[foal]

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If your memories aren't making the jump what is?

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Your consciousness.

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What would individuate your consciousness from other consciousnesses if not memories?

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Memories have meaning because 'we' experience them. That 'experiencing of something' is what consciousness is and it has nothing to do with memory. E.g. we can imagine an entity being constructed with our exact same memories, yet we still would not expect to experience what that entity experiences.