When Sleeping Beauty wakes up and observes a sequence, they are learning that this sequence occurs on a on a random day out of those days when they are awake.
That would be a valid description if she were awakened only on one day, with that day chosen through some unpredictable process. That is not the case here, though.
What you’re doing here is sneaking in an indexical—“today” is either Monday if Heads, and “today” is either Monday or Tuesday if Tails. See Part 2 for a discussion of this issue. To the extent that indexicals are ambiguous, they cannot be used in classical propositions. The only way to show that they are unambiguous is to show that there is an equivalent way of expressing that same thing that doesn’t use any indexical, and only uses well-defined entities—in which case you might as well use the equivalent expression that has no indexical.
That would be a valid description if she were awakened only on one day, with that day chosen through some unpredictable process. That is not the case here, though.
What you’re doing here is sneaking in an indexical—“today” is either Monday if Heads, and “today” is either Monday or Tuesday if Tails. See Part 2 for a discussion of this issue. To the extent that indexicals are ambiguous, they cannot be used in classical propositions. The only way to show that they are unambiguous is to show that there is an equivalent way of expressing that same thing that doesn’t use any indexical, and only uses well-defined entities—in which case you might as well use the equivalent expression that has no indexical.