Dead as a doornail

While out to lunch with my brother and his girlfriend this weekend, a comment about yellowing fingernails (because they can't breathe under nail polish/lacquer) spawned a discussion about whether nails are alive.

B: Nails are dead!
M: No, they aren't; they grow.
B: They're dead; that's why you don't feel anything when you cut them.
M: You don't feel anything because there aren't any nerves.
M: Mine are alive.
B: Well, mine aren't.