Yes, but all such strings stand on the same footing, can be equally validly be attributed to a given clone. That is exactly where the empirical incoherence comes from!
No. Let’s take a concrete physical realization of our thought experiment: a series of beam splitters. Each beam splitter transforms the incident beam into a superposition of beams, let’s say |A> + |B>. This is thus the state after the first beam splitter. After the second stage, a pair of beam splitters now, we will have two copies of that state; the part |A> of the first copy is exactly the same as the part |A> of the second: in particular, they will combine coherently.
To say that there is a fourfold distinguishability is to presuppose the identifiability of minds in time, nothing else.
You can make that choice, but in your model, it wouldn’t be a rational choice.
The other posters don’t seem to share your problems, but well: to have experienced something is to have a certain causal connection to it. Memory is not sufficient. This is not anti-physicalist: physics comes down to kinematics and dynamics. The kinematics concerns the state, while the dynamics concerns its evolution, and thus, its causal history. You seem to want to abolish the dynamics, because you recognize that in your model, there can’t be any meaningful dynamics on the level of minds if you want to be a physicalist, because the physical dynamics is insufficient to specify that of the mental realm. The problem is then just that you’re left with too impoverished a theory to make any meaningful assertions at all.
The wiki on swampman gives a good example of why causal history is necessary to give meaning to an assertion: suppose Davidson looks at a glass marble on a shelf. His utterance the next day concerning ‘the glass marble I saw yesterday’ then refers to that glass marble. But then suppose that there is another, identical marble behind the first one. In the case in which know the glass marbles were exchanged, nothing changes in Davidson’s memory or physical state; but the referent of his utterance changes nevertheless, now to the other glass marble.
But what now about swampman, making the same utterance? Which of the marbles does it refer to? Clearly, the question cannot be decided. The clones are in a similar situation: for a clone that now has card B, he cannot decide whether he previously has had card A or B. (But unlike the case of swampman, who should in principle trust his memory, the clone has every reason to distrust it, making the problem more severe in this case—but that really is just a side thread.) His assertions and beliefs simply fail to refer. A faith in scientific reasoning is then ungrounded: there is no specific history of observations that can be associated to the clone; thus, he cannot draw conclusions based on the history.
He can maybe shrug it all away, ignore the implications, and prefer some blissful ignorance—but of course, in that case, he probably would have stuck with a ‘shut up and calculate’ approach to quantum mechanics, which has after all the same explanatory power.
You can of course interpret it that way, if you aim to construct a strawman that goes essentially against everything that I’ve said in this thread. It wouldn’t be a very good way to argue, but I can’t stop you.