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cousin_it comments on Formalizing informal logic - Less Wrong
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With logical links as weak as those in your example, most arguments longer than 10 steps will reach incorrect conclusions anyway.
Agreed.
I have some notion that an argument tree could be translated or incorporated into a Bayes net model. There's an intuition (which we share) that, given links with a particular imperfect strength, arguments consisting of a few long chains are weaker than arguments that are "bushy" (offering many independent reasons for the conclusion). A Bayes net model would quantify that intuition.
In a perfect world, bushiness would indeed imply high reliability. Unfortunately in our world the different branches of the bush can have hidden dependencies, either accidental or maliciously inserted - they could even all be subtly different rewordings of one same argument - and the technique won't catch that. So ultimately I don't think we have invented a substitute for common sense just yet.