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j.edwards comments on 0 And 1 Are Not Probabilities - Less Wrong

34 Post author: Eliezer_Yudkowsky 10 January 2008 06:58AM

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Comment author: j.edwards 10 January 2008 07:49:18AM 6 points [-]

It's difficult to assign probability to incoherent statements, because since we can't mean anything by them, we can't assert a referent to the statement -- in that sense, the probability is indeterminate (additionally, one could easily imagine a language in which a statement such as "the green is either" has a perfectly coherent meaning -- and we can't say that's not what we meant, since we didn't mean anything). Recall also that each probability zero statement implies a probability one statement by its denial and vice versa, so one is equally capable of imagining them, if in a contrived way.

Comment author: Baruta07 31 October 2012 04:51:00PM 0 points [-]

Putting this in a slightly more coherent way. (I was having some trouble understanding the explanation, so I broke it down into layman's terms, might make it more easily understandable)

If I assign P(0) to "Green is either" Then I assign P(1) to the statement "Green is not either"

If you assign absolute certainty to any one statement you are, by definition assigning absolute impossibility to all other possibilities.

Comment author: Baruta07 31 October 2012 04:51:08PM 0 points [-]

Putting this in a slightly more coherent way. (I was having some trouble understanding the explanation, so I broke it down into layman's terms, might make it more easily understandable)

If I assign P(0) to "Green is either" Then I assign P(1) to the statement "Green is not either"

If you assign absolute certainty to any one statement you are, by definition assigning absolute impossibility to all other possibilities.