4 ms·
The reasoning in the article is correct. Cubicles 1-10 are occupied in both scenarios, but the observation of (self <= 10) is much less likely in the Doom Late
by lmkg 12y ago
The reasoning in the article is correct. Cubicles 1-10 are occupied in both scenarios, but the observation of (self <= 10) is much less likely in the Doom Late scenario. This means that if you observe (self <= 10), the conditional probability of Doom Soon is much higher.
They key point is that, if Doom Late occurred, then the probability of ending up in cubicle 1-10 is only 10%. So if the only observation that you have is that your cubicle is numbered 1-10, which is more likely: Doom Soon (50% absolute probability), or Doom Late (50% absolute) and you happened to end up in 1-10 (10% of the 50%)?
Therefore, the conditional probability of Doom Soon is higher than 50% based on the observation of self <= 10.
- livingparadox 12y agoThe premises in the argument can abstracted into the following: if doom_soon, then the probability of myself being in cubicles 1-10 is 100%; if doom_soon, then the probability of myself being in cubicles 11-100 is 0%; if doom_late, then the probability of myself being in cubicles 1-10 is 10%; if doom_late, then the probability of myself being in cubicles 11-100 is 90%; ??? Therefore if I am the cubicles 1-10, the probability of doom soon is 81%; In any logic class, this argument would quickly be pointed out as a fallacy. The statement of "if p, then q" says nothing about the truth of p, given q. Which is exactly what this argument seems to do, reason backwards from the conclusion when none of the premises are able to be logically inferred from the conclusion.
- livingparadox 12y agoI thought of a better way of explaining the invalidity of the argument. What would happen if, instead of inferring from our own presence in the cubicle, we take an external role. Furthermore, instead of taking the probability that a randomly selected person exists in of the two sets, we look at the probability that /someone/ exists in one of the two sets. If doom soon occurred, then the probability of cubicles 1-10 being occupied is 100%; If doom soon occurred, then the probability of cubicles 11-100 being occupied is 0%; If doom late occurred, then the probability of cubicles 1-10 being occupied is 100%; If doom late occurred, then the probability of cubicles 11-100 being occupied is 100%; So given those two probabilities, we have a 100% chance of cubicles 1-10 being occupied and a 50% chance of cubicles 11-100 being occupied. In either scenario, the occupancy status of cubicles 1-10 is assured. So checking in cubicles 1-10 gives us no meaningful information about which of the two scenarios occurred. Checking in cubicles 11-100 on the other hand /would/ affect our results. The occupancy of cubicles 11-100 on the other hand would tell us exactly which scenario occured.