Categorical 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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In this lecture we take another look at a topic we first covered back in chapter 2 (supposition) to dive a little deeper into how we did what we did back there. But more importantly, we introduce the concept of distribution, which will have huge significance over the next two chapters as we start evaluating
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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.
Logic Lectures 