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Cyan2 comments on Probability is in the Mind - Less Wrong

60 Post author: Eliezer_Yudkowsky 12 March 2008 04:08AM

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Comment author: Cyan2 12 March 2009 08:38:00PM 3 points [-]

Stephen R. Diamond, there are two distinct things in play here: (i) an assessment of the plausibility of certain statements conditional on some background knowledge; and (ii) the relative frequency of outcomes of trials in a counterfactual world in which the number of trials is very large. You've declared that probability can't be (i) because it's (ii) -- actually, the Kolmogorov axioms apply to both. Justification for using the word "probability" to refer to things of type (i) can be found in the first two chapters of this book. I personally call things of type (i) "probabilities" and things of type (ii) "relative frequencies"; the key is to recognize that they need different names.

On your further critiques:
(1) Eliezer is a determinist; see the quantum physics sequence.
(2) True. A logical argument is only as reliable as its premises, and every method for learning from empirical information is only as reliable as its inductive bias. Unfortunately, every extant practical method of learning has an inductive bias, and the no free lunch theorems give reason to believe that this is a permanent state of affairs.

I'm not sure what you mean in your last sentence...