There is numerical identity which means two things

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There is numerical identity, which means two things are physically exactly the same. Numerical identity is important for assigning praise and blame, it is also important for questions of personal survival. Numerical identity is different from qualitative identity, because two things are qualitatively identical when they are exactly similar. Olson uses the example of twins, twins can be qualitatively identical but they are not numerically identical. Numerical identity stays the same throughout your entire life, while your qualitative identity changes throughout your life.
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For example, would you say you are the same person as the day you were born? Probably not, you are much different now from then. Olson raises a common misunderstanding about the question of persistence. Under what possible circumstances does a person exist at one time identical to a person existing at another time? In simpler terms, if a person existed in the past, what does it take for that person to be you? Many philosophers define “person” based off specific mental properties and functionality. For example Locke says “a person is a thinking intelligent being, that has reason and reflection, and can consider itself as itself, the same thinking thing, in different times and places.” By Locke’s definition, a human in a vegetative state is not a person. Olson offers an answer to this common misunderstanding, which is “a person who exists at one time is identical with a person who exists at a second time if and only if the first person can, at the first time, remember an experience the second person has at the same time, or vice versa.” This raises the problem of the Memory Criterion, which simply states, if you were to go into a vegetative state, the resulting human vegetable would not be you, or not even necessarily a person at all.
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  • Summer '13
  • ElayShech
  • Ontology, person, Concepts in metaphysics, Olson

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