“You should anticipate having both experiences” sounds sort of paradoxical or magical, but I think this stems from a verbal confusion.
You can easily clear this confusion if you rephrase it as “You should anticipate having any of these experiences”. Then it’s immediately clear that we are talking about two separate screens. And it’s also clear that our curriocity isn’t actually satisfied. That the question “which one of these two will actually be the case” is still very much on the table.
Rob-y feels exactly as though he was just Rob-x, and Rob-z also feels exactly as though he was just Rob-x
Yes, this is obvious. Still as soon as we got Rob-y and Rob-z they are not “metaphysically the same person”. When Rob-y says “I” he is reffering to Rob-y, not Rob-z and vice versa. More specifically Rob-y is refering to some causal curve through time ans Rob-z is refering to another causal curve through time. These two curves are the same to some point, but then they are not.
Well, I think this one is actually correct. But, as I said in the previous comment, the statement “Today is Monday” doesn’t actually have a coherent truth value throughout the probability experiment. It’s not either True or False. It’s either True or True and False at the same time!
We can answer every coherently formulated question. Everything that is formally defined has an answer Being careful with the basics allows to understand which question is coherent and which is not. This is the same principle as with every probability theory problem.
Consider Sleeping-Beauty experiment without memory loss. There, the event Monday xor Tuesday also can’t be said to always happen. And likewise “Today is Monday” also doesn’t have a stable truth value throughout the whole experiment.
Once again, we can’t express Beauty’s uncertainty between the two days using probability theory. We are just not paying attention to it because by the conditions of the experiment, the Beauty is never in such state of uncertainty. If she remembers a previous awakening then it’s Tuesday, if she doesn’t—then it’s Monday.
All the pieces of the issue are already present. The addition of memory loss just makes it’s obvious that there is the problem with our intuition.