I was reminded of this by a short aside in the text:
For we learned: If a corpse lay in a house that had many (closed) doors all the doorways (through which the corpse might be carried) are unclean.
If one of them was (standing) open, that doorway is unclean while all the others are clean (since the corpse would be carried through that door.) If it was intended to take out the corpse through one of (the closed doors) . . ., this protects all the (other) doors.
Beth Shammai ruled: This (rule of intention) applies only where the intention was formed before the person in question was dead, but Beth Hillel ruled: Even if it was formed after he was dead.
All the doors are deemed to be “unclean” until the intention to use them is formed (Beth Shammai before death, Beth Hillel even after), because all routes are possible. Not the action of carrying, but the intention to carry, collapses the multiple possible states into one.
I find that pretty remarkable!