[gmuslera]

So if Theseus was aboard his ship for many years it would add another layer of it that ship still is his own?

In Vernon Vinge’s A Fire Upon The Deep you have pack of dogs that are not so smart individually, but they had a pack personality that was smart. Even (for one case in the book) the dogs could be replaced but the personality remained.

Changing individual cells doesn’t change what is the you of your consciousness and memories. Of course, even without cell replacement you change with time, new memories, insights and so on, but both changes happen at different abstraction levels.

[globnomulous]

Peter F. Hamilton's Pandora's Star contains a wonderful variant of this thought experiment: in the future he describes, memories are editable; so it's possible to commit a crime, like murder, and then wipe all memory of it, so that you are, from your own perspective, innocent. The justice system, of course, says otherwise. The metaphysics (whether or not it's possible to step into the same river twice) don't matter. Technological advancement dictates the answer to the philosophical question about continuity of the self and guilt.

[borski]

> Changing individual cells doesn’t change what is the you of your consciousness and memories.

It’s a metaphor.