-=Dark_Angel=-, P.I.3 Apr 2005

Of course truth can come from an unreliable source. By definition, an unreliable source is one in which there is very little correlation between the fact that the source has asserted a proposition, and the proposition's validity (a race of Liars has perfect negative correlation. A race of Randoms has 0 correlation.) Now your definition of a closed mind is one that asserts all propositions from an unreliable source to be false, apart from those that are obviously true. This is just someone who has confused 0 correlation with negative correlation.

About the hypothetical race of Liars. I think it is possible to establish truth from someone who always lies. The test is to see if we could find the answer to any question. As an example, suppose we want to know what the Liar had for breakfast. If we just ask him "What did you have for breakfast?" that wouldn't help because he could just say "I had Ely Cathedral for breakfast" and we've learnt next to nothing useful, because, as you say, there are unlimited possible untruths he could spout. But we can be more cunning than that: suppose I said to him "Consider the shortest possible description of what you had for breakfast. Is the first letter of that description an 'A'?" If he says "No" we know it begins with 'A', and we move on to the second letter of the description. If he says "Yes" we know it must begin with B...Z so we ask him "Is the first letter a B?" and so on. Do you agree I could establish what he had for breakfast by adopting that approach? Clearly it is applicable to other questions.