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Ideas for
'fragments/reports', 'Higher-Order Logic' and 'Truth by Convention'
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16 ideas
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
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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
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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
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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 / B. Logical Consequence / 5. Modus Ponens
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8078
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Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin]
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5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
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10064
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Quine quickly dismisses If-thenism [Quine, by Musgrave]
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5. Theory of Logic / C. Ontology of Logic / 4. Logic by Convention
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20296
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Logic needs general conventions, but that needs logic to apply them to individual cases [Quine, by Rey]
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8998
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Claims that logic and mathematics are conventional are either empty, uninteresting, or false [Quine]
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8999
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Logic isn't conventional, because logic is needed to infer logic from conventions [Quine]
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9000
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If a convention cannot be communicated until after its adoption, what is its role? [Quine]
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5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
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6023
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Every proposition is either true or false [Chrysippus, by Cicero]
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5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
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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
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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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