The future seems less definite than the present. I can imagine someone telling Yvain “Well, sure, we can assign a probability to whether there will be a major earthquake in California in the next ten years, because it hasn’t happened yet. But a proposition about the present is either true or false; probabilities aren’t appropriate for that.” I’ve never heard anyone say that, but I think it’s something people would say.
So why does that mean that it is good to have difficulty coming up with a good estimate of whether an existing statement is true? It seems like your hypothetical argument is obviously wrong from the Bayesian point-of-view, for example see this recent article. You sound like you don’t support this hypothetical argument, so I still don’t understand your original comment.
As I understand it, the purpose of Yvain’s post is to come up with specific propositions that he can use to convince people that probabilities are appropriate for thinking about propositions in general. calef’s comment above is a pedagogically useful proposition for this purpose because it satisfies most (if not all) of the criteria Yvain listed in his post. My comment to calef points out an additional point in its favor: The proposition is not about a future event, so it sidesteps a possible pedagogical failure mode that I described in the grandparent.
I think you misidentified what the word “this” refers to in my response to calef.
The best among the ones I’ve read this far. (E.T. Jaynes used “There once was life on Mars” as an example for something similar.) Though it doesn’t fully meet condition #2, as I guess most people wouldn’t give a damn about that. I’m not sure conditions #2, #4 and #5 are compatible.
“What is the probability there is microbial-like life (other than from earth) in our solar system?”
I’m having difficulty giving this a good estimate, myself, actually.
This is good because it’s not a future event.
Can you elaborate on what you mean by this comment, Nisan? I don’t see why that is relevant.
The future seems less definite than the present. I can imagine someone telling Yvain “Well, sure, we can assign a probability to whether there will be a major earthquake in California in the next ten years, because it hasn’t happened yet. But a proposition about the present is either true or false; probabilities aren’t appropriate for that.” I’ve never heard anyone say that, but I think it’s something people would say.
So why does that mean that it is good to have difficulty coming up with a good estimate of whether an existing statement is true? It seems like your hypothetical argument is obviously wrong from the Bayesian point-of-view, for example see this recent article. You sound like you don’t support this hypothetical argument, so I still don’t understand your original comment.
As I understand it, the purpose of Yvain’s post is to come up with specific propositions that he can use to convince people that probabilities are appropriate for thinking about propositions in general. calef’s comment above is a pedagogically useful proposition for this purpose because it satisfies most (if not all) of the criteria Yvain listed in his post. My comment to calef points out an additional point in its favor: The proposition is not about a future event, so it sidesteps a possible pedagogical failure mode that I described in the grandparent.
I think you misidentified what the word “this” refers to in my response to calef.
Aha! It suddenly makes sense. Thanks.
The best among the ones I’ve read this far. (E.T. Jaynes used “There once was life on Mars” as an example for something similar.) Though it doesn’t fully meet condition #2, as I guess most people wouldn’t give a damn about that. I’m not sure conditions #2, #4 and #5 are compatible.