# Stuart_Armstrong comments on Infinite Certainty - Less Wrong

22 09 January 2008 06:49AM

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Comment author: 09 January 2008 01:28:17PM 2 points [-]

The ratio of these two probabilities may be 1, but I deny that there's any actual probability that's equal to 1. P(|) is a mere notational convenience

I'd have to diagree with that. The axioms I've seen of probabilty/measure theory do not make the case that P() is a probability while P(|) is not - they are both, ulitmately, the same type of object (just taken from different measurable sets).

However, you don't need to appeal to this type of reasoning to get rid of P(A|A) = 1. Your probability of correctly remembering the beginning of the statement when reaching the end is not 1 - hence there is room for doubt. Even your probability of correctly understanding the statement is not 1.

P(P is never equal to 1) = ?

I know, I know, 'this statement is not true'.

Would this be an argument for allowing "probabilities of probabilities"? So that you can assign 99.9999% (that's enough 9's I feel) to the statement "P(P is never equal to 1)".