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RobbBB 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: RobbBB 21 November 2012 06:58:52PM *  13 points [-]

If you assign 0 to logical contradictions, you should assign 1 to the negations of logical contradictions. (Particularly since your confidence in bivalence and the power of negation is what allowed you to doubt the truth of the contradiction in the first place.) So it's strange to say that you feel safer appealing to 0s than to 1s.

For my part, I have a hard time convincing myself that there's simply no (epistemic) chance that Graham Priest is right. On the other hand, assigning any value but 1 to the sentence "All bachelors are bachelors" just seems perverse. It seems as though I could only get that sentence wrong if I misunderstand it. But what am I assigning a probability to, if not the truth of the sentence as I understand it?

Another way of saying this is that I feel queasy assigning a nonzero probability to "Not all bachelors are bachelors," (i.e., ¬(p → p)) even though I think it probably makes some sense to entertain as a vanishingly small possibility "All bachelors are non-bachelors" (i.e., p → ¬p, all bachelors are contradictory objects).