Okay, my point here was that the copies would not only have the same algorithm, but also the same physical structure arbitrarily finely, and I don’t need to assume the algorithmic ontology, I only need to remember that there’s only a finite amount of configurations of atoms that end up in human bodies, meaning that the number of distinct identities is upper bounded by a finite number. The search space is combinatorically large, but not infinitely large, which ensures that in an infinite universe, some states must be repeated exactly.
That’s why you’d meet yourself, eventually, it’s not because of the algorithmic ontology, but because there isn’t an infinite number of possibilities for your identity.
the copies would not only have the same algorithm, but also the same physical structure arbitrarily finely
I understand, I’m just rejecting the premise that “same physical structure” implies identity to me. (Perhaps confusingly, despite the fact that I’m defending the “physicalist ontology” in the context of this thread (in contrast to algorithmic ontology), I reject physicalism in the metaphysics sense.)
This also seems tangential, though, because the substantive appeals to the algorithmic ontology that get made in the decision theory context aren’t about physically instantiated copies. They’re about non-physically-instantiated copies of your algorithm. I unfortunately don’t know of a reference for this off the top of my head, but it has come up in some personal communications FWIW.
Okay, my point here was that the copies would not only have the same algorithm, but also the same physical structure arbitrarily finely, and I don’t need to assume the algorithmic ontology, I only need to remember that there’s only a finite amount of configurations of atoms that end up in human bodies, meaning that the number of distinct identities is upper bounded by a finite number. The search space is combinatorically large, but not infinitely large, which ensures that in an infinite universe, some states must be repeated exactly.
That’s why you’d meet yourself, eventually, it’s not because of the algorithmic ontology, but because there isn’t an infinite number of possibilities for your identity.
I understand, I’m just rejecting the premise that “same physical structure” implies identity to me. (Perhaps confusingly, despite the fact that I’m defending the “physicalist ontology” in the context of this thread (in contrast to algorithmic ontology), I reject physicalism in the metaphysics sense.)
This also seems tangential, though, because the substantive appeals to the algorithmic ontology that get made in the decision theory context aren’t about physically instantiated copies. They’re about non-physically-instantiated copies of your algorithm. I unfortunately don’t know of a reference for this off the top of my head, but it has come up in some personal communications FWIW.