Are Pets Muktzeh?

While the Daf continues plowing through Bava Metzia, many monetary topics are studied. Interestingly enough, someone once asked Rav Yaakov Hagiz (1620-1674) a question about whether a singing bird was muktzeh. He answered based on a recently studied daf. For those who don’t know the connection, this is quite a riddle. The Gemara never mentioned Shabbos, let alone muktzeh.
The Daf spent this week learning about kinyan sudar, alternatively referred to as kinyan chalipin. This is the go-to kinyan for religious purposes. At a wedding, the officiating rabbi makes a kinyan chalipin with the groom, on behalf of the bride. When the rRabbi hands his pen over to the groom, the groom takes the pen and thereby becomes responsible for everything he agreed to in the kesuba. The bride’s agent is in essence trading the pen for financial support. Similarly, when someone goes to a rav to sell chametz, he performs a kinyan chalipin with ther. The rabbi hands the congregant his pen, and the congregant transfers the authority to sell his chametz to the rabbi.