, who elaborates on the ideas of the 16th-century Rabbi Judah Loew ben Bezalel (the Maharal of Prague), and she writes:
"...woman requires fewer formal obligations because she is capable of attaining ideal levels of virtue without the rigorous mitzvah-training assigned to men and the added assistance of symbolic reminders: "God's Torah takes it for granted that our women have greater fervor and more faithful enthusiasm for their God-serving calling, and that this calling runs less danger in their case than in that of men from the temptations which occur in the course of business and professional life." (fn 43 in Ross, p. 262)
...What is noteworthy...is the subtle upgrade from an assertion of "separate but equal" to an implication that woman is superior."
(p. 36)
Tamar Ross goes on to state that even though Rabbi Zvi Yehuda Kook supports the exemption of women from positive time-bound mitzvot, "he too links women's exemption from time-bound mitzvot with their greater connectedness to the divine...he supports their assuming the mitzvot voluntarily. And if they recite the same blessing as men do, expressing gratitude for having been commanded to perform the act (...asher kideshanu bemitzvotav vetzivanu), he does not regard it as a blessing made in vain (berakha levatala)." (fns 48, 49 in Ross, p. 263)
(p. 37)
(ב) נשים ועבדים פטורים מפני שהיא מצות עשה שהזמן גרמא: הגה ומ"מ אם רוצים לעטפו ולברך עליו הרשות בידם כמו בשאר מצות עשה שהזמן גרמא [תוס' והרא"ש והר"ן פ"ב דר"ה ופ"ק דקידושין] אך מחזי כיוהרא לכן אין להן ללבוש ציצית הואיל ואינו חובת גברא [אגור סי' כ"ז] פי' אינו חייב לקנות לו טלית כדי שיתחייב בציצית. ולקמן בסימן י"ט אמר כשיש לו טלית מארבע כנפות ולובשו] טומטום ואנדרוגינוס חייבין מספק ויתעטפו בלא ברכה: [פי' טומטום לא נודע אם הוא זכר או נקיבה ואנדרוגינוס יש לו זכרות ונקבות] [הגה ולפי מה שנהגו נשים לברך במצות עשה שהזמן גרמא גם הם יברכו] [דברי עצמו]:
(2) Women and slaves are exempt [from wearing tzitzit] because it is a time-dependent commandment. Rem"a: And if they wish to wrap [in tzitzit] and say the blessing on them it is up to them to do so as with all time-dependent commandments (Tosafot and the Rosh and the Ran, Chapter 2, Rosh Hashanah, First Chapter of Kiddushin). However, it looks as if they are doing it to appear more observant than others, therefore, they should not wear tzitzit, as it is not a commandment of the person [rather of the object] (Agur Section 27). [And for slaves] This means we do not have to buy him a tallit in order that he be required to wear tzitzit as we see in Chapter 19 it says when he has a shawl with four corners he should wear it.The requirement for a tumtum and an androgynous is doubtful and so they should wrap without a blessing (Explanation: a tumtum does not know whether he/she is male/female, and an androgynous has both male and female genitals).Rem"a: And since it is our custom that women should say the blessing when they fulfill time-dependent commandments so should they (Divrei Atzmo)
Women and slaves are exempt because it is a positive time-bound mitzvah:
Hagah: And in any event, if they want to wrap and bless upon it, the control is in their hand as with the rest of the positive time-bound mitzvot. However, it appears as arrogance; thus they should not wear tzitzit because it is not a personal obligation [but of the object/garment].
(The text continues to say that a person is not obligated to go out and purchase a garment on which to place tzitzit, but if one has such a garment, then one is obligated to put tzitzit on it.)
טור אורח חיים סימן יז
סומא חייב בציצית ונשים ועבדים פטורים וטומטום ואנדרוגינוס חייבים מספק וכתב הרמב"ם ז"ל יתעטפו בלא ברכה והוא הולך לשיטתו שפירש שנשים אין יכולות לברך בדבר שהן פטורות אבל ר"ת כתב שיכולות לברך אף על פי שהן פטורות ויותר טוב שלא יברכו קטן היודע להתעטף אביו צריך ליקח לו ציצית לחנכו:
Rabbeinu Tam writes that [women] are allowed to bless [regarding the mitzvah of tzitzit] even though they are exempt, but it is better if they don't bless.
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משנה ברורה, הלכות ציצית, סימן יד (א)
ציצית שעשען אינו יהודי, פסול, דכתיב: "דבר אל בני ישראל," לאפוקי אינו יהודי. והאשה כשרה לעשותן. הגה: ויש מחמירין להצריך אנשים שיעשו אותן, וטוב לעשות כן לכתחלה:
Tzitzit that are made [worn] by a non-Jew are disqualified, as it is written "Speak to the Children of Israel," to exclude someone who is not Jewish. And a woman is legally permitted to wear them. Hagah: And some rule strictly to require men [only] to wear them, and it is good to do this in the first place (ideally).
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Some final comments
I conducted a general survey of sources, from biblical to modern times, relating to women's obligation (or not) regarding the mitzvah of tzitzit. To me it seems clear that originally the mitzvah could very logically be seen as directed to women as well as men. The manner in which the discussion is presented in the talmud, with R. Shimon's position - making women exempt due to the mitzvah's time-bound nature - stated repeatedly and only in his name, hints at his opinion being a minority opinion. Nevertheless, it is the position that became generally accepted, with different justifications cited later in the talmud and by rabbis thereafter. Some leniency has been inserted in the halakhah, allowing for women to wear tzitzit and to recite its blessing, although there does not seem to be clarity on this.