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Conrad 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: Conrad 12 March 2008 07:36:26PM 0 points [-]

::Okay, so unpack "ungrounded" for me. You've used the phrases "probability" and "calculated or measured likelihood of heads coming up", but I'm not sure how you're defining them.::

Ungrounded: That was a good movie. Grounded: That movie made money for the investors. Alternatively: I enjoyed it and recommend it. -- is for most purposes grounded enough.

::I'm going to do two things. First, I'm going to Taboo "probability" and "likelihood" (for myself -- you too, if you want). Second, I'm going to ask you exactly which specific observable event it is we're talking about. (First toss? Twenty-third toss? Infinite collection of tosses?) I have a definite feeling that our disagreement is about word usage.::

You yourself said that we're dealing with one throw of a rigged coin, of unknown riggage. I don't think we have have a disagreement, exactly, except it looks to me like the discussion's moot.

But look: if I can back up a bit, the notion that we can be dealing with a rigged coin, know that it's rigged, and say that the --er, chances-- of getting a heads is "really" 50%, because we Just Don't Know, is useless. At that point you're using 50-50 because we have two possible known outcomes:

But in fact we deal with unknown probabilities *all the time*. Probabilities are by default unknown, until we measure them by repeated trial and a lot of scratch-work. What about when you're dealing with a medication that might kill someone, or not: in the absence of any information, do you say that's 50-50?

Conrad.