This change does not change a person's identity. Hume's “bundle theory” defines personal identity as perceptions. The views are very similar and I don't think it matters which view we accept. Hume's theory of personal identity is like a more recent version of Locke's theory. Hume thinks that the self is a fiction while Locke believes that if there is no continuum of memory the person is not the same person. The only thing that would be at stake is whether you believe what you think about yourself is fiction or not and whether you are the same person or not. I think for many the thought of thinking of us as if we were fictitious would be a very disappointing thought. Personal identity is more than a continuum of memory. I agree with Locke that you need the continuum of memory to be the same person and that it is necessary to exist, but that's not all that defines personal identity. However, I don't think a person isn't the same person if they don't remember certain events. I agree with Hume that memory reveals personal identity. Personal identity is composed of bundles of
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