Wei_Dai comments on Timeless Identity - Less Wrong
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On the other hand, an ordinary human brain could undergo 100 years worth of ordinary quantum evolution along with its "copy", and probably 99 out of 100 naive human observers would still agree which one is the "original" and which is the "copy". It seems there must be a fact of the matter in this case, or else how did they reach agreement? By magic?
Given that physical continuity is an obvious fact of daily life, in our EEA and now, why can't "caring about physical continuity" be a part of our preferences/morality? In other words, if the above specially constructed sentient brain were to host a human mind, it doesn't seem implausible that it would consider both post-evolution versions of itself to be less valuable "copies" (due to loss of clear physical continuity) and would choose to avoid undergoing such quantum evolution if it could. This "physical continuity" may not have a simple definition in terms of fundamental physics, but then nobody said our values had to be simple...
EDIT: I've expanded this criticism into a discussion post.
Isn't this just a variant of the Sorites paradox? (I can use it to argue that identity can't have anything to do with synapse connections: suppose I destroy your synapses one at a time, where is the exact threshold at which you cease to be "you"?) I'm surprised at Parfit's high reputation if he made arguments like this one.