She is allowed any reasoning she wants to use. The condition explicitly stated in the thought problem (see https://en.wikipedia.org/wiki/Thought_experiment, for why we shouldn’t care about realism) is that experiences during the day will not help her to deduce what day it is, not that she can’t use it to determine her initial belief about the day or the coin.
What this means, is that if Xi represents her ordered experiences, with X0 representing only the experience of waking up as defined by the experiment, that Pr(Today=Monday|Xi+1) = Pr(Today=Monday|Xi) for all i>=0. Not that she can’t define Pr(Today=Monday|X0).
But you are right, there is no point in continuing if you insist on violating the problem statement.
As you’re defined it, the thought experiment is simply impossible to run in principle, since if you apply standard principles of probability, Pr(Today=Monday|Xi+1) is NOT equal to Pr(Today=Monday|Xi). It’s like saying that as a condition of your thought experiment, arguments about the solution must assume that pi is exactly equal to three.
And the purpose of a thought experiment, is to define how ideal concepts work when you can’t run them in principle. And strawman arguments do not change that.
She is allowed any reasoning she wants to use. The condition explicitly stated in the thought problem (see https://en.wikipedia.org/wiki/Thought_experiment, for why we shouldn’t care about realism) is that experiences during the day will not help her to deduce what day it is, not that she can’t use it to determine her initial belief about the day or the coin.
What this means, is that if Xi represents her ordered experiences, with X0 representing only the experience of waking up as defined by the experiment, that Pr(Today=Monday|Xi+1) = Pr(Today=Monday|Xi) for all i>=0. Not that she can’t define Pr(Today=Monday|X0).
But you are right, there is no point in continuing if you insist on violating the problem statement.
As you’re defined it, the thought experiment is simply impossible to run in principle, since if you apply standard principles of probability, Pr(Today=Monday|Xi+1) is NOT equal to Pr(Today=Monday|Xi). It’s like saying that as a condition of your thought experiment, arguments about the solution must assume that pi is exactly equal to three.
And the purpose of a thought experiment, is to define how ideal concepts work when you can’t run them in principle. And strawman arguments do not change that.