Chullin 11 - Principles of Status Quo (Chazakah) and Majority

Throughout the Talmud, we follow the principles of status quo (chazakah) and majority as self-evident. However, what is their source?

Chazakah says that we can assume things to stay the way they were when we last observed them (absent indications to the contrary). It is derived from the way the kohen inspects houses for signs of spiritual leprosy (tzaraat): once he sees a specific discoloration on a wall of a house, he can close the house off for seven days and pronounce it under quarantine. But how can he do it? Perhaps while he was going to the door, the discoloration became smaller or disappeared. We see that he is allowed to assume that the status quo has not changed. This principle can then be used in other areas of the law.

How do we know the principle of majority? - One who strikes his parent is to be executed. But how do we know that it is his real father? Since the majority of the cohabitations of a wife are with her husband, we can presume that her husband is the father of her children and execute the son based on this presumption.