What exactly do you mean by “different tools need to be used”? Can you give me an example?
I mean that Beauty should maintain full model of experiment, and use decision theory as well as probability theory (if latter is even useful, which it admittedly seems to be). If she didn’t keep track of full setup but only “a fair coin was flipped, so the odds are 1:1”, she would predictably lose when betting on the coin outcome.
Also, I’ve minted another “paradox” version. I can predict you’ll take issue with one of formulations in it, but what do you think about it?
A fair coin is flipped, hidden from you.
On Heads, you’re waken up on Monday, asked “what credence do you have that coin landed Heads?”; on Tuesday, you’re let go.
If coin landed Tails, you’re waken up on Monday and still asked “what credence do you have that coin landed Heads?”; then, with no memory erasure, you’re waken up on Tuesday, and experimenter says to you: “Name the credence that coin landed Heads, but you must name the exact same number as yesterday”. Afterwards, you’re let go.
If you don’t follow experiment protocol, you lose/lose out on some reward.
I suppose the participant is just supposed to lie about their credence here in order to “win”.
On Tuesday your credence in Heads supposed to be 0, but saying the true value would go against the experimental protocol unless you also said that your credence is 0 on Monday, which would also be a lie.
She certainly gets a reward for following experimental protocol, but beyond that… I concur there’s the problem, and I have the same issue with standard formulation asking for probability.
In particular, pushing problem out to morality “what should Sleeping Beauty answer so that she doesn’t feel as if she’s lying” doesn’t solve anything either; rather, it feels like asking question “is continuum hypothesis true?” providing only options ‘true’ and ‘false’, while it’s actually independent of ZFC axioms (claims of it or of its negation produce different models, neither proven to self-contradict).
P.S. One more analogue: there’s a field, and some people (experimenters) are asking whether it rained recently with clear intent to walk through if it didn’t; you know it didn’t rain but there are mines all over the field. I argue you should mention the mines first (“that probability—which by the way will be 1⁄2 - can be found out, conforms to epistemology, but isn’t directly usable anywhere”) before saying if there was rain.
I mean that Beauty should maintain full model of experiment, and use decision theory as well as probability theory (if latter is even useful, which it admittedly seems to be). If she didn’t keep track of full setup but only “a fair coin was flipped, so the odds are 1:1”, she would predictably lose when betting on the coin outcome.
Also, I’ve minted another “paradox” version. I can predict you’ll take issue with one of formulations in it, but what do you think about it?
I suppose the participant is just supposed to lie about their credence here in order to “win”.
On Tuesday your credence in Heads supposed to be 0, but saying the true value would go against the experimental protocol unless you also said that your credence is 0 on Monday, which would also be a lie.
I don’t understand this formulation. If Beauty always says that the probability of Heads is 1⁄7, does she win? Whatever “win” means...
She certainly gets a reward for following experimental protocol, but beyond that… I concur there’s the problem, and I have the same issue with standard formulation asking for probability.
In particular, pushing problem out to morality “what should Sleeping Beauty answer so that she doesn’t feel as if she’s lying” doesn’t solve anything either; rather, it feels like asking question “is continuum hypothesis true?” providing only options ‘true’ and ‘false’, while it’s actually independent of ZFC axioms (claims of it or of its negation produce different models, neither proven to self-contradict).
P.S. One more analogue: there’s a field, and some people (experimenters) are asking whether it rained recently with clear intent to walk through if it didn’t; you know it didn’t rain but there are mines all over the field.
I argue you should mention the mines first (“that probability—which by the way will be 1⁄2 - can be found out, conforms to epistemology, but isn’t directly usable anywhere”) before saying if there was rain.