Opposite Propositions
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We have covered the first act of the mind (simple apprehension) and the second act of the mind (judgment). With chapter 7, we begin to study the third act of the mind: inference. And we begin with the classic form of deductive argument, the categorical syllogism.
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We end our exploration of chapter 6 where we began it–with equivalent propositions. There are three types covered here–conversion, obversion, and contraposition–and by adding these to the four relationships covered in the Square of Opposition we have now acquired an impressive number of ways we can wring extra truth out of the simplest categorical propositions.
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It’s almost time to reveal what is, in my opinion, the single greatest diagram in western philosophy. But before we can do that, we have to learn about subalternate propositions.
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Here we get to the heart of traditional logic: the ability to learn what we don’t know from things we already do know, even things we know to be false. We do this through propositions of equivalence and opposition.
Logic Lectures 