Great example! I tried to get the same result with biased coin.
I think what Halfer misses is that probability of coin P is not the same that probability that the last toss of the coin was P. We can collect partial information about the last toss via different ways including observation selection effects. We can replace coin in your example with Sun exploding in the past and destroying earth with some chance. In that case, a priopi P of explosion is not the same that there was explosion but we survived (the example needs some polishing).
Great example! I tried to get the same result with biased coin.
I think what Halfer misses is that probability of coin P is not the same that probability that the last toss of the coin was P. We can collect partial information about the last toss via different ways including observation selection effects. We can replace coin in your example with Sun exploding in the past and destroying earth with some chance. In that case, a priopi P of explosion is not the same that there was explosion but we survived (the example needs some polishing).