No, I understand that, I'm saying that, while Copy B is not the same person as Copy A, he IS the same person as Copy A was before being copied, at least as much as Copy A is.
What would you do if you discovered you were Copy B in such an experiment? Because presumably he would do the same thing.
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I find myself able to agree with this in the case of rocks, but not in the case of apples. An apple doesn't require the eye of the beholder. There's no danger that a different observer, at a different scale, would claim that there are really two apples if you look close enough.
Apples do require categorization by an observer to some extent.
Is a nearly decayed apple still an apple? At what point does it stop being an apple? At what point does a fertilized apple blossom get to be called an apple?