After a somewhat lengthy account of the Rabbinic theories of contagion we read about several disputes between Beit Hillel and Beit Shammai.
On three occasions we read “What is the underlying point of the dispute?” (Be’mai kamiflegei?)
The first time the issue is whether or not you can use a utensil whose outside contracted tumah through a liquid. Beit Shammai says ‘no’, Beit Hillel, ‘yes’. The second time has to do with whether you can use a table which is second in line from tumah. Here, too, Beit Shammai says ‘no’, Beit Hillel ‘yes’. The third time the issue is whether or not you can rely on a waiter to have knowledge of the laws regarding meals. Beit Hillel says you cannot rely on a waiter who is ignorant of such laws, while Beit Shammai says you can.
The halachah follows Beit Hillel for the first two and Beit Shammai for the third.
What is the underlying point of the dispute?