What it is for me to persist is for there to be, instantiated in some system, an algorithm with a particular relation to the algorithm which characterizes me at present.
Emphasis added. I think "instantiates an algorithm of type X" qualifies as a physical specification in the relevant sense; Platonism is not a problem. However to answer the post you would need to define (or point us in the direction of) the "particular relation" you have in mind.
However to answer the post you would need to define (or point us in the direction of) the "particular relation" you have in mind.
The particular relation where x is the future algorithm and y is the algorithm which characterizes me now is " x is psychologically continuous with y". If x contains memories of y's experiences, or if x contains memories of the experiences of intervening algorithms which in turn contain memories of y, or if x and y are linked by any series of algorithms connected in this way we would have good reason to thi...
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