What is the source for the concept that Jews have to practice Tikkun Olam, and where in the classical Jewish sources is this concept defined? It seems people throw this term around a lot in the context of social justice causes. I don't remember seeing anywhere in the Torah or Gemara about this term having that meaning; am I wrong?
The more general sense of "tikkun olam," making the world at large a more G-dly place, comes (although I don't know if the actual phrase does) from the Arizal's description of the spiritual "World of Tohu" that "broke apart" and scattered sparks of G-dliness throughout the cosmos. Every time something in our world is used in serving Hashem, its sparks are "corrected" and uplifted, and the world is brought closer to being a "dwelling-place for Him."
The popular notion that "tikkun olam" means supporting various fashionable "progressive" causes derives from a broadening/distortion of this idea.
LeTaken Olam b'malchut sha-dai appears in the daily Aleinu, of course.
Tikkun Olam appears as a cause in the Mishna in a very focused sense, for instance Chapter 4 of tractate Gittin cites a number of "public policy enactments", because of Tikkun Olam; most notably, don't pay too much ransom for a kidnapped Jew, or else unfriendly non-Jews will get in the regular habit of kidnapping them. Another tikkun olam enactment mentioned there is Hillel's pruzbul.
I first read about Tikkun Olam from commentators on works of the Arizal and Zohar, Moshe Chaim Luzatto, Rabbi Avraham Kook. Rebbe Nachman taught and talked about repairing the world. From my understanding of this reading, tikkun olam seems to be the mystical component of mitzvot.
Doing the 613 mitzvot is engaging in Tikkun Olam, and is making the world a better place. Tikkun according to some of the deeper explanations, is why we human beings were created in the first place (our purpose). In order to direct and focus that repair, we received and aggreed to the holy covenant, essentially the manual on how to make the world a better place.
The "sod" very deep explanations of mitzvot are not in opposition to literal, emotional, ethical and deep spiritual explanations. One of the more beautiful aspects of Jewish thinking (as opposed to dualistic western worldviews) is that all 5 perspectives are correct. There has been a 'blackout' on sod, kabbalistic explanations (for good and interesting reasons), so not everyone hears this even if they have yeshiva level educations.
Tikkun Olam is the reason in theoretical Kabbalah why anyone would even bother with pursuing enlightenment or understanding or wisdom. It puts the spiritual to good use in a very practical way. It is a perspective for why one does mitzvot, not a 'you must do thus and such'. That level of understanding is what someone earlier referred to as secular greenies and activists. Agree with the comment that secular peace and justice people may not understand why they are changing the world's diapers, some may, but it doesn't really matter because is still better than not doing anything at all. Poopashuey, we have to drive on the same roads as everyone else, and it affects us all. In this Jewish philosophical system of Lurianic Kabbala, even the secular actions have sacred as well as practical consequences.
EDIT: Specific verses from the sages: Derech HaShem by one of our sages, the RaMChaL, try page 83 http://books.google.com/books?id=Zx4PTan5OO0C&pg=PA61&source=gbs_toc_r&cad=4#v=onepage&q=1%3A5%3A7&f=false
You will see this translated as either "repair" or "rectification".
Rebbe Nachman ~200 years after RamChal spoke of repairing souls. His books aren't online or I'd give you a quote. Here is a dvar Torah with these concepts: http://www.breslov.org/dvar/zmanim/elul1_5762.html
Rectification was addressed by subsequent Chazal where it developed into mussar literature. One would apply repair to their souls first, to develop a clean heart and closeness to G-d, as David HaMelech, Asaph, and the Navim taught. The inner change affects an outer change, otherwise one may sustain spiritual injury. (Unless they're just doing it like a car wash or buying clothes for disaster victims,etc.) This repair of the inner world, accomplished by meditation and prayer and thought, prepares one for living on a higher plane of existence closer to G-d. Tikkun Olam is part of G-d's greater plan of rectification of this entire universe, according to the Sages.
When Adam sinned, he "broke" the world. Now that the world as been broken, we must fix it and no longer break it any more.
(מסילת ישרים - Mesillat Yesharim http://www.shechem.org/torah/mesyesh/h1.htm)
והנה על העיקר הזה העירונו זכרונם לברכה במדרש קהלת (רבה, ז) שאמרו, זה לשונם: ראה את מעשה האלהים וגו' (קהלת ז), בשעה שברא הקדוש ברוך הוא את אדם הראשון, נטלו והחזירו על כל אילני גן עדן ואמר לו, ראה מעשי כמה נאים ומשובחים הן, וכל מה שבראתי בשבילך בראתי, תן דעתך שלא תקלקל ותחריב את עולמי. כללו של דבר, האדם לא נברא בעבור מצבו בעולם הזה אלא בעבור מצבו בעולם הבא, אלא שמצבו בעולם הזה הוא אמצעי למצבו בעולם הבא שהוא תכליתו
(Translation - Path of the Just: http://www.shechem.org/torah/mesyesh/1.htm)
When the Holy One Blessed be He created Adam, He took him and caused him to pass before all the trees of the Garden of Eden. He said to him, `See how beautiful and praiseworthy are my works; and all that I have created, I have created for your sake. Take heed that you do not damage and destroy my world.'
She talks about the five uses of the term tikun olam:
- Aleynu - Eliminate evil and actually establishing a new world order.
- Bereshit Rabbah - physically fix Creation
- Rabbinic law like Gittin, Pesachim, and Shvi'it - changing untenable laws to fix a broken system
- Arizal's writings and other mystical texts - repairing the broken klipot.
- 1950s America - Social justice work
She comes to the conclusion that no one knows why the term was brought back into parlance each time or how it changed its meaning so many times (note that none of the concepts are much related).
She ends on her own interpretation of its modern origins:
These four strands, though complementary in some ways, also remain in tension with one another in some other important ways.
By combining the major themes of these four strands, we come to a definition of tikkun olam as the process of fixing large societal problems, while maintaining a belief that our actions can have a positive effect on the greater human and divine world.