Formal Logic
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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.
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Swiss mathematician Leonhard Euler (rhymes with “boiler”) gave us an ingenious system for representing the four basic categorical propositions with diagrams consisting of two circles each. For many students, these “Euler’s Circles” make it much clearer exactly what the A, E, I, and O propositions are saying (and what they’re not saying).
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The number of categorical propositions is infinite, but every single one of them is one of just four types. Here’s how we identify them.
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We begin Part Two and chapter 5 by sharpening our understanding of the logical propositions we use to express our judgments–and to introduce the very specific kind of proposition we’ll be working with for the next three chapters: the categorical proposition.
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As we move into Part Two (“Expressing Truth”) and chapter 5 (“Judgments and Propositions”), we can all benefit from this oldie but goodie. The “Schoolhouse Rock” short features ran on Saturday morning television in the 1970s and 1980s, between the cartoons. They were frequently brilliant both musically and pedagogically, and “The Tale of Mr. Morton”
Logic Lectures 