Categorical Propositions
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With this lecture, we begin to learn about compound syllogisms, which allow us much greater flexibility in the ways we analyze the world logically.
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Here’s the exciting conclusion of section 7.3, covering the final two rules of validity and two handy corollaries that make it easier (and faster) to recognize the validity (or invalidity) of syllogisms that rely on particular premises.
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In this lecture, I tacitly acknowledge that it was insane for the author of our text, whoever he was, to put all five rules of validity into a single section of the text. We’ll take section 7.3 in two parts, and in this part I cover the first three rules of validity, which all deal
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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.
Logic Lectures 