It actually often makes sense that the probability of an event having happened is determined by what has been found to happen (as a consequence of it)...
The reason why the Double-halfer splits the probability P(Tails) = 1/2 between P(Monday-Tails) and P(Tuesday-Tails) is because they treat them as excl...
This inference follows if we consider what is excluded by the condition "Hippo or Tiger". The case where Leonard is seeing a second enclosure on his p...
(I had assumed that the H-path was the left path at half of the forks, but this is inconsequential since Leonard always forgets which path he took.) Y...
Are you evaluating the probabilities of the three possible outcomes occurring from the point of view of an external observer or from Sleeping Beauty's...
@"Michael" Consider Leonard Shelby's journey through the "Sleeping Beauty Zoo". In this zoo, each fork in the path presents two options - one path (H-...
It's precisely because they mean different things that I've provided detailed arguments for deducing 1 from 2 (alongside with other premises). However...
They indeed are. As you get involved in the experiment and your perspective shifts from the timeline (before the experiment begins) to the episodic on...
This overlooks the issue that your credence can change over time when your epistemic perspective changes. If your separate uses of the expression P(H)...
When I previously addressed this inference of yours, I conceded that it is generally valid, but I also pointed out that it involved a possible conflat...
The issue arises from a conflation of two distinct ways of individuating events and counting probabilities. We can see this more clearly if we disting...
You are correct that this would be wrong. The entire aim of my variation (and the Leonard Shelby variation before it) was to highlight that there is i...
The issue with making n small is that it allows Sleeping Beauty on Wednesday to decrease her credence P(H) regarding the origin of the single note. Th...
This is because, when the experimental protocol is expanded to enable Sleeping Beauty to hand notes to her future self in such a manner, the episodes ...
Her probability of writing a note is 1/100 on each occasion she awakens. Since she awakens twice when the coin lands tails, her probability of writing...
Yes, indeed, which is why I edged my specification by stipulating that the occasions to write a note were rare. If Sleeping Beauty would receive two n...
I believe Elga was mistaken about this. There actually is some information that becomes available to Sleeping Beauty when she awakens, though the natu...
Actually, I suggested that P(X) could be understood as referring to the ratio of |{X}| to (|{X}| + |{not-X}|) in epistemically identical situations wi...
The passer-by sees all of the flashes and does not know the genetic status of the fireflies producing them. This is analogous to Sleeping Beauty exper...
@"Michael" Let me adjust my previous firefly case to meet your objection. We can assume that half of the fireflies have gene XYZ, which causes them to...
When Sleeping Beauty awakens, she could potentially be experiencing either a guaranteed awakening (i.e. T-Monday or H-Monday) or an optional awakening...
I find it unusual that you maintain that when faced with a potential outcome O in a situation S, your credence P(O) should only reflect the intrinsic ...
I have indeed conceded that the inference is valid (as are the applications of Bayes' theorem predicated on it) as long as we avoid equivocating the m...
While this kind of inference is often valid, it doesn't apply in the Sleeping Beauty problem. Credences, or probabilities, can be thought of as ratios...
In my original cosmopolitan analogy, the equal Italian and Tunisian populations mirrors the even likelihood of the coin landing on either side in the ...
If I were to adjust the analogy, suppose that meeting a Tunisian pedestrian guarantees that you have met or will meet their sibling either in the prev...
To fine-tune the analogy, let's assume that there are an equal number of Tunisians and Italians, that they are out for the same duration, and that Tun...
The conclusion doesn't follow because, while the biconditional expressed in P3 is true, this biconditional does not guarantee a one-to-one corresponde...
You are introducing premises *P2 and *P3 in an attempt to emphasize a perceived disanalogy between the cosmopolitan meeting scenario and the Sleeping ...
Your point (2) doesn't factor into my argument. I've consistently held to the premise, as dictated by the problem statement, that Sleeping Beauty awak...
In the Sleeping Beauty problem, she isn't asked to estimate the probability of being awakened in the future with the coin having landed heads. Instead...
However, you seem to agree that in this scenario, one is twice as likely to encounter a Tunisian. The conclusion that there are twice as many Tunisian...
You accepted the validity of the reasoning when probability was deduced from frequencies in the Tunisian-meetings scenario. Why is this reasoning acce...
To fill in your number 2 with no circularity, we can draw a parallel to the first example: 2a. Tunisian-meetings are twice as likely because there are...
I see. I was filling up a template that you had provided where P(Monday) = 2/3, thus making it clear that we were quantifying awakening episodes. In t...
But why wouldn't it make sense? For example, if you're an immigration lawyer and your secretary has arranged for you to meet with twice as many Tunisi...
In essence, you're saying that even though a distant event currently lies beyond your ability to influence it (due to the fact that any influence you ...
This is due to the expansion of the universe, which is a general relativistic effect. It is unrelated to the shifting of the simultaneity plane due to...
I am not relying on 1, but it would be a valid inference if we assume that P(T) = 2*P(H). This assumption would hold if we define P(T) as P(T) =def |{...
The rationality of Sleeping Beauty betting on T upon awakening isn't because this bet has a positive expected value. In fact, it's the other way aroun...
Indeed, I have long insisted (taking a hint from @"fdrake" and Laureano Luna) that the following statements are biconditional: "The coin landed (or wi...
The galaxies you are moving towards would have come into view regardless of your motion, only at a later time as measured by your clock. Similarly, th...
In Special Relativity, an observer can be identified with an inertial reference frame in which they are at rest, and relative to which they make all t...
In earlier messages? Yes. I shouldn't have used this prior in the context of the Thirder intepretation of P(H). I was unclear between the individuatio...
P(Heads|Unique) = 1 and P(Heads) = 1/3 (since 1/3 of expected awakenings are H-awakenings) P(Unique|Heads) is therefore 1, as expected. P(Monday|Heads...
My argument follows a consistent line of reasoning. Given Sleeping Beauty's understanding of the experimental setup, she anticipates the proportion of...
For the first case, we can use priors of P(H) = 1/2 and P(W) = 3/4, given that there are three awakenings in the four possible scenarios (H&Mon, H&Tue...
In this variation, it seems to me that being awakened does provide Michael with relevant evidence. Given that the coin landing on tails results in one...
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