The question is not “what is the probability that the coin would have landed heads”. The question is, “what is the probability that the coin has in fact landed heads”!
If you are interested in the objective probability of the coin flip,the it only has one value because it is only one event. In a deterministic universe the objective probability is 1, in a suitably indeterministic universe it is always 0.5.
If you think the questions “what will it be” and “what was it” are different, you are dealing with subjective probability, because the difference the passage of time makes is a difference in the information available to you, the subject.
Failing to distinguish objective and subjective probability leads to confusion. For instance, the sleeping beauty paradox is only a paradox if you expect all observers to calculate the same probability despite the different information available to them.
The question is not “what is the probability that the coin would have landed heads”. The question is, “what is the probability that the coin has in fact landed heads”!
If you are interested in the objective probability of the coin flip,the it only has one value because it is only one event. In a deterministic universe the objective probability is 1, in a suitably indeterministic universe it is always 0.5.
If you think the questions “what will it be” and “what was it” are different, you are dealing with subjective probability, because the difference the passage of time makes is a difference in the information available to you, the subject.
Failing to distinguish objective and subjective probability leads to confusion. For instance, the sleeping beauty paradox is only a paradox if you expect all observers to calculate the same probability despite the different information available to them.