Nazir, Chapter 2, Mishnah 2. This is a fascinating Mishnah, which uses a highly unusual case to teach us a halachah essentially identical to that of the previous Mishnah. In the previous Mishnah we dealt with a person who takes a vow of nezirus but makes his nezirus contingent on items that are not forbidden to a nazir at all, such as figs.
The Case of the Cow:
The Mishnah opens: "Amrah parah zo: hareini nezirah im omedes ani" - this cow said: I am hereby a nezirah if I stand up. Picture a man whose cow is lying down and who is trying to get her up on her feet, and at times raising a cow is extremely hard work. As he struggles with her, he puts words in the cow's mouth, as though she had declared: "I am hereby a nezirah if I get up." In other words, the cow has accepted nezirus upon herself if she stands, and therefore she stubbornly stays where she is, since she has no desire to be a nezirah. Against this backdrop the man goes on to say: I am hereby a nazir from the meat of this cow if I do not succeed in getting her up. Here is the parallel to the previous Mishnah: just as there is no such thing as nezirus from figs, so too there is no such thing as nezirus from the meat of a cow.
The Case of the Door:
A second example: "Amar hadeles hazeh: hareini nazir im niftachani" - this door said: I am hereby a nazir if he opens me. A man is trying to open a door and cannot manage it, so he puts words in the door's mouth, as though it had said: "I am hereby a nezirah if he gets me to open - I have no interest in opening, and I will not open." The man therefore declares: I hereby take a vow of nezirus if I am unable to open it. But the nezirus he expresses is nezirus from the door - he forbids the door upon himself, and a door certainly has no connection whatsoever to the laws of nezirus.
And in both cases this is what happened: the man himself did not succeed in raising the cow or in opening the door, but the cow got up on her own and the door opened on its own, or else another person opened it. It turns out that the result was not achieved through the efforts of the one taking the vow, and therefore the vow of nezirus takes effect - for he made his nezirus contingent on his being unable to raise her or to open it, and that is indeed what occurred, since the thing came about in another way.
The central question, then, is that in both cases the man vowed nezirus from something from which there is no nezirus at all: there is no such thing as nezirus from the meat of a cow or nezirus from a door.
The Dispute Between Beis Shammai and Beis Hillel:
Beis Shammai say: "Nazir" - in both cases he is a nazir, just as we saw in the previous Mishnah regarding nezirus from figs: he is considered a nazir on the strength of his opening statement that he is going to be a nazir, and he cannot retract it merely because he qualified his words with something irrelevant to nezirus.
And Beis Hillel say: "Eino nazir" - he is not a nazir, in accordance with their position in the previous Mishnah: since he qualified the nezirus with something irrelevant to nezirus, the nezirus does not take hold.
The Position of Rabbi Yehudah:
Similar to what we saw in the previous Mishnah - where Rabbi Yehudah clarified that even according to Beis Shammai there is no actual nezirus here, but rather a vow forbidding the object - so too here: "Af k'she'amru Beis Shammai, lo amru ela b'omer: harei parah zo alai korban im amadti" - even when Beis Shammai said this, they said it only about one who says: this cow is forbidden to me like a korban if I stood her up. The man's true intention was that the cow should be forbidden to him like a korban, that is, a vow not to derive benefit from it - whether from the cow or from the door - if he would be unable to raise her or to open it. That is the meaning of Beis Shammai's words, and it has nothing to do with actual nezirus.
In summary: in this Mishnah we learned two cases in which a person makes nezirus contingent on things from which there is no nezirus - the meat of a cow and a door - where the cow stood up and the door opened, but not through his own efforts. Beis Shammai hold that he is a nazir on the strength of his opening statement, while Beis Hillel hold that he is not a nazir, since he qualified the nezirus with something irrelevant to it. Rabbi Yehudah clarifies that even according to Beis Shammai there is nothing here but a vow forbidding benefit from the object, and not actual nezirus.