Combining Texts
Ideas for
'Mahaprajnaparamitashastra', 'Lectures on Aesthetics' and 'Higher-Order Logic'
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9 ideas
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10588
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First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro]
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5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10298
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Some say that second-order logic is mathematics, not logic [Shapiro]
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10299
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If the aim of logic is to codify inferences, second-order logic is useless [Shapiro]
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5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
10300
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Logical consequence can be defined in terms of the logical terminology [Shapiro]
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5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10290
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Second-order variables also range over properties, sets, relations or functions [Shapiro]
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5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10590
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Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro]
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10296
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The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro]
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10297
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The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro]
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10292
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Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro]
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