My question is concerning the frequentist approach to probability. Assume that you tossed a coin but don't see the outcome. Does it make sense to say that it shows head with a probability of 0.5? Or doesn't it make sense to say that because it either is or is not heads?
I would argue that it does make sense because otherwise you would not be allowed to e.g. speak about the probability of your opponent in poker holding a certain combination of cards (he either has them or not...) which is clearly nonsensical. This would mean that at the end what counts is not whether something is or is not but your knowledge about the fact. But perhaps this is an axiomatic issue?
This would also have profound consequences for the interpretation of confidence intervals. You are always told that you are not allowed to say that there is a 95% probability that e.g. the true mean is within the interval because it either is or is not - so no probability here.
But in case you are allowed to speak of probabilities of hidden outcomes you would also be allowed to say that the true mean is within the confidence interval with 95% probability. Or am I mistaken?