I think you’re making a mistake here. The connection between P(the sun will rise tomorrow/there will be a source of light in the sky tomorrow) and P(the sun will continue to exist forever/this will continue forever) is not trivial, and you are confusing high confidence in P(the sun will rise tomorrow) with a mistaken confidence in the additional claim “and this will continue to be true forever”.
I think the correct way to do Bayesian updating on this situation is to consider these two hypotheses separately. P(the sun will rise tomorrow) will behave according to a Laplace rule in your world. But P(the sun will consist forever) should have a very low initial prior as anything existing forever is an extraordinary claim, and observing an additional sunrise is only weak evidence in favour of it being true. Conversely the decay of other objects around you (a fire running out, for example) is weak evidence against this claim, if only by analogy.
In the spirit of only trying to explain that which is actually true I think it’s also worth noting that the sun visibly changes quite a lot before extinguishing, so an ideal Bayesian would correctly deduce that something extraordinary is happening. In the presence of a sun that will soon extinguish our Bayesian agent will remark that the inductive argument ‘the sun rose every morning of my life, therefore it will exist forever’ doesn’t properly explain the changes that are visible, and the hypothesis will take a corresponding hit in probability.
My intent was less to imply p(the sun will rise forever), but rather that the p(the sun will rise tommorrow) will eventually be very wrong. Of course as you mention the sun would start to look weird which should trigger uncertainty, but that is more the particulars of the example, than the spirit of the thought experiment behind it imo.
I think you’re making a mistake here. The connection between P(the sun will rise tomorrow/there will be a source of light in the sky tomorrow) and P(the sun will continue to exist forever/this will continue forever) is not trivial, and you are confusing high confidence in P(the sun will rise tomorrow) with a mistaken confidence in the additional claim “and this will continue to be true forever”.
I think the correct way to do Bayesian updating on this situation is to consider these two hypotheses separately. P(the sun will rise tomorrow) will behave according to a Laplace rule in your world. But P(the sun will consist forever) should have a very low initial prior as anything existing forever is an extraordinary claim, and observing an additional sunrise is only weak evidence in favour of it being true. Conversely the decay of other objects around you (a fire running out, for example) is weak evidence against this claim, if only by analogy.
In the spirit of only trying to explain that which is actually true I think it’s also worth noting that the sun visibly changes quite a lot before extinguishing, so an ideal Bayesian would correctly deduce that something extraordinary is happening. In the presence of a sun that will soon extinguish our Bayesian agent will remark that the inductive argument ‘the sun rose every morning of my life, therefore it will exist forever’ doesn’t properly explain the changes that are visible, and the hypothesis will take a corresponding hit in probability.
My intent was less to imply p(the sun will rise forever), but rather that the p(the sun will rise tommorrow) will eventually be very wrong. Of course as you mention the sun would start to look weird which should trigger uncertainty, but that is more the particulars of the example, than the spirit of the thought experiment behind it imo.