Combining Texts
Ideas for
'works', 'Model Theory' and 'Logicism Revisited'
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11 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 / 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 / 3. If-Thenism
10061
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The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave]
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10065
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Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave]
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5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction
10121
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Contradiction is not a sign of falsity, nor lack of contradiction a sign of truth [Pascal]
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5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10049
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Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave]
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10050
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A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave]
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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
10481
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Models in model theory are structures, not sets of descriptions [Hodges,W]
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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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