We also find the din of Bikur in Hilchos Rosh Hashanna. Ashkenazim begin Slichos no less than four days before Rosh Hashanna. The Elya Rabba (see MB OC 581:SK6) says this is because by Rosh Hashanna it says (Bamidbar 29:1-2) וּבַחֹדֶשׁ הַשְּׁבִיעִי בְּאֶחָד לַחֹדֶשׁ, מִקְרָא קֹדֶשׁ יִהְיֶה לָכֶם כָּל-מְלֶאכֶת עֲבֹדָה לֹא תַעֲשׂוּ: יוֹם תְּרוּעָה, יִהְיֶה לָכֶם. וַעֲשִׂיתֶם עֹלָה לְרֵיחַ נִיחֹחַ, which we interpret to mean that you should make yourselves into a Korban Olah for Rosh Hashanna; since some Olos (namely, the Tamid,) require bikkur, you too should examine yourselves for spiritual blemishes no less than four days before you do your avoda of Rosh Hashanna.
Rav Shternbuch in his Taam VaDaas here suggests that Bikkur is an expression of Chivuv Mitzvos, an expression of our love for the precious mitzvos. In truth, you can examine the korban in one day just as well as you can in four days. The additional days accomplish nothing. (See Note 2.) But the additional examination shows a passion, an infatuation with the mitzva, that drives you to do the mitzva in the best possible way; it quadruples the preparation, and this is meritorious. In fact, that is how Rashi uses the din Bikkur in Passuk 6, where he says that the reason Pesach Mitzrayim needed bikkur while Pesach Doros does not is because the Jews of that time lacked mitzvos or merits that would distinguish them from their Egyptian neighbors and that would justify doing a miracle to redeem them. So Hashem gave them the din of Bikkur so that they would become involved and busy in preparing for the Mitzva four days before. The zechus of that extra effort helped them merit Yetzias Mitzrayim.
What I liked about Rav Shternbuch's observation was that he connects this Din Bikkur to peoples' behavior before Sukkos. I know hilchos Dalem Minim, I've grown Esrogim, and I can confidently pick a Lulav and Esrog in ten minutes. I always found the obsessive and minute checking people do on their daled minim to be odd. He says that this is a minhag Yisrael, and it is the equivalent of Bikkur; check again, and again, and again, even though you know exactly what you're going to find, because this is hiddur mitzvah. One might speculate as to why only particular mitzvos have this din; it's easy to surmise that it is found by daled minim because they have a special din of hiddur. Tamid is still tzarich iyun.
By the way, if you are going to accuse me of baalebatisheh thinking because I'm speculating about Taamei Hamitzvos, go and look at the last Rambam in Hilchos Temura, to wit:
Another place you find the term bikkur is, of course, in Bikkur Cholim. The Gaon (Aderes Eliahu Devarim 1:12) says that the reason the Gemara (Pesachim 30b and Sotah 12) derives Bikkur cholim from the word ילכו is because the tachlis of Bikkur Cholim is the הליכה, the walking, the preparation. I never understood this Gaon. I asked this question on an earlier post on this week's parsha which discusses S'char Halicha, here. But it might be that this is the whole idea of Bikkur- overdo the preparation. The הכנה is very important, the הכנה has independent significance. Do more than would be necessary just to ensure that you can do the mitzva. Plan it out, be super meticulous, ensure that you do it in the most perfect and thorough manner. If this is what Bikkur means, then ילכו is indeed the paradigm of hachana.
Here is the Gaon:
ילכו זה ביקור חולים מפני שבכל המצוות ההליכה אינה תכלית המצוה אבל כאן ההליכה עצמה היא המצוה
My problem is that in every mitzva, going is preparation, and doing is the fulfillment. Here too, going is preparation, and visiting, standing there and commiserating or getting him something, or whatever you do when you're mevaker choleh, is the mitzva. Evidently, the going is a greater part of this mitzva. What does that mean? Why is that true? How does the Gaon know it, and how do Chazal know it?
Michael, in the comments, proposes that because Bikur Cholim is like קבלת פני השכינה, the walking has a special meaning (like by Aliya Le'Regel (see Teshuvos Chasam Sofer ChM 176, and the story with the lady and Reb Yochanan in Sota 22a and Bava Metziah 107a as I mention in the post I cited above, both involving presenting one's self before the Shechina.) I found that Harav Avraham Shapiro is quoted as having taken essentially the same approach, as follows:
I've been thinking about this, and I'm pretty convinced that this is a legitimate approach.
- The reason Reb Yochanan agreed that there is special schar halicha for tefilla is because tefilla is the only moment where we are עומדים לפני המלך, where we are standing in the presence of the Ribono shel Olam.
- Tefillos, as Rebbi Yehoshua ben Levi in Brachos 26b says, כנגד תמידים תקנום, so it stands to reason that this aspect of עומד לפני המלך was present in the Tmidim as well.
- As Rav Hirsch says, the Temidim, in a sense, are an extension of the experience of the Pesach in Mitzrayim, which was the moment that Klal Yisrael met the Ribono shel Olam, when the Ribono shel Olam Himself was present to smite the Mitzrim and save the Ivrim.
- And perhaps this is the pshat by bikkur cholim as well- that we should view bikkur cholim like aliyah le'regel, as if we're coming into Hashem's presence.
This is not like Rav Shternbuch's approach.
Note 1. Rashi and most mefarshim hold that the four-day-examination rule applies to all Pesachim and not only the Pesach Mitzrayim. The only aspect of bikkur that distinguished Pesach Mitzrayim is that it was made Hekdesh on the tenth, a requirement not found by Pesach Doros, which you can and should be makdish right before you bring it in to the Azara. I believe the Rambam argues and holds that there is no din Bikkur at all by Pesach Doros. Support for this is found in פרי מגדים מש"ז סי' ת'ל,מנחת חינוך מצוה ה, and here.
Note 2. Some honorable mefarshim say that the extra days allow you to decide whether a blemish is temporary or permanent. I seriously don't know what he is talking about; 1. if this were so, it would apply to all korbanos; 2. even a temporarily blemished animal cannot be sacrificed while it is blemished; 3. it would only apply to animals with some blemish.