My father replaced the lenses on his glasses. Then he replaced the frame when it later broke. Same type of lenses and same model of frame. He claims they're still the same pair of glasses. When I argue he's wrong and that they're now a different pair, he claims the same could therefore be said of him as he's replaced all his cells several times since he originally bought the glasses but, since he's still him, the glasses are still the glasses. Who's right?
"Is the same as" is ambiguous. It could mean "same thing" or "same kind of thing" or even "same thing but not necessarily same stuff". Your father is speaking in the last sense--the glasses look the same, and moreover, the 3 pairs of glasses are built through successive fixes. You can avoid the verbal paradox by asking "the same in what respect?" The glasses are not the same stuff, and they do not have all the same physical properties (such as weaknesses in the glass and frame) but they are the same style and they are constructed successively out of one another.
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