Combining Texts
Ideas for
'Unconscious Cerebral Initiative', 'The Logical Syntax of Language' and 'Model Theory'
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8 ideas
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10478
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Since first-order languages are complete, |= and |- have the same meaning [Hodges,W]
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5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
13342
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Carnap defined consequence by contradiction, but this is unintuitive and changes with substitution [Tarski on Carnap]
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5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10477
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|= in model-theory means 'logical consequence' - it holds in all models [Hodges,W]
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5. Theory of Logic / C. Ontology of Logic / 4. Logic by Convention
13251
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Each person is free to build their own logic, just by specifying a syntax [Carnap]
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5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
10474
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|= should be read as 'is a model for' or 'satisfies' [Hodges,W]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10473
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Model theory studies formal or natural language-interpretation using set-theory [Hodges,W]
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10475
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A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W]
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10481
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Models in model theory are structures, not sets of descriptions [Hodges,W]
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