You can arrange the situation so that the two probabilities are 1⁄10,000 and 1⁄2. Then just ask, “Do you think the coin came up heads or tails”? If they say they are not sure, they agree with the halfer position.
In other words, “how sure are you” does mean something besides how much you want to bet.
There is a difference between “How sure are you that if we looked at the coin now, it is heads?” and “How sure are you that if we looked at the coin only once, at the end of the experiment, it is heads?”
In the first variant, the thirder position is unambiguously true.
I the second variant, I suspect that you really need more precision in the words to answer it. I think a halfer interpretation of this question is at least plausible under some definitions of “how sure”
Unless “how sure” refers explicitly to well specified bet, many attempts to define it will end up being circular.
You can arrange the situation so that the two probabilities are 1⁄10,000 and 1⁄2. Then just ask, “Do you think the coin came up heads or tails”? If they say they are not sure, they agree with the halfer position.
In other words, “how sure are you” does mean something besides how much you want to bet.
There is a difference between “How sure are you that if we looked at the coin now, it is heads?” and “How sure are you that if we looked at the coin only once, at the end of the experiment, it is heads?”
In the first variant, the thirder position is unambiguously true.
I the second variant, I suspect that you really need more precision in the words to answer it. I think a halfer interpretation of this question is at least plausible under some definitions of “how sure”
Unless “how sure” refers explicitly to well specified bet, many attempts to define it will end up being circular.
If I am very sure of something, I would be surprised to see the opposite. I don’t need a bet to determine whether I’m surprised or not.