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. It seems to make sense to ask about probability of various facts being a certain way (in certain mutually exclusive possible states), or about probability of joint facts (that is, dependencies between facts) being a certain way, but it doesn’t seem to me that asking about probabilities of different facts in themselves is a sensible idea.
(Universal prior, for example, can be applied to talk about the joint probability distribution over the possible states of a particular sequence of past and future observations, that describes a single fact of the history of observations by one agent.)
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.
God is an exceedingly unlikely property of our branch of the physical world at the present time. Implementations of various ideas of God can be found in other worlds that I don’t know how to compare to our own in a way that’s analogous to “probability”. The Moscow vs. New York example illustrates the difficulty with comparing worlds that are not different hypotheses about how the same world could be, but two distinct objects.
(I don’t privilege the God worlds in particular, the thought experiment where the Moon is actually made out of Gouda is an equivalent example for this purpose.)
The Moscow vs. New York example illustrates the difficulty with comparing worlds that are not different hypotheses about how the same world could be, but two distinct objects.
There doesn’t seem to be a problem here. The comparison resolves to something along the lines of:
Consider all hypotheses about the physical world of the present time which include the object “Moscow”.
Based on all the information you have calculate the probability that any one of those is the correct hypothesis.
Do the same with “New York”.
Compare those two numbers.
???
Profit.
Instantiate ”???” with absurdly contrived bets with Omega as necessary. Rely on the same instantiation to a specific contrived decision to be made to resolve any philosophical issues along the lines of “What does probability mean anyway?” and “What is ‘exist’?”.
What you describe is the interpretation that does make sense. You are looking at properties of possible ways that the single “real world” could be. But if you don’t look at this question specifically in the context of the real world (the single fact possibilities for whose properties you are considering), then Moscow as an abstract idea would have as much strength as Mordor, and “probability of Moscow” in Middle-earth would be comparatively pretty low.
(Probability then characterizes how properties fit into worlds, not how properties in themselves compare to each other, or how worlds compare to each other.)
God is an exceedingly unlikely property of our branch of the physical world at the present time.
Our disagreement here somewhat baffles me, as I think we’ve both updated in good faith and I suspect I only have moderately more/different evidence than you do. If you’d said “somewhat unlikely” rather than “exceedingly unlikely” then I could understand, but as is it seems like something must have gone wrong.
Specifically, unfortunately, there are two things called God; one is the optimal decision theory, one is a god that talks to people and tells them that it’s the optimal decision theory. I can understand why you’d be skeptical of the former even if I don’t share the intuition, but the latter god, the demon who claims to be God, seems to me to likely exist, and if you think that god is exceedingly unlikely then I’m confused why. Like, is that just your naive impression or is it a belief you’re confident in even after reflecting on possible sources of overconfidence, et cetera?
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. It seems to make sense to ask about probability of various facts being a certain way (in certain mutually exclusive possible states), or about probability of joint facts (that is, dependencies between facts) being a certain way, but it doesn’t seem to me that asking about probabilities of different facts in themselves is a sensible idea.
(Universal prior, for example, can be applied to talk about the joint probability distribution over the possible states of a particular sequence of past and future observations, that describes a single fact of the history of observations by one agent.)
(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.
Really? God isn’t less probable than New York?
God is an exceedingly unlikely property of our branch of the physical world at the present time. Implementations of various ideas of God can be found in other worlds that I don’t know how to compare to our own in a way that’s analogous to “probability”. The Moscow vs. New York example illustrates the difficulty with comparing worlds that are not different hypotheses about how the same world could be, but two distinct objects.
(I don’t privilege the God worlds in particular, the thought experiment where the Moon is actually made out of Gouda is an equivalent example for this purpose.)
There doesn’t seem to be a problem here. The comparison resolves to something along the lines of:
Consider all hypotheses about the physical world of the present time which include the object “Moscow”.
Based on all the information you have calculate the probability that any one of those is the correct hypothesis.
Do the same with “New York”.
Compare those two numbers.
???
Profit.
Instantiate ”???” with absurdly contrived bets with Omega as necessary. Rely on the same instantiation to a specific contrived decision to be made to resolve any philosophical issues along the lines of “What does probability mean anyway?” and “What is ‘exist’?”.
What you describe is the interpretation that does make sense. You are looking at properties of possible ways that the single “real world” could be. But if you don’t look at this question specifically in the context of the real world (the single fact possibilities for whose properties you are considering), then Moscow as an abstract idea would have as much strength as Mordor, and “probability of Moscow” in Middle-earth would be comparatively pretty low.
(Probability then characterizes how properties fit into worlds, not how properties in themselves compare to each other, or how worlds compare to each other.)
Our disagreement here somewhat baffles me, as I think we’ve both updated in good faith and I suspect I only have moderately more/different evidence than you do. If you’d said “somewhat unlikely” rather than “exceedingly unlikely” then I could understand, but as is it seems like something must have gone wrong.
Specifically, unfortunately, there are two things called God; one is the optimal decision theory, one is a god that talks to people and tells them that it’s the optimal decision theory. I can understand why you’d be skeptical of the former even if I don’t share the intuition, but the latter god, the demon who claims to be God, seems to me to likely exist, and if you think that god is exceedingly unlikely then I’m confused why. Like, is that just your naive impression or is it a belief you’re confident in even after reflecting on possible sources of overconfidence, et cetera?