The point is that the meaning of a classical proposition must not change throughout the scope of the problem being considered. When we write A1, …, An |= P, i.e. “A1 through An together logically imply P”, we do not apply different structures to each of A1, …, An, and P.
The trouble with using “today” in the Sleeping Beauty problem is that the situation under consideration is not limited to a single day; it spans, at a minimum, both Monday and Tuesday, and arguably Sunday and/or Wednesday also. Any properly constructed proposition used in discussing this problem should make sense and be unambiguous regardless of whether Beauty or the experimenters are uttering the proposition, and whether they are uttering it on Sunday, Monday, Tuesday, or Wednesday.
The point is that the meaning of a classical proposition must not change throughout the scope of the problem being considered. When we write A1, …, An |= P, i.e. “A1 through An together logically imply P”, we do not apply different structures to each of A1, …, An, and P.
The trouble with using “today” in the Sleeping Beauty problem is that the situation under consideration is not limited to a single day; it spans, at a minimum, both Monday and Tuesday, and arguably Sunday and/or Wednesday also. Any properly constructed proposition used in discussing this problem should make sense and be unambiguous regardless of whether Beauty or the experimenters are uttering the proposition, and whether they are uttering it on Sunday, Monday, Tuesday, or Wednesday.