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timtyler comments on GroupThink, Theism ... and the Wiki - Less Wrong
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I think I would describe what you are talking about as being Bayesian statistics - plus a whole bunch of unspecified rules (the "i" s).
What I was saying is that there isn't a standard set of rules of deductive reasoning axioms that is considered to be part of Bayesian statistics. I would not dispute that you can model deductive reasoning using Bayesian statistics.
Tim-Good, your distinction sounds correct to me.