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According to Wikipedia, the Ship of Theseus problem questions whether an object that has had all of its components replaced is still fundamentally the same object.

<pedantry> If each part is replaced in series, and the identity of the object remains the same after each step, then clearly the object remains the same. For humans identity is thus based on recognizing what you have seen before; it acknowledges mutable state. In this case, if you consider the brand as a mutable property of the object, then yes, the identity of PLT-Scheme and Racket are the same. </pedantry>

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