If you knew the initial conditions precisely enough, you would know whether the coin was in a white or black region of phase space, and you would then have a probability of either 1 or 0 for it coming up heads.
Not necessarily, because of quantum uncertainty and indeterminism—and yes, they can affect macroscopic systems.
The deeper point is, whilst there is a subjective ignorance-based kind of probability, that does not by itself
mean there is not an objective, in-the-territory kind of 0<p<1 probability. The latter would be down to
how the universe works, and you can’t tell how the universe works by making conceptual, philosophical-style arguments.
So the kind of probability that is in the mind is in the mind, and the other kind is a separate issue. (Of course, the existence of objective probability doesn’t follow from the existence of subjective probability any more than its
non existence does).
Not necessarily, because of quantum uncertainty and indeterminism—and yes, they can affect macroscopic systems.
The deeper point is, whilst there is a subjective ignorance-based kind of probability, that does not by itself mean there is not an objective, in-the-territory kind of 0<p<1 probability. The latter would be down to how the universe works, and you can’t tell how the universe works by making conceptual, philosophical-style arguments.
So the kind of probability that is in the mind is in the mind, and the other kind is a separate issue. (Of course, the existence of objective probability doesn’t follow from the existence of subjective probability any more than its non existence does).