The Metaphysics of Waffle Makers

I made waffles the other night for dinner in honor of the Feast of the Annunciation. M is wonderful and does the dishes every night. When he got to the waffle maker we had the following conversation:

M: How should I wash the waffle maker?
S: Just wipe it down with a paper towel.
M: Should I immerse it in hot, soapy water?
S: Well, that would break it. Would it even be a waffle maker then?
M: If it did not function as a waffle maker would it still be one?
S: I don’t think it would be. Maybe we could put it in a 20 lb bag of rice for a week and then it would work again.
M: What if I completely rewired it, would it still be the same waffle maker or a new one?
S: It would be the same one, I think.
M: Do waffle makers persist through part replacement?