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Johnicholas comments on Formalization is a rationality technique - Less Wrong
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Could you expand? I don't follow you.
For the argument to be wrong, only one of its subarguments has to be wrong. So the correct equation is
P(whole argument is wrong) = 1 - P(first subargument is right) * P(second subargument is right | first argument is right)
I don't believe he's speaking of two subarguments which together imply the main argument, but two subarguments each of which independently implies the main argument. Thus, they would both have to be false
The logical operator between the two subarguments was ambiguous -- I assumed the total argument would be something like a lemma and a theorem that depends on the lemma, not a disjunction of propositions.
If the arguments are chained together, then this is true, but the original poster was talking about independent lines of reasoning leading to the same conclusion. For arguments which are truly independent, then his formulation is correct.
Alrighty, I gotcha.