I mean I am not convinced by the claim that Bob is wrong.
Bob’s prior probability is 50%. Bob sees no new evidence to update this prior so the probability remains at 50%.
I don’t favour an objective notion of probabilities. From my OP:
2. Bayesian Reasoning Probability is a property of the map (agent’s beliefs), not the territory (environment).For an observation O to be evidence for a hypothesis H, P(O|H) must be > P(O|¬H).The wake-up event is equally likely under both Heads and Tails scenarios, thus provides no new information to update priors.The original 50⁄50 probability should remain unchanged after waking up.
Probability is a property of the map (agent’s beliefs), not the territory (environment).
For an observation O to be evidence for a hypothesis H, P(O|H) must be > P(O|¬H).
The wake-up event is equally likely under both Heads and Tails scenarios, thus provides no new information to update priors.
The original 50⁄50 probability should remain unchanged after waking up.
So I am unconvinced by your thought experiments? Observing nothing new I think the observers priors should remain unchanged.
I feel like I’m not getting the distinction you’re trying to draw out with your analogy.
Yes, Bob is right. Because the probability is not a property of the coin. It’s ‘about’ the coin in a sense, but it also depends on Bob’s knowledge, including knowledge about location in time (Dave) or possible worlds (Carol).
I mean I am not convinced by the claim that Bob is wrong.
Bob’s prior probability is 50%. Bob sees no new evidence to update this prior so the probability remains at 50%.
I don’t favour an objective notion of probabilities. From my OP:
So I am unconvinced by your thought experiments? Observing nothing new I think the observers priors should remain unchanged.
I feel like I’m not getting the distinction you’re trying to draw out with your analogy.
Yes, Bob is right. Because the probability is not a property of the coin. It’s ‘about’ the coin in a sense, but it also depends on Bob’s knowledge, including knowledge about location in time (Dave) or possible worlds (Carol).