Eliezer_Yudkowsky comments on Infinite Certainty - Less Wrong
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For one reason, again, if we're in any conventional (i.e. not paraconsistent) logic, admitting any contradiction entails that I can prove any proposition to be true.
Yes, but conditioned on the truth of some statement P&~P, my probability that logic is paraconsistent is very high.
Bayesianism is all about ratios of probabilities, yes, but we can write these ratios without ever using the P(|) notation if we please.