And the whole controversy comes from the ambiguity, where people confuse probability that the coin is Heads with probability that the coin is Heads weighted by the number of awakenings you have.
I don’t think this is confusion. Obviously no one thinks that any outsider’s probability should be different from 1⁄2, it is just that:
You should explicitly specify whether by “degree of belief for the coin having come up heads” you mean in this experiment or in this awakening.
Thirders think that “this awakening” is the correct way to define subjective probability, you think “this experiment” is the correct way to define subjective probability. It is a matter of definitions, and no confusion is necessarily involved.
I don’t think this is confusion. Obviously no one thinks that any outsider’s probability should be different from 1⁄2, it is just that:
Thirders think that “this awakening” is the correct way to define subjective probability, you think “this experiment” is the correct way to define subjective probability. It is a matter of definitions, and no confusion is necessarily involved.