Well you tried to answer the question. I suggested your answer was ridiculous and explained why and I have been rebutting your responses since then. So no, we’re not going in circles. I’m objecting to your answer to the updating question and rebutting your responses to my objection.
Here is what happened in this thread.
You suggested that Beauty would have estimated heads at 1⁄3 prior to the experiment.
I said ‘Wha?!?’
You tried to make Beauty’s pre-experiment estimation about what she was going to say when she woke up.
I pointed out that that question was about a different event (the saying) than the question “What is your credence now for the proposition that our coin landed heads?” is about (the coin flip)
You claimed that it didn’t make sense to ask that question (about the coin having landed heads) before the coin flip happens.
I showed how even though English requires us to use tense we can make the question time symmetrical by inventing temporal coordinates (t1) and speaking of subjective probability of heads at t1 at any time Beauty exists.
You claimed that the probability of heads at the end of the experiment was somehow different from the probability of heads at some other time (presumably when she is asked).
I pointed out that time is irrelevant and what matters is her information- an elementary point which I shouldn’t have to make to someone who was last night trashing the OP for supposedly not knowing anything about probability (and I’m a philosopher not a math guy!).
In conclusion: My claim is that for Beauty to answer 1⁄3 for the probability of the time invariant event “coin toss by experimenter at time t1 being heads” she needs to get new information since the prior for that even is obviously 1⁄2. No one has ever pointed to what new information she gets. You tried to claim that Beauty updates as soon as she gets the details of the experiment: but that can’t be right. The details of the experiment can’t alter the outcome of a fair coin toss. So where is the updating?!
Well you tried to answer the question. I suggested your answer was ridiculous and explained why and I have been rebutting your responses since then. So no, we’re not going in circles. I’m objecting to your answer to the updating question and rebutting your responses to my objection.
Here is what happened in this thread.
You suggested that Beauty would have estimated heads at 1⁄3 prior to the experiment.
I said ‘Wha?!?’
You tried to make Beauty’s pre-experiment estimation about what she was going to say when she woke up.
I pointed out that that question was about a different event (the saying) than the question “What is your credence now for the proposition that our coin landed heads?” is about (the coin flip)
You claimed that it didn’t make sense to ask that question (about the coin having landed heads) before the coin flip happens.
I showed how even though English requires us to use tense we can make the question time symmetrical by inventing temporal coordinates (t1) and speaking of subjective probability of heads at t1 at any time Beauty exists.
You claimed that the probability of heads at the end of the experiment was somehow different from the probability of heads at some other time (presumably when she is asked).
I pointed out that time is irrelevant and what matters is her information- an elementary point which I shouldn’t have to make to someone who was last night trashing the OP for supposedly not knowing anything about probability (and I’m a philosopher not a math guy!).
In conclusion: My claim is that for Beauty to answer 1⁄3 for the probability of the time invariant event “coin toss by experimenter at time t1 being heads” she needs to get new information since the prior for that even is obviously 1⁄2. No one has ever pointed to what new information she gets. You tried to claim that Beauty updates as soon as she gets the details of the experiment: but that can’t be right. The details of the experiment can’t alter the outcome of a fair coin toss. So where is the updating?!