Wait, what? “The sun will rise tomorrow” also has a probability of 1.0 given that “The sun will rise tomorrow and then never rise again”, so the sun rising tomorrow should make you update in favor of that hypothesis too. Why did you choose to focus on a hypothesis saying the future (starting from the day after tomorrow) will be like the past (tomorrow)? This is circular—the problem of induction all over again.
Yes, the probability of that will also increase after the first day—it is perfectly consistent for the probability of both hypotheses to increase. But the day after that, the probability of the sun rising the next 10,000 days has increased even more, and the probability of your hypothesis has dropped to zero.
As I said in the post, people do in fact formulate universal hypotheses, namely ones which will suggest that the future is like the past. But you don’t have to assume the future will be like the past to do this; as I said in the previous comment, you might even be assuming that the future will NOT be like the past. The Bayesian reasoning will work just the same.
But the day after that, the probability of the sun rising the next 10,000 days has increased even more, and the probability of your hypothesis has dropped to zero.
Who says this will happen in the first place? Even if you personally know that the sun will rise tomorrow like it always did, you’re not allowed to use that fact while solving the problem of induction.
Maybe an important insight into why the justification of induction remains so puzzling. We should be justifying induction as a policy, not as a magic-bullet formula which works in each and every instance.
Wait, what? “The sun will rise tomorrow” also has a probability of 1.0 given that “The sun will rise tomorrow and then never rise again”, so the sun rising tomorrow should make you update in favor of that hypothesis too. Why did you choose to focus on a hypothesis saying the future (starting from the day after tomorrow) will be like the past (tomorrow)? This is circular—the problem of induction all over again.
Yes, the probability of that will also increase after the first day—it is perfectly consistent for the probability of both hypotheses to increase. But the day after that, the probability of the sun rising the next 10,000 days has increased even more, and the probability of your hypothesis has dropped to zero.
As I said in the post, people do in fact formulate universal hypotheses, namely ones which will suggest that the future is like the past. But you don’t have to assume the future will be like the past to do this; as I said in the previous comment, you might even be assuming that the future will NOT be like the past. The Bayesian reasoning will work just the same.
Who says this will happen in the first place? Even if you personally know that the sun will rise tomorrow like it always did, you’re not allowed to use that fact while solving the problem of induction.
The only reason that I’m using it is because in real life we update more than once.
But if you want to focus on the single update, yes, both hypotheses become more probable.
Maybe an important insight into why the justification of induction remains so puzzling. We should be justifying induction as a policy, not as a magic-bullet formula which works in each and every instance.