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shminux comments on The path of the rationalist - Less Wrong
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TIL: Eliezer is not a rationalist.
TYL: So8res is using the word "beliefs" in a slightly idiosyncratic way, to refer to things one simply treats as true and as fit subjects for logical rather than probabilistic inference.
(Though, even with this more reasonable reading of So8res's statements about "beliefs", I still don't think I agree. A perfect reasoner with unlimited resources would do everything probabilistically, but a human being with limited memory and attention span and calculating ability may often do best to adopt the approximation of just treating some things as true and some as false. With, of course, some policy of always being willing to revisit that when enough evidence against something "true" turns up -- but I don't think the corrigibility of a belief stops it being a belief, even in (what I take to be) So8res's sense.
I'm not sure this is idiosyncratic. As far as I can tell this is one of the most common colloquial meanings of beliefs.
Hmm, maybe. I'd have thought most people would say something is a "belief" if you assign it (say) 80% probability and act accordingly, but perhaps I'm wrong.
They also do that. "Believe" can mean both "confident of" and "somewhat doubtful of". The former contrasts the state of mind with ignorance, the latter with knowledge.
In which case, it isn't true that according to their usage rationalists are supposed not to have beliefs.
Logical inference is probability-preserving. It does not require that you assign infinite certainty to your axioms.
If your axioms are a1,a2,a3,...,a10 each with probability 0.75, and if they are independent, then a1 & a2 & ... & a10 (which is a valid logical inference from a1, ..., a10) has probability about 0.06. In the absence of independence, the probability could be anywhere from 0 to 0.75.
Perhaps by "probability-preserving" you mean something like: if you start with a bunch of axioms then anything you infer from them has probability no smaller than Pr(all axioms are correct). I agree, logical inference is probability-preserving in that sense, but note that that's fully compatible with (e.g.) it being possible to draw very improbable conclusions from axioms each of which on its own has probability very close to 1.