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potato comments on Probability is in the Mind - Less Wrong

60 Post author: Eliezer_Yudkowsky 12 March 2008 04:08AM

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Comment author: potato 27 July 2011 07:22:38PM *  0 points [-]

Hate to be a stickler for this sort of thing, but even in the bayesian interpretation there are probabilities in the world, it's just that they are facts about the world and the knowledge the agents have of the world in combination. It's a fact that a perfect bayesian given P(a), P(a|b), and P(a|~b) will ascribe P(b|a), a probability of P(a|b)P(a) / P(b), and that that is the best value to give P(b|a).

If an agent has perfect knowledge then it need not ascribe any non-1 probability to any proposition it holds. But it is a fact about agents in the world that without perfect knowledge they ascribe non-1 probabilities to their propositions if they're working right. Bayesian reasoning is the field which tells us the optimal probability to assign to a proposition given the rest of our information, but that that is the optimal probability given the rest of our information is a fact about the world. FOr any proposition 'a', if a perfect bayesian says 'P(a) = y:x' based off of some premise list P, then any agent who concludes 'a' from "P" (or any other equivalently cogent premise list) will be right y:x of the time, and wrong 1 - y:x of the time regardless of what "a" actually says.

Some might say, "There is no sweetness in the world; sweetness is in your mind's interpretation of the world." The correct response is "Since 'in' is a transitive relation, and my mind's interpretation of the world is in the world, sweetness is in the world. It's just that to learn about sweetness you can't just study sugar crystals, you have to study brains too." The situation here is similar-ish.

It is important that facts about the probabilities of statements be facts about the world; if they weren't then how would we find our priors? Priors seem to require that we be capable of checking "P(this woman having cancer) = such and such" by checking the world. In fact, I believe EY say's almost word for word that priors are fact about the world in "an intuitive explanation of Bayes theorem": "Actually, priors are true or false just like the final answer - they reflect reality and can be judged by comparing them against reality. For example, if you think that 920 out of 10,000 women in a sample have breast cancer, and the actual number is 100 out of 10,000, then your priors are wrong. " -- EY

Let us not forget that the map is a part of the territory; the map's accuracy is a fact about the territory as much as a fact about the map. You can study a map till you're blue in the head, and you still won't know how accurate it is unless you look at the corresponding territory.

Comment author: wedrifid 27 July 2011 08:23:14PM 1 point [-]

You may appreciate Probability is Subjectively Objective. It's the followup to this post and happens to be my favorite post on lesswrong!

Comment author: potato 28 July 2011 09:47:59PM 0 points [-]

I can see why it is your favorite post. It's also extremely relevant to the position I expressed in my post, thank you. But I'm not sure that I can't hold my position above while being an objectively-subjective bayesian; I'll retract my post if I find that I can't.

Comment author: wedrifid 28 July 2011 11:19:32PM 0 points [-]

But I'm not sure that I can't hold my position above while being an objectively-subjective bayesian; I'll retract my post if I find that I can't.

My impression was not that you would be persuaded to retract but that you'd feel vindicated. The positions are approximately the same (with slightly different labels attached). I don't think I disagree with you at all.