The Mishnah says that R' Elozor Ben Azaryah permits a cow to go out with a Retzuah between its horns. The Gemoro says that R' Elozor Ben Azaryah's own cow went out like this, but then clarifies that it was his neighbour's cow, but he did not object.
Did he actually hold this is permitted (like it seems from the Mishna)?
If he held it is permitted, it is obvious that he would not object, and the Gemoro is presumably not criticizing him for not objecting, just stating a
fact. If he held this is forbidden - presumably when the Mishna says he permits, that is also just because he did not object to his neighbour
Kol Tuv,
Meir Eliezer Bergman, Manchester UK
The Ben Yehoyada says that Rebbi Elazar held that it was Mutar for the cow to carry the strip between it's horns. He explains that the Gemara says that he did not object because it was only through Rebbi Elazar's failure to object that it became apparent that he in fact was of the opinion that the act was permitted.
However, the Yerushalmi in Shabbos (5:4) says that the cow only went out on Shabbos on one occasion, and Rebbi Elazar's face went black from the fasts that he fasted. Either this was because he decided that he had ruled incorrectly (Meiri Shabbos 54a), or because he had not actually meant to permit the cow to carry the strip on Shabbos, since the Rabanan prohibit it, only to say that in his opinion it would be permitted (Korban ha'Eidah on Yerushalmi ibid.).
Dov Freedman
In daf al hadaf a discussion was brought about this point. It says possibly how the issur of an animal doing work might be only an issur aseh connected with time which according to Reb Elazar women were possibly exempt from keeping. I do not have the sefer to hand, please can you check - thanks.
YCD
Daf Al Hadaf lists a number of Acharonim that prove from our Gemara that women are obligated in Shevisas Beheimah. Had women been exempt, the Chachamim would not have been upset with Rebbi Elazar ben Azaryah for letting the woman walk her cow in this manner (see Minchas Chinuch, Musach ha'Shabbos #39).
Daf Al Hadaf then quotes Yesodei Yeshurun (Harav Gedalyah Felder) vol. 5 p.364, who suggests that Rebbi Elazar indeed permitted the cow to wear the strap for that very reason. The Rabanan disagreed because the women was married, so her husband had a Kinyan Peiros on the cow (as is the rule with all of a wife's possessions), and they maintained that a Kinyan Peiros is tantamount to a Kinyan ha'Guf, making it a man's cow.
(This does not follow a simple reading of the Gemara, nor does it answer Meir Bergman's question.)
Be well,
Mordecai Kornfeld
Kollel Iyun Hadaf