I
"And Yitzchak went out to speak in the field, towards evening time...(Breishit 24:63).
The Gemara derives from this verse that Yitzchak founded tefilat minchah. Nonetheless, the time prescribed for this prayer is based upon the service of the Korban Tamid in the Bet Hamikdash (B'rachot 26b). The Mishna in Brachot (26a) records a dispute regarding the time restriction of Minchah. "Tefilat Haminchah [can be recited] until the evening; Rebbe Yehuda says until plag haminchah [one and a quarter halachic hours (sha'ot zemaniyot) before sunset]." The first opinion in the Mishnah is quite clear. The afternoon sacrifice cannot be offered after the day as ended; so, too, tefilat minchah can no longer be recited past this time. Why, though, does Rebbe Yehudah choose plag minchah as the deadline for this prayer? Probably, because he holds that plag is the cut-off point for the afternoon korban tamid.
However, Tosfot (ibid.) seems to understand otherwise. They explain that the normal practice in the Bet Hamikdash was to begin the afternoon tamid at nine and a half hours (halachic hours). The service culminated with the incense offering (k'toret) , which coincided with plag minchah. Rebbe Yehudah insists that our prayers match the time frame of the normal practice in the Bet Hamikdash. In other words Rebbe Yehudah also agrees that the afternoon tamid may be offered the entire day, even after plag minchah. Rather, he maintains that the time restriction does not follow the theoretical, permitted schedule of the tamid, only the practical time in which it was actually brought. (Based upon Lechem Mishnah, Rambam Tefilah, chapter 3).
II
Interestingly, the Gemara, (Brachot 27a) extends this dispute to the beginning, earliest time for the evening prayer. According to the first Tanna of the Mishnah, one must wait until the aforementioned "evening" point has been reached. [A full understanding of this concept and how it relates to shkiah, tzet hakochavim etc. is beyond our present scope]. Rebbe Yehudah, though, would allow the evening prayer from plag minchah onwards.
What is the connection between their Minchah dispute to the issue of Maariv? Maariv has nothing to do with the korban tamid. Shouldn't the nightly prayer just be governed by the onset of night?
A simple answer relates to the counterpart of the evening prayer, namely, - hekter chalavim v'evarim - the burning of fats and limbs upon the altar. This service was allowed all day and all night. Thus, in essence, Maariv is not a nightime prayer, per se. It is the prayer which fills in the void, of when there are no other prayers. Once shacharit andminchah pass, Maariv - hekter chalavim v'evarim - can automatically set in. Thus, the deadline for minchah can, in fact, decide the onset of Maariv.
The Bet Halevi (1:9) offers a reverse reasoning. [The incentive of the Bet Halevi is an attempt to resolve a particular contradiction in the Rosh on Masechet Brachot]. Perhaps, the argument by minchah really stems from a more basic dispute regarding maariv, or night itself. After all, the reasoning of Tosfot (section I) - that Rebbe Yehudah chose the actual time, as opposed to the true halachic deadline - doesn't seem to be a full explanation. Why didn't Rebbe Yehudah follow the true cut off point of "evening"?
The Bet Halevi reasons that the Tanaim dispute the status of plag haminchah, per se. According to Rebbe Yehudah, plag haminchah is considered - to some degree (see Tosfot (ibid. 27a) as to the onset of shabbat) - to have the halachic status of night. Thus, the nightime prayer of maariv begins then. Once maariv has been set fromplag onwards, minchah cannot be prayed any longer. For this reason, Rebbe Yehudah had to prefer the practical time of the tamid, rather than the true deadline which is well past plag haminchah. According to this approach, a dispute about maariv is what affected their dispute regarding minchah.
III
The Gemara (ibid.) rules that one may conduct himself either according to Rebbe Yehudah or according to the first Tanna of the Mishnah. The Rishonim and Poskim discuss the issue of tarti dsatri - incosistency in this matter, resulting in contradiction. See Shulchan Aruch (O.C. 233,267).
Shabbat Shalom!
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