Combining Texts
Ideas for
'Axiomatic Theories of Truth (2005 ver)', 'Of the Laws of Ecclesiastical Polity' and 'Higher-Order Logic'
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11 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 / C. Ontology of Logic / 1. Ontology of Logic
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15652
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We can use truth instead of ontologically loaded second-order comprehension assumptions about properties [Halbach]
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5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic
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15651
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Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true' [Halbach]
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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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