All that and no mention of the Ship of Theseus? This isn’t exactly a new question. You can never step in the same river twice.
I don’t know that it applies to the constancy of consciousness or personal identity, but on a baser level an object’s definition can be thought of as dependent on its utility. An umbrella with a hole in it is still an umbrella, as it still mostly performs the function of keeping rain off of your head; an umbrella with no skin is not an umbrella at all, any more than a skeleton is an animal. Depending on how the umbrella is used it could be considered any number of other things.
