If psychological continuity is both sufficient for identity and multiply realizable simultaneously, the view entails that one entity instantiates contradictory first-person properties, violating the indiscernibility of identicals.
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indiscernibility of identicals(Leibniz's Law as applied to the identity vs. constitution distinction)
The principle that if two things are identical, they must share all the same properties; constitution (unlike identity) does not conform to this principle
instantiates(as used in metaphysics)
To instantiate means to be a specific example or instance of something more general. For example, a red apple instantiates the property 'redness.'
psychological continuity(Philosophy of personal identity)
A relation holding between a person at one time and a being at a later time when the later being inherits the memories, intentions, beliefs, and psychological states of the earlier person.