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MBlume comments on Formalization is a rationality technique - Less Wrong
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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.