Could you explain what is the difference you see between these two position?
In the second one you specifically describe “the ability to correctly guess tails in 2⁄3 of the experiments”, whereas in the first you more loosely describe “thinking that the coin landed Tails with 2⁄3 probability”, which I previously read as being a probability per-awakening rather than per-coin-flip.
Would it be less misleading if I change the first phrase like this:
The Bailey is the claim that the coin is actually more likely to be Tails when I participate in the experiment myself. That is, my awakening on Monday or Tuesday gives me evidence that lawfully update me to thinking that the coin landed Tails with 2⁄3 probability in this experiment, not just on average awakening.
In the second one you specifically describe “the ability to correctly guess tails in 2⁄3 of the experiments”, whereas in the first you more loosely describe “thinking that the coin landed Tails with 2⁄3 probability”, which I previously read as being a probability per-awakening rather than per-coin-flip.
Would it be less misleading if I change the first phrase like this: