Actually I think it moves away from philosophy at this point and becomes a question of practicality- at what point in a detailed copy is it "close enough to be you"? As humans (and with the rest of life) we're in that weird state between being totally static (like a frozen crystal) and being completely chaotic (like the center of the sun) - at the "edge of chaos" so to speak. Life is in that border-land where it's just stable enough and yet just chaotic enough. So when the temperature of the room changes there are atoms and systems that adjust within us in order that certain critical atomic structures stay in-tact. It's like a controlled slide into chaos- chunks being stable enough for just long enough to create other small islands of somewhat-stability.

If it turns out that the thing critical to our being is deep within our neurons, and that the computations that take place are similar to quantum computing and rely on sub-atomic processes, and that the rest of the body (among other things) keeps its environment stable enough to "keep state," then the machine needed to copy the mind would end up destroying the original. Or, if it doesn't read atomic information at that level of detail, the "copy" will have a similar infrastructure but will instantly be divergent from the original because the "current" thoughts of the original will not have copied.

I mean, putting aside philosophy and actually getting down to the brass tacks so we can start building this machine. (: