Different abstract facts aren’t mutually exclusive, so one can’t compare them by “probability”, just as you won’t compare probability of Moscow with probability of New York.
You just prompted me to make that comparison. I’ve been to New York. I haven’t been to Moscow. I’ve also met more people who have talked about what they do in New York than I have people who talk about Moscow. I assign at least ten times as much confidence to New York as I do Moscow. Both those probabilities happen to be well above 99%. I don’t see any problem with comparing them just so long as I don’t conclude anything stupid based on that comparison.
There’s a point behind what you are saying here—and an important point at that—just one that perhaps needs a different description.
I assign at least ten times as much probability New York as I do Moscow.
What does this mean, could you unpack? What’s “probability of New York”? It’s always something like “probability that I’m now in New York, given that I’m seating in this featureless room”, which discusses possible states of a single world, comparing the possibility that your body is present in New York to same for Moscow. These are not probabilities of the cities themselves. I expect you’d agree and say that of course that doesn’t make sense, but that’s just my point.
I assign at least ten times as much probability New York as I do Moscow.
What does this mean, could you unpack?
It wasn’t my choice of phrase:
just as you won’t compare probability of Moscow with probability of New York
When reading statements like that that are not expressed with mathematical formality the appropriate response seems to be resolving to the meaning that fits best or asking for more specificity. Saying you just can’t do the comparison seems to a wrong answer when you can but there is difficulty resolving ambiguity. For example you say “the answer to A is Y but you technically could have meant B instead of A in which case the answer is Z”.
I actually originally included the ‘what does probability of Moscow mean?’ tangent in the reply but cut it out because it was spammy and actually fit better as a response to the nearby context.
These are not probabilities of the cities themselves. I expect you’d agree and say that of course that doesn’t make sense, but that’s just my point.
Based on the link from the decision theory thread I actually thought you were making a deeper point than that and I was trying to clear a distraction-in-the-details out of the way.
The point I was making is that people do discuss probabilities of different worlds that are not seen as possibilities for some single world. And comparing probabilities of different worlds in themselves seems to be an error for basically the same reason as comparing probabilities of two cities in themselves is an error. I think this is an important error, and realizing it makes a lot of ideas about reasoning in the context of multiple worlds clearly wrong.
(I’m not sure ‘compare’ is the right word here.)
You just prompted me to make that comparison. I’ve been to New York. I haven’t been to Moscow. I’ve also met more people who have talked about what they do in New York than I have people who talk about Moscow. I assign at least ten times as much confidence to New York as I do Moscow. Both those probabilities happen to be well above 99%. I don’t see any problem with comparing them just so long as I don’t conclude anything stupid based on that comparison.
There’s a point behind what you are saying here—and an important point at that—just one that perhaps needs a different description.
What does this mean, could you unpack? What’s “probability of New York”? It’s always something like “probability that I’m now in New York, given that I’m seating in this featureless room”, which discusses possible states of a single world, comparing the possibility that your body is present in New York to same for Moscow. These are not probabilities of the cities themselves. I expect you’d agree and say that of course that doesn’t make sense, but that’s just my point.
It wasn’t my choice of phrase:
When reading statements like that that are not expressed with mathematical formality the appropriate response seems to be resolving to the meaning that fits best or asking for more specificity. Saying you just can’t do the comparison seems to a wrong answer when you can but there is difficulty resolving ambiguity. For example you say “the answer to A is Y but you technically could have meant B instead of A in which case the answer is Z”.
I actually originally included the ‘what does probability of Moscow mean?’ tangent in the reply but cut it out because it was spammy and actually fit better as a response to the nearby context.
Based on the link from the decision theory thread I actually thought you were making a deeper point than that and I was trying to clear a distraction-in-the-details out of the way.
The point I was making is that people do discuss probabilities of different worlds that are not seen as possibilities for some single world. And comparing probabilities of different worlds in themselves seems to be an error for basically the same reason as comparing probabilities of two cities in themselves is an error. I think this is an important error, and realizing it makes a lot of ideas about reasoning in the context of multiple worlds clearly wrong.
log-odds
Oh, yes, that. Thankyou.